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Photoinduced Chern insulating states in semi-Dirac materials

2016-08-08
Kush Saha
Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D … Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D systems in the presence of an electromagnetic field. We show that a Chern insulating state emerges in a semi-Dirac system with two gapless Dirac nodes in the presence of light. In particular, we show that the intensity of a circularly polarized light can be used as a knob to generate topological states with nonzero Chern number. In addition, for fixed intensity and frequency of the light, a semi-Dirac system with two gapped Dirac nodes with trivial band topology can reveal the topological transition as a function of polarization of the light.
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Flat bands in fractal-like geometry

2018-05-01
Biplab Pal , Kush Saha
We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding … We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different generations of a SPG network, we find multiple degenerate and non-degenerate completely flat bands, depending on the configuration of parameters of the Hamiltonian. Moreover, we find a generic formula to determine the number of such bands as a function of the generation index $\ell$ of the fractal geometry. We show that the flat bands and their neighboring dispersive bands have remarkable features, the most interesting one being the spin-1 conical-type spectrum at the band center without any staggered magnetic flux, in contrast to the Kagome lattice. We furthermore investigate the effect of the magnetic flux in these lattice settings and show that different combinations of fluxes through such fractal unit cells lead to richer spectrum with a single isolated flat band or gapless electron- or hole-like flat bands. Finally, we discuss a possible experimental setup to engineer such fractal flat band network using single-mode laser-induced photonic waveguides.
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Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field

2011-11-28
Tobias Graß , Kush Saha , K. Sengupta +1 more
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a … We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2) hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a non-monotonic dependence on the gauge field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at non-zero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
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Phonon-induced topological insulation

2014-05-08
Kush Saha , Ion Garate
We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak-coupling regime, long-wavelength phonons may favor topological phases in Dirac insulators with direct and narrow band … We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak-coupling regime, long-wavelength phonons may favor topological phases in Dirac insulators with direct and narrow band gaps. This phenomenon originates from electron-phonon matrix elements, which change qualitatively under a band inversion. A similar mechanism applies to weak Coulomb interactions and spin-independent disorder; however, the influence of these on band topology is largely independent of temperature. As applications of the theory, we evaluate the temperature dependence of the critical thickness and the critical stoichiometric ratio for the topological transition in CdTe/HgTe quantum wells and in BiTl(S${}_{1\ensuremath{-}\ensuremath{\delta}}$Se${}_{\ensuremath{\delta}}{)}_{2}$, respectively.
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Unconventional scanning tunneling conductance spectra for graphene

2010-04-30
Kush Saha , I. Paul , K. Sengupta
We compute the tunneling conductance of graphene as measured by a scanning tunneling microscope (STM) with a normal/superconducting tip. We demonstrate that for undoped graphene with zero Fermi energy, the … We compute the tunneling conductance of graphene as measured by a scanning tunneling microscope (STM) with a normal/superconducting tip. We demonstrate that for undoped graphene with zero Fermi energy, the first derivative of the tunneling conductance with respect to the applied voltage is proportional to the density of states of the STM tip. We also show that the shape of the STM spectra for graphene doped with impurities depends qualitatively on the position of the impurity atom in the graphene matrix and relate this unconventional phenomenon to the pseudospin symmetry of the Dirac quasiparticles in graphene. We suggest experiments to test our theory.
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Fibonacci optical lattices for tunable quantum quasicrystals

2015-12-29
Kevin Singh , Kush Saha , S. A. Parameswaran +1 more
We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation … We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of the energies and wave functions of ultracold atoms loaded into such a lattice demonstrate a multifractal energy spectrum, a singular continuous momentum-space structure, and the existence of controllable edge states. These results open the door to cold atom quantum simulation experiments in tunable or dynamic quasicrystalline potentials, including topological pumping of edge states and phasonic spectroscopy.
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Thermopower in an anisotropic two-dimensional Weyl semimetal

2020-01-03
Ipsita Mandal , Kush Saha
We investigate the generation of an electric current from a temperature gradient in a two-dimensional Weyl semimetal with anisotropy in both the presence and absence of a quantizing magnetic field. … We investigate the generation of an electric current from a temperature gradient in a two-dimensional Weyl semimetal with anisotropy in both the presence and absence of a quantizing magnetic field. We show that the anisotropy leads to doping dependences of thermopower and thermal conductivities which are different from those in isotropic Dirac materials. Additionally, we find that a quantizing magnetic field in such systems leads to an interesting magnetic field dependence of the longitudinal thermopower, resulting in unsaturated thermoelectric coefficients. Thus, the results presented here will serve as a guide to achieving high thermopower and a thermoelectric figure of merit in graphene-based materials, as well as organic conductors such as $\ensuremath{\alpha}$-BEDT-${\mathrm{TTF}}_{2}{\mathrm{I}}_{3}$.
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Theory of bulk-surface coupling in topological insulator films

2014-12-11
Kush Saha , Ion Garate
We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk … We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk scattering matrix elements and confirm the importance of bulk-surface coupling in transport and photoemission experiments, assessing its dependence on temperature, carrier density, film thickness and particle-hole asymmetry.
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Superfluid-insulator transition of two-species bosons with spin-orbit coupling

2012-10-01
Saptarshi Mandal , Kush Saha , K. Sengupta
Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional … Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude $t$ and in the presence of a spin-orbit coupling characterized by a tunable strength $\ensuremath{\gamma}$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\ensuremath{\gamma}$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\ensuremath{\gamma}=0$, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\ensuremath{\gamma}$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\ensuremath{\gamma}$ for nonzero $t$. We propose experiments to test our theory.
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Detecting Band Inversions by Measuring the Environment: Fingerprints of Electronic Band Topology in Bulk Phonon Linewidths

2015-10-23
Kush Saha , Katherine Légaré , Ion Garate
The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases, and quantum information. While recent … The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases, and quantum information. While recent studies suggest that dissipative baths can induce topological phases in intrinsically trivial quantum materials, the backaction of topological invariants on dissipative baths is overlooked. By exploring this backaction for a centrosymmetric Dirac insulator coupled to phonons, we show that the linewidths of bulk optical phonons can reveal electronic band inversions. This result is the first known example where topological phases of an open quantum system may be detected by measuring the bulk properties of the surrounding environment.
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Interplay between topology and disorder in a two-dimensional semi-Dirac material

2018-01-24
P. V. Sriluckshmy , Kush Saha , Roderich Moessner
We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent … We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes---single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.
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Casimir force on an interacting Bose–Einstein condensate

2010-04-06
Shyamal Biswas , Jayanta K. Bhattacharjee , Dwipesh Majumder +2 more
We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the … We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.
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Nonlinear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals

2021-05-18
Sai Satyam Samal , Snehasish Nandy , Kush Saha
It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of … It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of time-reversal invariant and non-centrosymmetric materials. While the BCD in two-dimensional Dirac systems is known to be finite only in the presence of either substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones or higher order warping of the Fermi surface, we argue that the low-energy Dirac quasiparticles arising from the merging of a pair of Dirac points without any tilt or warping of the Fermi surface can lead to a nonzero BCD. Remarkably, in such systems, the BCD is found to be independent of Dirac velocity as opposed to the Dirac dispersion with a tilt or warping effects. We further show that the proposed systems can naturally host helicity-dependent photocurrent due to their linear momentum-dependent Berry curvatures. Finally, we discuss an important byproduct of this work, i.e., nonlinear anomalous Nernst effect as a second-order thermal response.
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Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain

2013-10-24
Vincenzo Alba , Kush Saha , Masudul Haque
At large values of the anisotropy Δ, the open-boundary Heisenberg spin- chain has eigenstates displaying localization at the edges. We present a Bethe ansatz description of this 'edge-locking' phenomenon in … At large values of the anisotropy Δ, the open-boundary Heisenberg spin- chain has eigenstates displaying localization at the edges. We present a Bethe ansatz description of this 'edge-locking' phenomenon in the entire Δ > 1 region. We focus on the simplest spin sectors, namely the highly polarized sectors with only one or two overturned spins, i.e., one-particle and two-particle sectors.
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Berry curvature and Hall viscosities in an anisotropic Dirac semimetal

2019-01-25
Francisco Peña-Benítez , Kush Saha , Piotr Surówka
We investigate parity-odd nondissipative transport in an anisotropic Dirac semimetal in two spatial dimensions. The analysis is relevant for interacting electronic systems with merging Dirac points at charge neutrality. For … We investigate parity-odd nondissipative transport in an anisotropic Dirac semimetal in two spatial dimensions. The analysis is relevant for interacting electronic systems with merging Dirac points at charge neutrality. For such systems the dispersion relation is relativistic in one direction and nonrelativistic in the other. We give a proposal of how to calculate the Berry curvature for this system and use it to derive more than one odd viscosities, in contrast to rotationally invariant systems. We observe that in such a model the odd part of viscosity tensor is parametrized by two independent transport coefficients and one that is identically zero.
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Phases and collective modes of Rydberg atoms in an optical lattice

2014-02-14
Kush Saha , Subhasis Sinha , K. Sengupta
We chart out the possible phases of laser driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up(down) components correspond … We chart out the possible phases of laser driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up(down) components correspond to the excited(ground) states of the Rydberg atoms and use them to demonstrate the realization of a canted Ising antiferromagnetic (CIAF) Mott phase of the atoms in these systems. We also show that on lowering the lattice depth, the quantum melting of the CIAF and density-wave (DW) Mott states (which are also realized in these systems) leads to supersolid (SS) phases of the atoms. We provide analytical expressions for the phase boundaries and collective excitations of these phases in the hardcore limit within mean-field theory and discuss possible experiments to test our theory.
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Spin-polarized STM spectra of Dirac electrons on the surface of a topological insulator

2011-10-24
Kush Saha , Sourin Das , K. Sengupta +1 more
We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low … We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low bias voltages $V$. We show that $G(V)$ exhibits an unconventional dependence on the direction of magnetization of the tip and can be used to measure the magnitude of the local out-of-plane spin orientation of the Dirac Fermions on the surface. We also demonstrate that if the in-plane rotational symmetry on the surface of the topological insulator is broken by an external field, then $G(V)$ acquires a dependence on the azimuthal angle of the magnetization of the tip. We explain the role of the Dirac Fermions in this unconventional behavior and suggest experiments to test our theory.
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Hinge-mode dynamics of periodically driven higher-order Weyl semimetals

2022-06-23
Somsubhra Ghosh , Kush Saha , K. Sengupta
We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime … We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for both discrete (square pulse) and continuous (cosine) periodic drive protocols. We analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet hinge modes. Near them, these hinge modes penetrate into the bulk and eventually become indistinguishable from the bulk modes. We provide an analytic, albeit perturbative, expression for the Floquet Hamiltonian using Floquet perturbation theory (FPT) which explains this phenomenon and leads to analytic expressions of these special frequencies. We also show that in the large drive amplitude regime, the zero energy hinge modes corresponding to the static tight-binding Hamiltonian display qualitatively different dynamics at these special frequencies. We discuss possible local density of state measurement using a scanning tunneling microscope which can test our theory.
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Nonlinear dynamical response of interacting bosons to synthetic electric field

2020-10-26
Arko Roy , Soumya Bera , Kush Saha
We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation … We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation in a strong time-dependent synthetic vector potential manifesting itself as the synthetic electric field. We show that the vector potential can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the increase in the strength of the vector potential. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the gauge potential ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to a play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics.
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Valley-selective Landau-Zener oscillations in semi-Dirac <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math> junctions

2017-07-19
Kush Saha , Rahul Nandkishore , S. A. Parameswaran
We study transport across $p\ensuremath{-}n$ junctions of gapped two-dimensional semi-Dirac materials: nodal semimetals whose energy bands disperse quadratically and linearly along distinct crystal axes. The resulting electronic properties---relevant to materials … We study transport across $p\ensuremath{-}n$ junctions of gapped two-dimensional semi-Dirac materials: nodal semimetals whose energy bands disperse quadratically and linearly along distinct crystal axes. The resulting electronic properties---relevant to materials such as ${\mathrm{TiO}}_{2}/{\mathrm{VO}}_{2}$ multilayers and $\ensuremath{\alpha}$-(BEDT-TTF)${}_{2}{\mathrm{I}}_{3}$ salts---continuously interpolate between those of mono- and bilayer graphene as a function of propagation angle. We demonstrate that tunneling across the junction depends on the orientation of the tunnel barrier relative to the crystalline axes, leading to strongly nonmonotonic current-voltage characteristics, including negative differential conductance in some regimes. In multivalley systems, these features provide a natural route to engineering valley-selective transport.
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Ultracold bosons in a synthetic periodic magnetic field: Mott phases and reentrant superfluid-insulator transitions

2010-11-29
Kush Saha , K. Sengupta , Koushik Ray
We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector … We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the non-interacting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several re-entrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in real space for odd (even) $q$ and suggest experiments to test our theory.
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Mirror anomaly and anomalous Hall effect in type-I Dirac semimetals

2019-02-07
Snehasish Nandy , Kush Saha , A. Taraphder +1 more
In addition to the well-known chiral anomaly, Dirac semimetals have been argued to exhibit a mirror anomaly, a close analog to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The … In addition to the well-known chiral anomaly, Dirac semimetals have been argued to exhibit a mirror anomaly, a close analog to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular steplike anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized Hamiltonian), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized Hamiltonian. In particular, we show that the anomalous Hall response continuously approaches zero as one approaches the mirror symmetric angle in a type-I Dirac semimetal as opposed to the singular Hall response in a type-II Dirac semimetal. Moreover, we show that, under certain conditions, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time-reversal symmetry breaking.
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Probing mirror anomaly and classes of Dirac semimetals with circular dichroism

2021-03-11
Abhirup Roy Karmakar , Snehasish Nandy , G. P. Das +1 more
We theoretically investigate the optical activity of three-dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of … We theoretically investigate the optical activity of three-dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of the mirror-symmetric planes of the materials exhibit a notable dichroic behavior. In particular, for different orientations of the light field with respect to the mirror-symmetric plane, the CD in type-II DSMs can detect the presence of mirror anomaly by showing sharply distinct patterns at the mirror-symmetric angle. Interestingly, we find that the CD can also distinguish type-II DSMs having only one Dirac point at a time-reversal invariant momentum from type-I DSMs with a pair of Dirac points on the rotation axis of the crystals.Received 11 May 2020Accepted 16 February 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013230Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMagneto-optical effectWeyl fermionsPhysical SystemsDirac semimetalTopological materialsCondensed Matter, Materials & Applied Physics
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Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators

2015-05-12
Sthitadhi Roy , Kush Saha , Sourin Das
The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe … The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic property of these surface states, namely, the spin-momentum locking. We show that the information regarding the spin textures, so extracted, for different surfaces can be put together to reconstruct the parameters characterizing the bulk band structure of the material, hence acting as a hologram. For specific TI materials such as ${\text{Bi}}_{2}{\text{Se}}_{3},\phantom{\rule{4.pt}{0ex}}{\text{Bi}}_{2}{\text{Te}}_{3}$, and ${\text{Sb}}_{2}{\text{Te}}_{3}$, the planar surface states are distinct from one another with regard to their spectrum and the associated spin texture for each angle $\ensuremath{\theta}$ which the normal to the surface makes with the crystal-growth axis. We develop a tunnel Hamiltonian between such arbitrary surfaces and a spin-polarized scanning tunneling microscope (STM) which provides a unique fingerprint of the dispersion and the associated spin texture corresponding to each $\ensuremath{\theta}$. Additionally, the theory presented in this paper can be used to extract the value of $\ensuremath{\theta}$ for a given arbitrary planar surface from the STM spectra itself, hence effectively mimicking x-ray spectroscopy.
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GRAPHENE: JUNCTIONS AND STM SPECTRA

2012-07-18
Moitri Maiti , Kush Saha , K. Sengupta
The presence of low-energy Dirac-like quasiparticles is one of the central features responsible for plethora of recent theoretical and experimental studies on graphene. In this review, we focus on the … The presence of low-energy Dirac-like quasiparticles is one of the central features responsible for plethora of recent theoretical and experimental studies on graphene. In this review, we focus on the effect of the Dirac nature of these quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness d and arbitrary gate voltages V 0 applied across the barrier region. The second aspect involves study of the presence of localized magnetic impurities in graphene in which we discuss the unconventional nature of Kondo physics in graphene and the tunablity of Kondo effect with a gate voltage. We also chart out the nature of scanning tunneling conductance spectra for both doped and undoped graphene in the presence of impurities and discuss the effect of Dirac nature of graphene quasiparticles on such spectra. In particular, we provide a detailed analysis of the phenomenon that that the position of the impurity in the graphene matrix plays a crucial role in determining the nature of the STM specta.
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Anomalous pumping in the non-Hermitian Rice-Mele model

2025-01-14
Abhishek Kumar , Sarbajit Mazumdar , S. D. Mahanti +1 more
We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and … We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static one-dimensional (1D) RM model, we find two independent tuning knobs that can drive the topological transition, namely, non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we use a finite-size generalized Brillouin zone (GBZ) scheme to show that the edge modes can be distinguished from the non-hermiticity induced skin modes. Moreover, this scheme can capture the state pumping of topological edge modes as a function of $\gamma$ in the static 1D RM model and it further provides insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Furthermore, we show that the standard topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, we observe that it depends upon the driving protocols and strength of the non-Hermiticity ($\gamma$). With increasing $\gamma$, the adiabatic pumping for non-trivial protocols is destroyed first and then re-emerges as an anomalous pumping which does not have any Hermitian counterpart. Additionally, we observe that even a trivial adiabatic protocol can give rise to pumping as opposed to the Hermitian system. This is attributed to the inherent point gap physics of non-Hermitian system which we explain by reformulating a non-Bloch topological invariant for the 1+1D RM model. This invariant explains the number of pumped charges (in each period) for all the driving protocols.
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Interacting bosons in two-dimensional lattices with localized dissipation

2019-10-01
Arko Roy , Kush Saha
Motivated by the recent experiment [Takafumi Tomita \emph{et al.}, Sci. Adv. {\bf 3}, (2017)], we study the dynamics of interacting bosons in a two-dimensional optical lattice with local dissipation. Together … Motivated by the recent experiment [Takafumi Tomita \emph{et al.}, Sci. Adv. {\bf 3}, (2017)], we study the dynamics of interacting bosons in a two-dimensional optical lattice with local dissipation. Together with the Gutzwiller mean-field theory for density matrices and Lindblad master equation, we show how the onsite interaction between bosons affects the particle loss for various strengths of dissipation. For moderate dissipation, the trend in particle loss differs significantly near the superfluid-Mott boundary than the deep superfluid regime. While the loss is suppressed for stronger dissipation in the deep superfluid regime, revealing the typical quantum Zeno effect, the loss near the phase boundary shows non-monotonic dependence on the dissipation strength. We furthermore show that close to the phase boundary, the long-time dynamics is well contrasted with the dissipative dynamics deep into the superfluid regime. Thus the loss of particle due to dissipation may act as a probe to differentiate strongly-correlated superfluid regime from its weakly-correlated counterpart.
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Nonlinear response of interacting bosons in a quasiperiodic potential

2023-01-13
Debamalya Dutta , Arko Roy , Kush Saha
We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the … We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the model admits both localized and delocalized phases depending on the strength of the incommensurate potential $V_0$. We show that the particle current contains only odd harmonics in the delocalized phase in contrast to the localised phase where both even and odd harmonics are identified. The relative magnitudes of these even and odd harmonics and sharpness of the peaks can be tuned by varying frequency and the number of cycles of the applied pulse, respectively. In the presence of repulsive interactions, the amplitudes of the even and odd harmonics further depend on the relative strengths of the interaction $U$ and the potential $V_0$. We illustrate that the disorder and interaction-induced phases can be distinguished and characterized through the particle current. Finally, we discuss the dynamics of field induced excitation responsible for exhibiting higher harmonics in the current spectrum.
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Thermoelectric response in two-dimensional nodal-point semimetals

2023-01-01
Ipsita Mandal , Kush Saha
In this review, the thermoelectric properties in nodal-point semimetals with two bands are discussed. For the two-dimensional (2D) cases, it is shown that the expressions of the thermoelectric coefficients take … In this review, the thermoelectric properties in nodal-point semimetals with two bands are discussed. For the two-dimensional (2D) cases, it is shown that the expressions of the thermoelectric coefficients take different values depending on the nature of the scattering mechanism responsible for transport, by considering examples of short-ranged disorder potential and screened charged impurities. An anisotropy in the energy dispersion spectrum invariably affects the thermopower quite significantly, as illustrated by the results for a node of semi-Dirac semimetal and a single valley of graphene. The scenario when a magnetic field of magnitude $B$ is applied perpendicular to the plane of the 2D semimetal is also considered. The computations for three-dimensional (3D) cases necessarily involve the inclusion of nontrivial Berry phase effects. In addition to demonstrating the expressions for the response tensors, the exotic behaviour observed in planar Hall and planar thermal Hall set-ups is also discussed.
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Flat Bands in Three-dimensional Lattice models with Non-trivial Hopf Index

2024-07-01
Ivan Dutta , Kush Saha
Abstract We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized … Abstract We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.
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Detecting topological invariants by measuring the environment: fingerprints of electronic band topology in bulk phonon linewidths

2015-06-08
Kush Saha , Katherine Légaré , Ion Garate
Recent studies have shown that dissipative baths can induce topological phases in quantum materials. In this work, we turn the tables and reveal the back action of topological invariants on … Recent studies have shown that dissipative baths can induce topological phases in quantum materials. In this work, we turn the tables and reveal the back action of topological invariants on the environment. In a centrosymmetric Dirac insulator, we find that the linewidths of bulk phonons contain generic features that reflect the topology of the electronic structure.

Study of low dimensional lattice systems

2013-01-01
Kush Saha

Probing surface states exposed by crystal terminations at arbitrary orientations of 3D topological insulators

2014-11-05
Sthitadhi Roy , Kush Saha , Sourin Das
Topologically protected surface states appearing on a planar surface exposed by cleaving a crystal of 3D topological insulator ({\it e.g.,} $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3$) are distinct from each other for … Topologically protected surface states appearing on a planar surface exposed by cleaving a crystal of 3D topological insulator ({\it e.g.,} $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3$) are distinct from each other for different crystal terminations, characterized by the angle ($\theta$) which, the normal to the surface makes with the crystal growth axis. The exposed planar surfaces for a given $\theta$ show a spin texture which is specific to the angle $\theta$ where only the $\theta=0,\pi$ surfaces have a spin texture consistent with perfect spin-momentum locking while the $\theta \neq 0, \pi$ surfaces deviate from it. This variety in spin texture arises due to the $\theta$ dependent contribution of orbital parity of the bulk Hamiltonian in construction of these surface states. In this article we show that, current due to spin polarized tunneling of electrons injected into the surface states may provide information unique to the surface corresponding to a given $\theta$. Hence our study provides a proposal for experimentally probing and distinguishing these different surfaces by directly coupling to the spin textures of the surface states. We also show that the study of the spin textures for different surfaces put together acts like a hologram of the bulk band structure of the material.

Surface-to-bulk scattering in topological insulator films

2015-03-04
Kush Saha , Ion Garate

Higher harmonic generation in interacting bosons in optical lattices

2020-03-23
Arko Roy , Soumya Bera , Kush Saha
We study the generation of higher harmonics using intense light field in an interacting bosonic gas loaded in a one-dimensional optical lattice. We find that the strong light pulse can … We study the generation of higher harmonics using intense light field in an interacting bosonic gas loaded in a one-dimensional optical lattice. We find that the strong light pulse can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the variation in the strength of the light field. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the light field ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics. We conclude with a possible experimental outlook of the obtained results.

Unconventional pumping in non-Hermitian Rice-Mele model

2021-10-07
Abhishek Kumar , Kush Saha
We study the Rice-Mele (RM) model in the presence of an asymmetric hopping-induced non-Hermitian parameter, $\gamma$. In particular, we examine the effect of non-Hermiticity on the topological boundary modes and … We study the Rice-Mele (RM) model in the presence of an asymmetric hopping-induced non-Hermitian parameter, $\gamma$. In particular, we examine the effect of non-Hermiticity on the topological boundary modes and topological pumping. For weak and moderate values of $\gamma$, the inherent topological edge modes remain localized at the boundaries, whereas the bulk modes are pumped to the boundary, leading to the typical non-Hermitian skin modes. Using generalized Brillouin zone (GBZ) scheme, we show that the non-Hermiticity-induced skin modes can be distinguished from the topological boundary modes. Upon increasing $\gamma$, the topological boundary mode localized at one edge is pumped to the other edge, leading to an unconventional state pumping. This is in contrast to the standard topological pumping where adiabatic evolution of the parameters of the RM model leads to the pumping. We further show that the usual topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, it depends upon the driving protocols and strength of the non-Hermiticity. With increasing $\gamma$, the adiabatic pumping is destroyed first and then re-emerges as an unconventional pumping which does not have any Hermitian counterpart.

Vector Chirality $κ$ Driven Topological Phase Transition and the Associated Anomalous Hall Conductivity Tuning in a Non-Collinear Antiferromagnet

2022-01-01
Subhadip Pradhan , Kartik Samanta , Kush Saha +1 more
Based on the first-principles electronic structure calculations and subsequent symmetry adapted effective low-energy $\textbf{k.p}$ theory, we show the switching of the vector chirality, $\kappa$, in a noncollinear antiferromagnet (AFM), Mn$_3$Sn, … Based on the first-principles electronic structure calculations and subsequent symmetry adapted effective low-energy $\textbf{k.p}$ theory, we show the switching of the vector chirality, $\kappa$, in a noncollinear antiferromagnet (AFM), Mn$_3$Sn, as an unconventional route to topological phase transition from a nodal-ring to a Weyl point semimetal. Specifically, we find that the switching of $\kappa$ leads to gaping out an elliptic nodal-ring everywhere at the Fermi-level except for a pair of points on the ring. As a consequence, the topological phase transition switches the anomalous Hall conductivity (AHC) from zero to a giant value. Furthermore, we theoretically demonstrate how the controlled manipulation of the chiral AFM order keeping $\kappa$ unaltered favors unusual rotation of Weyl-points on the ring. This in turn enables us to tune in-plane components of the AHC by a collective uniform rotations of spins in the AFM unit cell.
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Non-trivial Flat Bands in Three Dimensions

2023-01-01
Ivan Dutta , Kush Saha
We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in … We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.
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Anomalous pumping in the non-Hermitian Rice-Mele model

2021-01-01
Abhishek Kumar , Sarbajit Mazumdar , S. D. Mahanti +1 more
We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and … We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static 1D RM model, we observe two independent tuning knobs that drive the topological transition, viz., non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we made use of the finite-size generalized Brillouin zone (GBZ) scheme. This scheme captures the state pumping of topological edge modes in the static 1D RM model and provides further insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Finally, we apply three types of adiabatic protocols to study TCP in the 1+1D RM model. We further explain the number of pumped charges (in each period) using a non-Bloch topological invariant. This exactly explains the presence of different pumping phases in the non-Hermitian RM model as we tune the non-Hermitian parameter $\gamma$. We observe that in a non-Hermitian system, even a trivial adiabatic protocol can lead to pumping that has no Hermitian counterpart.
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Current-induced spin polarisation in Rashba-Dresselhaus systems under different point groups

2024-08-09
Akash Dey , Ashis Nandy , Kush Saha
Non-magnetic materials without inversion symmetry typically exhibit strong Rashba spin-orbit coupling (SOC), enabling the well-known Rashba Edelstein effect where an external electrical current induces transverse spin polarisation. In this study, … Non-magnetic materials without inversion symmetry typically exhibit strong Rashba spin-orbit coupling (SOC), enabling the well-known Rashba Edelstein effect where an external electrical current induces transverse spin polarisation. In this study, we demonstrate that electrically induced spin polarisation in non-magnetic materials, for example, electronic systems within quantum-well geometries, can significantly be influenced by the system's point-group symmetries, such as $C_n$ and $C_{nv}$. These symmetries allow various linear and higher-order momentum, $k-$varying SOC Hamiltonian. Specifically, we show that surfaces having $C_{n}$ point-group symmetry, which permits specific linear and cubic Rashba and Dresselhaus SOC terms, can lead to both orthogonal and non-orthogonal spin polarisations with respect to the applied field. In contrast, surfaces with $C_{nv}$ symmetry exhibit only transverse spin polarisation, regardless of the linear and cubic SOC terms. We further find contrasting spin polarisation for cubic-in-$k$ SOC as compared to the linear-in-$k$ SOC when energy is varied, for example, through doping. Additionally, we show that the surfaces with $C_{n}$ symmetry may exhibit persistent spin current, depending on the relative strength between different momentum-dependent SOC terms. Our finding emphasizes the significance of crystal symmetry in understanding and manipulating induced spin polarisation in noncentrosymmetric materials, especially in surface/interface systems.
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Disorder-induced delocalization and reentrance in a Chern-Hopf insulator

2024-08-07
Soumya Bera , Ivan Dutta , Roderich Moessner +1 more
The Chern-Hopf insulator is an unconventional three-dimensional topological insulator with a bulk gap and gapless boundary states without protection from global discrete symmetries. This study investigates its fate in the … The Chern-Hopf insulator is an unconventional three-dimensional topological insulator with a bulk gap and gapless boundary states without protection from global discrete symmetries. This study investigates its fate in the presence of disorder. We find it stable up to moderate disorder by analyzing the surface states and the zero energy bulk density of states using large-scale numerical simulation and the self-consistent Born approximation. The disordered Chern-Hopf insulator shows reentrant behavior: the disorder initially enhances the topological phase before driving it across an insulator-diffusive metal transition. We examine the associated critical exponents via finite-size scaling of the bulk density of states, participation entropy, and two-terminal conductance. We estimate the correlation length exponent $\nu\simeq 1.0(1)$, consistent with the clean two-dimensional Chern universality and distinct from the integer quantum Hall exponent.
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Frequency-selective amplification of nonlinear response in strongly correlated bosons

2024-09-12
Aditya Prakash , Debamalya Dutta , Arko Roy +1 more
We present a protocol to generate enhanced non-linear responses of incident pulses in the density wave phase within the extended Bose-Hubbard model using the concept of resonance-induced amplification (RIA). This … We present a protocol to generate enhanced non-linear responses of incident pulses in the density wave phase within the extended Bose-Hubbard model using the concept of resonance-induced amplification (RIA). This method enables the selection of an incident pulse frequency to amplify the desired harmonic order. We characterize the enhancement of the non-linear harmonic spectra under various frequencies and field strengths of the incident pulses, and demonstrate that an optimal field strength is necessary to realize our protocol.
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Anomalous pumping in the non-Hermitian Rice-Mele model

2025-01-13
Abhishek Kumar , Sarbajit Mazumdar , S. D. Mahanti +1 more
Abstract We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect … Abstract We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static one-dimensional (1D) RM model, we find two independent tuning knobs that can drive the topological transition, namely, non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we use a finite-size generalized Brillouin zone (GBZ) scheme to show that the edge modes can be distinguished from the non-hermiticity induced skin modes. Moreover, this scheme can capture the state pumping of topological edge modes as a function of $\gamma$ in the static 1D RM model and it further provides insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Furthermore, we show that the standard topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, we observe that it depends upon the driving protocols and strength of the non-Hermiticity ($\gamma$). With increasing $\gamma$, the adiabatic pumping for non-trivial protocols is destroyed first and then re-emerges as an anomalous pumping which does not have any Hermitian counterpart. Additionally, we observe that even a trivial adiabatic protocol can give rise to pumping as opposed to the Hermitian system. This is attributed to the inherent point gap physics of non-Hermitian system which we explain by reformulating a non-Bloch topological invariant for the 1+1D RM model. This invariant explains the number of pumped charges (in each period) for all the driving protocols.
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Spin-imbalance induced buried topological edge currents in Mott \& topological insulator heterostructures

2025-01-26
Rahul Ghosh , Subhajyoti Pal , Kush Saha +1 more
We theoretically investigate the heterostructure between a ferrimagnetic Mott insulator and a time-reversal invariant topological band insulator on the two-dimensional Lieb lattice with periodic boundary conditions. Our Hartree-Fock and slave-rotor … We theoretically investigate the heterostructure between a ferrimagnetic Mott insulator and a time-reversal invariant topological band insulator on the two-dimensional Lieb lattice with periodic boundary conditions. Our Hartree-Fock and slave-rotor mean-field results incorporate long-range Coulomb interactions. We present charge and magnetic reconstructions at the two edges of the heterostructure and reveal how \textit{buried} topological edge modes adapt to these heterostructure edge reconstructions. In particular, we demonstrate that the interface magnetic field induces a spin imbalance in the edge modes while preserving their topological character and metallic nature. We show that this imbalance leads to topologically protected buried spin and charge currents. The inherent spin-momentum locking ensures that left and right movers contribute to the current at the two buried interfaces in opposite directions. We show that the magnitude of the spin-imbalance induced charge and spin current can be tuned by adjusting the spin-orbit coupling of the bulk topological insulator relative to the correlation strength of the bulk Mott insulator. Thus, our results demonstrate a controlled conversion of a spin Hall effect into an analog of a charge Hall effect driven by band topology and interaction effects. These topologically protected charge and spin currents pave the way for advances in low-energy electronics and spintronic devices.
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Disorder-induced delocalization and reentrance in a Hopf-Chern insulator

2025-05-09
Soumya Bera , Ivan Dutta , Roderich Moessner +1 more

Disorder-induced delocalization and reentrance in a Hopf-Chern insulator

2025-05-09
Soumya Bera , Ivan Dutta , Roderich Moessner +1 more

Spin-imbalance induced buried topological edge currents in Mott \& topological insulator heterostructures

2025-01-26
Rahul Ghosh , Subhajyoti Pal , Kush Saha +1 more
We theoretically investigate the heterostructure between a ferrimagnetic Mott insulator and a time-reversal invariant topological band insulator on the two-dimensional Lieb lattice with periodic boundary conditions. Our Hartree-Fock and slave-rotor … We theoretically investigate the heterostructure between a ferrimagnetic Mott insulator and a time-reversal invariant topological band insulator on the two-dimensional Lieb lattice with periodic boundary conditions. Our Hartree-Fock and slave-rotor mean-field results incorporate long-range Coulomb interactions. We present charge and magnetic reconstructions at the two edges of the heterostructure and reveal how \textit{buried} topological edge modes adapt to these heterostructure edge reconstructions. In particular, we demonstrate that the interface magnetic field induces a spin imbalance in the edge modes while preserving their topological character and metallic nature. We show that this imbalance leads to topologically protected buried spin and charge currents. The inherent spin-momentum locking ensures that left and right movers contribute to the current at the two buried interfaces in opposite directions. We show that the magnitude of the spin-imbalance induced charge and spin current can be tuned by adjusting the spin-orbit coupling of the bulk topological insulator relative to the correlation strength of the bulk Mott insulator. Thus, our results demonstrate a controlled conversion of a spin Hall effect into an analog of a charge Hall effect driven by band topology and interaction effects. These topologically protected charge and spin currents pave the way for advances in low-energy electronics and spintronic devices.
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Anomalous pumping in the non-Hermitian Rice-Mele model

2025-01-14
Abhishek Kumar , Sarbajit Mazumdar , S. D. Mahanti +1 more
We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and … We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static one-dimensional (1D) RM model, we find two independent tuning knobs that can drive the topological transition, namely, non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we use a finite-size generalized Brillouin zone (GBZ) scheme to show that the edge modes can be distinguished from the non-hermiticity induced skin modes. Moreover, this scheme can capture the state pumping of topological edge modes as a function of $\gamma$ in the static 1D RM model and it further provides insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Furthermore, we show that the standard topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, we observe that it depends upon the driving protocols and strength of the non-Hermiticity ($\gamma$). With increasing $\gamma$, the adiabatic pumping for non-trivial protocols is destroyed first and then re-emerges as an anomalous pumping which does not have any Hermitian counterpart. Additionally, we observe that even a trivial adiabatic protocol can give rise to pumping as opposed to the Hermitian system. This is attributed to the inherent point gap physics of non-Hermitian system which we explain by reformulating a non-Bloch topological invariant for the 1+1D RM model. This invariant explains the number of pumped charges (in each period) for all the driving protocols.
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Anomalous pumping in the non-Hermitian Rice-Mele model

2025-01-13
Abhishek Kumar , Sarbajit Mazumdar , S. D. Mahanti +1 more
Abstract We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect … Abstract We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static one-dimensional (1D) RM model, we find two independent tuning knobs that can drive the topological transition, namely, non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we use a finite-size generalized Brillouin zone (GBZ) scheme to show that the edge modes can be distinguished from the non-hermiticity induced skin modes. Moreover, this scheme can capture the state pumping of topological edge modes as a function of $\gamma$ in the static 1D RM model and it further provides insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Furthermore, we show that the standard topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, we observe that it depends upon the driving protocols and strength of the non-Hermiticity ($\gamma$). With increasing $\gamma$, the adiabatic pumping for non-trivial protocols is destroyed first and then re-emerges as an anomalous pumping which does not have any Hermitian counterpart. Additionally, we observe that even a trivial adiabatic protocol can give rise to pumping as opposed to the Hermitian system. This is attributed to the inherent point gap physics of non-Hermitian system which we explain by reformulating a non-Bloch topological invariant for the 1+1D RM model. This invariant explains the number of pumped charges (in each period) for all the driving protocols.
View PDF Chat

Frequency-selective amplification of nonlinear response in strongly correlated bosons

2024-09-12
Aditya Prakash , Debamalya Dutta , Arko Roy +1 more
We present a protocol to generate enhanced non-linear responses of incident pulses in the density wave phase within the extended Bose-Hubbard model using the concept of resonance-induced amplification (RIA). This … We present a protocol to generate enhanced non-linear responses of incident pulses in the density wave phase within the extended Bose-Hubbard model using the concept of resonance-induced amplification (RIA). This method enables the selection of an incident pulse frequency to amplify the desired harmonic order. We characterize the enhancement of the non-linear harmonic spectra under various frequencies and field strengths of the incident pulses, and demonstrate that an optimal field strength is necessary to realize our protocol.
View PDF Chat

Current-induced spin polarisation in Rashba-Dresselhaus systems under different point groups

2024-08-09
Akash Dey , Ashis Nandy , Kush Saha
Non-magnetic materials without inversion symmetry typically exhibit strong Rashba spin-orbit coupling (SOC), enabling the well-known Rashba Edelstein effect where an external electrical current induces transverse spin polarisation. In this study, … Non-magnetic materials without inversion symmetry typically exhibit strong Rashba spin-orbit coupling (SOC), enabling the well-known Rashba Edelstein effect where an external electrical current induces transverse spin polarisation. In this study, we demonstrate that electrically induced spin polarisation in non-magnetic materials, for example, electronic systems within quantum-well geometries, can significantly be influenced by the system's point-group symmetries, such as $C_n$ and $C_{nv}$. These symmetries allow various linear and higher-order momentum, $k-$varying SOC Hamiltonian. Specifically, we show that surfaces having $C_{n}$ point-group symmetry, which permits specific linear and cubic Rashba and Dresselhaus SOC terms, can lead to both orthogonal and non-orthogonal spin polarisations with respect to the applied field. In contrast, surfaces with $C_{nv}$ symmetry exhibit only transverse spin polarisation, regardless of the linear and cubic SOC terms. We further find contrasting spin polarisation for cubic-in-$k$ SOC as compared to the linear-in-$k$ SOC when energy is varied, for example, through doping. Additionally, we show that the surfaces with $C_{n}$ symmetry may exhibit persistent spin current, depending on the relative strength between different momentum-dependent SOC terms. Our finding emphasizes the significance of crystal symmetry in understanding and manipulating induced spin polarisation in noncentrosymmetric materials, especially in surface/interface systems.
View PDF Chat

Disorder-induced delocalization and reentrance in a Chern-Hopf insulator

2024-08-07
Soumya Bera , Ivan Dutta , Roderich Moessner +1 more
The Chern-Hopf insulator is an unconventional three-dimensional topological insulator with a bulk gap and gapless boundary states without protection from global discrete symmetries. This study investigates its fate in the … The Chern-Hopf insulator is an unconventional three-dimensional topological insulator with a bulk gap and gapless boundary states without protection from global discrete symmetries. This study investigates its fate in the presence of disorder. We find it stable up to moderate disorder by analyzing the surface states and the zero energy bulk density of states using large-scale numerical simulation and the self-consistent Born approximation. The disordered Chern-Hopf insulator shows reentrant behavior: the disorder initially enhances the topological phase before driving it across an insulator-diffusive metal transition. We examine the associated critical exponents via finite-size scaling of the bulk density of states, participation entropy, and two-terminal conductance. We estimate the correlation length exponent $\nu\simeq 1.0(1)$, consistent with the clean two-dimensional Chern universality and distinct from the integer quantum Hall exponent.
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Flat Bands in Three-dimensional Lattice models with Non-trivial Hopf Index

2024-07-01
Ivan Dutta , Kush Saha
Abstract We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized … Abstract We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.
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Nonlinear response of interacting bosons in a quasiperiodic potential

2023-01-13
Debamalya Dutta , Arko Roy , Kush Saha
We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the … We theoretically study the electric pulse-driven non-linear response of interacting bosons loaded in an optical lattice in the presence of an incommensurate superlattice potential. In the non-interacting limit $(U=0)$, the model admits both localized and delocalized phases depending on the strength of the incommensurate potential $V_0$. We show that the particle current contains only odd harmonics in the delocalized phase in contrast to the localised phase where both even and odd harmonics are identified. The relative magnitudes of these even and odd harmonics and sharpness of the peaks can be tuned by varying frequency and the number of cycles of the applied pulse, respectively. In the presence of repulsive interactions, the amplitudes of the even and odd harmonics further depend on the relative strengths of the interaction $U$ and the potential $V_0$. We illustrate that the disorder and interaction-induced phases can be distinguished and characterized through the particle current. Finally, we discuss the dynamics of field induced excitation responsible for exhibiting higher harmonics in the current spectrum.
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Non-trivial Flat Bands in Three Dimensions

2023-01-01
Ivan Dutta , Kush Saha
We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in … We report the presence of exactly and nearly flat bands with non-trivial topology in three-dimensional (3D) lattice models. We first show that an exactly flat band can be realized in a 3D lattice model characterized by a 3D topological invariant, namely Hopf invariant. In contrast, we find another distinct 3D model, exhibiting both 2D Chern and 3D Hopf invariant, namely Hopf-Chern insulator, that can host nearly or perfect flat bands across different 2D planes. Such a Hopf-Chern model can be constructed by introducing specific hopping along the orthogonal direction of a simple two-orbital 2D Chern insulator in the presence of in-plane nearest-neighbor and next-nearest hopping among different orbitals. While the Chern planes host nearly perfect flat bands, the orthogonal planes can host both perfect or nearly perfect flat bands with zero Chern number at some special parameter values. Interestingly, such a 3D lattice construction from 2D allows finite Hopf invariant too. Finally, we show that higher Chern models can also be constructed in the same lattice setup with only nearest and next-nearest hopping, but the appearance of flat bands along high-symmetric path in the Brillouin zone requires longer-range hopping. We close with a discussion on possible experimental platforms to realize the models.
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Thermoelectric response in two-dimensional nodal-point semimetals

2023-01-01
Ipsita Mandal , Kush Saha
In this review, the thermoelectric properties in nodal-point semimetals with two bands are discussed. For the two-dimensional (2D) cases, it is shown that the expressions of the thermoelectric coefficients take … In this review, the thermoelectric properties in nodal-point semimetals with two bands are discussed. For the two-dimensional (2D) cases, it is shown that the expressions of the thermoelectric coefficients take different values depending on the nature of the scattering mechanism responsible for transport, by considering examples of short-ranged disorder potential and screened charged impurities. An anisotropy in the energy dispersion spectrum invariably affects the thermopower quite significantly, as illustrated by the results for a node of semi-Dirac semimetal and a single valley of graphene. The scenario when a magnetic field of magnitude $B$ is applied perpendicular to the plane of the 2D semimetal is also considered. The computations for three-dimensional (3D) cases necessarily involve the inclusion of nontrivial Berry phase effects. In addition to demonstrating the expressions for the response tensors, the exotic behaviour observed in planar Hall and planar thermal Hall set-ups is also discussed.
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Hinge-mode dynamics of periodically driven higher-order Weyl semimetals

2022-06-23
Somsubhra Ghosh , Kush Saha , K. Sengupta
We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime … We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for both discrete (square pulse) and continuous (cosine) periodic drive protocols. We analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet hinge modes. Near them, these hinge modes penetrate into the bulk and eventually become indistinguishable from the bulk modes. We provide an analytic, albeit perturbative, expression for the Floquet Hamiltonian using Floquet perturbation theory (FPT) which explains this phenomenon and leads to analytic expressions of these special frequencies. We also show that in the large drive amplitude regime, the zero energy hinge modes corresponding to the static tight-binding Hamiltonian display qualitatively different dynamics at these special frequencies. We discuss possible local density of state measurement using a scanning tunneling microscope which can test our theory.
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Vector Chirality $κ$ Driven Topological Phase Transition and the Associated Anomalous Hall Conductivity Tuning in a Non-Collinear Antiferromagnet

2022-01-01
Subhadip Pradhan , Kartik Samanta , Kush Saha +1 more
Based on the first-principles electronic structure calculations and subsequent symmetry adapted effective low-energy $\textbf{k.p}$ theory, we show the switching of the vector chirality, $\kappa$, in a noncollinear antiferromagnet (AFM), Mn$_3$Sn, … Based on the first-principles electronic structure calculations and subsequent symmetry adapted effective low-energy $\textbf{k.p}$ theory, we show the switching of the vector chirality, $\kappa$, in a noncollinear antiferromagnet (AFM), Mn$_3$Sn, as an unconventional route to topological phase transition from a nodal-ring to a Weyl point semimetal. Specifically, we find that the switching of $\kappa$ leads to gaping out an elliptic nodal-ring everywhere at the Fermi-level except for a pair of points on the ring. As a consequence, the topological phase transition switches the anomalous Hall conductivity (AHC) from zero to a giant value. Furthermore, we theoretically demonstrate how the controlled manipulation of the chiral AFM order keeping $\kappa$ unaltered favors unusual rotation of Weyl-points on the ring. This in turn enables us to tune in-plane components of the AHC by a collective uniform rotations of spins in the AFM unit cell.
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Unconventional pumping in non-Hermitian Rice-Mele model

2021-10-07
Abhishek Kumar , Kush Saha
We study the Rice-Mele (RM) model in the presence of an asymmetric hopping-induced non-Hermitian parameter, $\gamma$. In particular, we examine the effect of non-Hermiticity on the topological boundary modes and … We study the Rice-Mele (RM) model in the presence of an asymmetric hopping-induced non-Hermitian parameter, $\gamma$. In particular, we examine the effect of non-Hermiticity on the topological boundary modes and topological pumping. For weak and moderate values of $\gamma$, the inherent topological edge modes remain localized at the boundaries, whereas the bulk modes are pumped to the boundary, leading to the typical non-Hermitian skin modes. Using generalized Brillouin zone (GBZ) scheme, we show that the non-Hermiticity-induced skin modes can be distinguished from the topological boundary modes. Upon increasing $\gamma$, the topological boundary mode localized at one edge is pumped to the other edge, leading to an unconventional state pumping. This is in contrast to the standard topological pumping where adiabatic evolution of the parameters of the RM model leads to the pumping. We further show that the usual topological pumping due to the adiabatic and periodic variation of the model parameters survives even with finite $\gamma$. However, it depends upon the driving protocols and strength of the non-Hermiticity. With increasing $\gamma$, the adiabatic pumping is destroyed first and then re-emerges as an unconventional pumping which does not have any Hermitian counterpart.

Nonlinear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals

2021-05-18
Sai Satyam Samal , Snehasish Nandy , Kush Saha
It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of … It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of time-reversal invariant and non-centrosymmetric materials. While the BCD in two-dimensional Dirac systems is known to be finite only in the presence of either substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones or higher order warping of the Fermi surface, we argue that the low-energy Dirac quasiparticles arising from the merging of a pair of Dirac points without any tilt or warping of the Fermi surface can lead to a nonzero BCD. Remarkably, in such systems, the BCD is found to be independent of Dirac velocity as opposed to the Dirac dispersion with a tilt or warping effects. We further show that the proposed systems can naturally host helicity-dependent photocurrent due to their linear momentum-dependent Berry curvatures. Finally, we discuss an important byproduct of this work, i.e., nonlinear anomalous Nernst effect as a second-order thermal response.
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Probing mirror anomaly and classes of Dirac semimetals with circular dichroism

2021-03-11
Abhirup Roy Karmakar , Snehasish Nandy , G. P. Das +1 more
We theoretically investigate the optical activity of three-dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of … We theoretically investigate the optical activity of three-dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of the mirror-symmetric planes of the materials exhibit a notable dichroic behavior. In particular, for different orientations of the light field with respect to the mirror-symmetric plane, the CD in type-II DSMs can detect the presence of mirror anomaly by showing sharply distinct patterns at the mirror-symmetric angle. Interestingly, we find that the CD can also distinguish type-II DSMs having only one Dirac point at a time-reversal invariant momentum from type-I DSMs with a pair of Dirac points on the rotation axis of the crystals.Received 11 May 2020Accepted 16 February 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013230Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMagneto-optical effectWeyl fermionsPhysical SystemsDirac semimetalTopological materialsCondensed Matter, Materials & Applied Physics
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Anomalous pumping in the non-Hermitian Rice-Mele model

2021-01-01
Abhishek Kumar , Sarbajit Mazumdar , S. D. Mahanti +1 more
We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and … We study topological charge pumping (TCP) in the Rice-Mele (RM) model with irreciprocal hopping. The non-Hermiticity gives rise to interesting pumping physics, owing to the presence of skin effect and exceptional points. In the static 1D RM model, we observe two independent tuning knobs that drive the topological transition, viz., non-Hermitian parameter $\gamma$ and system size $N$. To elucidate the system-size dependency, we made use of the finite-size generalized Brillouin zone (GBZ) scheme. This scheme captures the state pumping of topological edge modes in the static 1D RM model and provides further insight into engineering novel gapless exceptional edge modes with the help of adiabatic drive. Finally, we apply three types of adiabatic protocols to study TCP in the 1+1D RM model. We further explain the number of pumped charges (in each period) using a non-Bloch topological invariant. This exactly explains the presence of different pumping phases in the non-Hermitian RM model as we tune the non-Hermitian parameter $\gamma$. We observe that in a non-Hermitian system, even a trivial adiabatic protocol can lead to pumping that has no Hermitian counterpart.
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Nonlinear dynamical response of interacting bosons to synthetic electric field

2020-10-26
Arko Roy , Soumya Bera , Kush Saha
We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation … We theoretically study the non-linear response of interacting neutral bosonic gas in a synthetically driven one-dimensional optical lattice. In particular, we examine the bosonic analogue of electronic higher harmonic generation in a strong time-dependent synthetic vector potential manifesting itself as the synthetic electric field. We show that the vector potential can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the increase in the strength of the vector potential. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the gauge potential ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to a play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics.
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Higher harmonic generation in interacting bosons in optical lattices

2020-03-23
Arko Roy , Soumya Bera , Kush Saha
We study the generation of higher harmonics using intense light field in an interacting bosonic gas loaded in a one-dimensional optical lattice. We find that the strong light pulse can … We study the generation of higher harmonics using intense light field in an interacting bosonic gas loaded in a one-dimensional optical lattice. We find that the strong light pulse can generate reasonably high harmonics in the insulating regime, while the superfluid regime exhibits only a few harmonics. In the insulating regime, the number of harmonics increases with the variation in the strength of the light field. This originates primarily due to the field-driven resonant and non-resonant excitations in the neutral Mott state and their recombination with the ground state. If the repulsive interaction between two atoms ($U$) is close to the strength of the light field ($A_0$), the resonant quasiparticle-quasihole pairs on nearest-neighbor sites, namely dipole states are found to play a dominant role in the generating higher harmonics. However, in the strong-field limit $A_0\gg U$, the nonresonant states where quasiparticle-quasihole pairs are not on nearest-neighbor sites give rise to higher harmonics. We conclude with a possible experimental outlook of the obtained results.

Thermopower in an anisotropic two-dimensional Weyl semimetal

2020-01-03
Ipsita Mandal , Kush Saha
We investigate the generation of an electric current from a temperature gradient in a two-dimensional Weyl semimetal with anisotropy in both the presence and absence of a quantizing magnetic field. … We investigate the generation of an electric current from a temperature gradient in a two-dimensional Weyl semimetal with anisotropy in both the presence and absence of a quantizing magnetic field. We show that the anisotropy leads to doping dependences of thermopower and thermal conductivities which are different from those in isotropic Dirac materials. Additionally, we find that a quantizing magnetic field in such systems leads to an interesting magnetic field dependence of the longitudinal thermopower, resulting in unsaturated thermoelectric coefficients. Thus, the results presented here will serve as a guide to achieving high thermopower and a thermoelectric figure of merit in graphene-based materials, as well as organic conductors such as $\ensuremath{\alpha}$-BEDT-${\mathrm{TTF}}_{2}{\mathrm{I}}_{3}$.
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Interacting bosons in two-dimensional lattices with localized dissipation

2019-10-01
Arko Roy , Kush Saha
Motivated by the recent experiment [Takafumi Tomita \emph{et al.}, Sci. Adv. {\bf 3}, (2017)], we study the dynamics of interacting bosons in a two-dimensional optical lattice with local dissipation. Together … Motivated by the recent experiment [Takafumi Tomita \emph{et al.}, Sci. Adv. {\bf 3}, (2017)], we study the dynamics of interacting bosons in a two-dimensional optical lattice with local dissipation. Together with the Gutzwiller mean-field theory for density matrices and Lindblad master equation, we show how the onsite interaction between bosons affects the particle loss for various strengths of dissipation. For moderate dissipation, the trend in particle loss differs significantly near the superfluid-Mott boundary than the deep superfluid regime. While the loss is suppressed for stronger dissipation in the deep superfluid regime, revealing the typical quantum Zeno effect, the loss near the phase boundary shows non-monotonic dependence on the dissipation strength. We furthermore show that close to the phase boundary, the long-time dynamics is well contrasted with the dissipative dynamics deep into the superfluid regime. Thus the loss of particle due to dissipation may act as a probe to differentiate strongly-correlated superfluid regime from its weakly-correlated counterpart.
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Mirror anomaly and anomalous Hall effect in type-I Dirac semimetals

2019-02-07
Snehasish Nandy , Kush Saha , A. Taraphder +1 more
In addition to the well-known chiral anomaly, Dirac semimetals have been argued to exhibit a mirror anomaly, a close analog to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The … In addition to the well-known chiral anomaly, Dirac semimetals have been argued to exhibit a mirror anomaly, a close analog to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular steplike anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized Hamiltonian), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized Hamiltonian. In particular, we show that the anomalous Hall response continuously approaches zero as one approaches the mirror symmetric angle in a type-I Dirac semimetal as opposed to the singular Hall response in a type-II Dirac semimetal. Moreover, we show that, under certain conditions, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time-reversal symmetry breaking.
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Berry curvature and Hall viscosities in an anisotropic Dirac semimetal

2019-01-25
Francisco Peña-Benítez , Kush Saha , Piotr Surówka
We investigate parity-odd nondissipative transport in an anisotropic Dirac semimetal in two spatial dimensions. The analysis is relevant for interacting electronic systems with merging Dirac points at charge neutrality. For … We investigate parity-odd nondissipative transport in an anisotropic Dirac semimetal in two spatial dimensions. The analysis is relevant for interacting electronic systems with merging Dirac points at charge neutrality. For such systems the dispersion relation is relativistic in one direction and nonrelativistic in the other. We give a proposal of how to calculate the Berry curvature for this system and use it to derive more than one odd viscosities, in contrast to rotationally invariant systems. We observe that in such a model the odd part of viscosity tensor is parametrized by two independent transport coefficients and one that is identically zero.
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Flat bands in fractal-like geometry

2018-05-01
Biplab Pal , Kush Saha
We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding … We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different generations of a SPG network, we find multiple degenerate and non-degenerate completely flat bands, depending on the configuration of parameters of the Hamiltonian. Moreover, we find a generic formula to determine the number of such bands as a function of the generation index $\ell$ of the fractal geometry. We show that the flat bands and their neighboring dispersive bands have remarkable features, the most interesting one being the spin-1 conical-type spectrum at the band center without any staggered magnetic flux, in contrast to the Kagome lattice. We furthermore investigate the effect of the magnetic flux in these lattice settings and show that different combinations of fluxes through such fractal unit cells lead to richer spectrum with a single isolated flat band or gapless electron- or hole-like flat bands. Finally, we discuss a possible experimental setup to engineer such fractal flat band network using single-mode laser-induced photonic waveguides.
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Interplay between topology and disorder in a two-dimensional semi-Dirac material

2018-01-24
P. V. Sriluckshmy , Kush Saha , Roderich Moessner
We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent … We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes---single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single- and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.
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Valley-selective Landau-Zener oscillations in semi-Dirac <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math> junctions

2017-07-19
Kush Saha , Rahul Nandkishore , S. A. Parameswaran
We study transport across $p\ensuremath{-}n$ junctions of gapped two-dimensional semi-Dirac materials: nodal semimetals whose energy bands disperse quadratically and linearly along distinct crystal axes. The resulting electronic properties---relevant to materials … We study transport across $p\ensuremath{-}n$ junctions of gapped two-dimensional semi-Dirac materials: nodal semimetals whose energy bands disperse quadratically and linearly along distinct crystal axes. The resulting electronic properties---relevant to materials such as ${\mathrm{TiO}}_{2}/{\mathrm{VO}}_{2}$ multilayers and $\ensuremath{\alpha}$-(BEDT-TTF)${}_{2}{\mathrm{I}}_{3}$ salts---continuously interpolate between those of mono- and bilayer graphene as a function of propagation angle. We demonstrate that tunneling across the junction depends on the orientation of the tunnel barrier relative to the crystalline axes, leading to strongly nonmonotonic current-voltage characteristics, including negative differential conductance in some regimes. In multivalley systems, these features provide a natural route to engineering valley-selective transport.
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Photoinduced Chern insulating states in semi-Dirac materials

2016-08-08
Kush Saha
Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D … Two-dimensional (2D) semi-Dirac materials are characterized by a quadratic dispersion in one direction and a linear dispersion along the orthogonal direction. We study the topological phase transition in such 2D systems in the presence of an electromagnetic field. We show that a Chern insulating state emerges in a semi-Dirac system with two gapless Dirac nodes in the presence of light. In particular, we show that the intensity of a circularly polarized light can be used as a knob to generate topological states with nonzero Chern number. In addition, for fixed intensity and frequency of the light, a semi-Dirac system with two gapped Dirac nodes with trivial band topology can reveal the topological transition as a function of polarization of the light.
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Fibonacci optical lattices for tunable quantum quasicrystals

2015-12-29
Kevin Singh , Kush Saha , S. A. Parameswaran +1 more
We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation … We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of the energies and wave functions of ultracold atoms loaded into such a lattice demonstrate a multifractal energy spectrum, a singular continuous momentum-space structure, and the existence of controllable edge states. These results open the door to cold atom quantum simulation experiments in tunable or dynamic quasicrystalline potentials, including topological pumping of edge states and phasonic spectroscopy.
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Detecting Band Inversions by Measuring the Environment: Fingerprints of Electronic Band Topology in Bulk Phonon Linewidths

2015-10-23
Kush Saha , Katherine Légaré , Ion Garate
The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases, and quantum information. While recent … The interplay between topological phases of matter and dissipative baths constitutes an emergent research topic with links to condensed matter, photonic crystals, cold atomic gases, and quantum information. While recent studies suggest that dissipative baths can induce topological phases in intrinsically trivial quantum materials, the backaction of topological invariants on dissipative baths is overlooked. By exploring this backaction for a centrosymmetric Dirac insulator coupled to phonons, we show that the linewidths of bulk optical phonons can reveal electronic band inversions. This result is the first known example where topological phases of an open quantum system may be detected by measuring the bulk properties of the surrounding environment.
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Detecting topological invariants by measuring the environment: fingerprints of electronic band topology in bulk phonon linewidths

2015-06-08
Kush Saha , Katherine Légaré , Ion Garate
Recent studies have shown that dissipative baths can induce topological phases in quantum materials. In this work, we turn the tables and reveal the back action of topological invariants on … Recent studies have shown that dissipative baths can induce topological phases in quantum materials. In this work, we turn the tables and reveal the back action of topological invariants on the environment. In a centrosymmetric Dirac insulator, we find that the linewidths of bulk phonons contain generic features that reflect the topology of the electronic structure.

Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators

2015-05-12
Sthitadhi Roy , Kush Saha , Sourin Das
The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe … The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic property of these surface states, namely, the spin-momentum locking. We show that the information regarding the spin textures, so extracted, for different surfaces can be put together to reconstruct the parameters characterizing the bulk band structure of the material, hence acting as a hologram. For specific TI materials such as ${\text{Bi}}_{2}{\text{Se}}_{3},\phantom{\rule{4.pt}{0ex}}{\text{Bi}}_{2}{\text{Te}}_{3}$, and ${\text{Sb}}_{2}{\text{Te}}_{3}$, the planar surface states are distinct from one another with regard to their spectrum and the associated spin texture for each angle $\ensuremath{\theta}$ which the normal to the surface makes with the crystal-growth axis. We develop a tunnel Hamiltonian between such arbitrary surfaces and a spin-polarized scanning tunneling microscope (STM) which provides a unique fingerprint of the dispersion and the associated spin texture corresponding to each $\ensuremath{\theta}$. Additionally, the theory presented in this paper can be used to extract the value of $\ensuremath{\theta}$ for a given arbitrary planar surface from the STM spectra itself, hence effectively mimicking x-ray spectroscopy.
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Surface-to-bulk scattering in topological insulator films

2015-03-04
Kush Saha , Ion Garate

Theory of bulk-surface coupling in topological insulator films

2014-12-11
Kush Saha , Ion Garate
We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk … We present a quantitative microscopic theory of the disorder- and phonon-induced coupling between surface and bulk states in topological insulator (TI) films. We find a simple structure for the surface-to-bulk scattering matrix elements and confirm the importance of bulk-surface coupling in transport and photoemission experiments, assessing its dependence on temperature, carrier density, film thickness and particle-hole asymmetry.
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Probing surface states exposed by crystal terminations at arbitrary orientations of 3D topological insulators

2014-11-05
Sthitadhi Roy , Kush Saha , Sourin Das
Topologically protected surface states appearing on a planar surface exposed by cleaving a crystal of 3D topological insulator ({\it e.g.,} $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3$) are distinct from each other for … Topologically protected surface states appearing on a planar surface exposed by cleaving a crystal of 3D topological insulator ({\it e.g.,} $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3$) are distinct from each other for different crystal terminations, characterized by the angle ($\theta$) which, the normal to the surface makes with the crystal growth axis. The exposed planar surfaces for a given $\theta$ show a spin texture which is specific to the angle $\theta$ where only the $\theta=0,\pi$ surfaces have a spin texture consistent with perfect spin-momentum locking while the $\theta \neq 0, \pi$ surfaces deviate from it. This variety in spin texture arises due to the $\theta$ dependent contribution of orbital parity of the bulk Hamiltonian in construction of these surface states. In this article we show that, current due to spin polarized tunneling of electrons injected into the surface states may provide information unique to the surface corresponding to a given $\theta$. Hence our study provides a proposal for experimentally probing and distinguishing these different surfaces by directly coupling to the spin textures of the surface states. We also show that the study of the spin textures for different surfaces put together acts like a hologram of the bulk band structure of the material.

Phonon-induced topological insulation

2014-05-08
Kush Saha , Ion Garate
We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak-coupling regime, long-wavelength phonons may favor topological phases in Dirac insulators with direct and narrow band … We develop an approximate theory of phonon-induced topological insulation in Dirac materials. In the weak-coupling regime, long-wavelength phonons may favor topological phases in Dirac insulators with direct and narrow band gaps. This phenomenon originates from electron-phonon matrix elements, which change qualitatively under a band inversion. A similar mechanism applies to weak Coulomb interactions and spin-independent disorder; however, the influence of these on band topology is largely independent of temperature. As applications of the theory, we evaluate the temperature dependence of the critical thickness and the critical stoichiometric ratio for the topological transition in CdTe/HgTe quantum wells and in BiTl(S${}_{1\ensuremath{-}\ensuremath{\delta}}$Se${}_{\ensuremath{\delta}}{)}_{2}$, respectively.
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Phases and collective modes of Rydberg atoms in an optical lattice

2014-02-14
Kush Saha , Subhasis Sinha , K. Sengupta
We chart out the possible phases of laser driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up(down) components correspond … We chart out the possible phases of laser driven Rydberg atoms in the presence of a hypercubic optical lattice. We define a pseudospin degree of freedom whose up(down) components correspond to the excited(ground) states of the Rydberg atoms and use them to demonstrate the realization of a canted Ising antiferromagnetic (CIAF) Mott phase of the atoms in these systems. We also show that on lowering the lattice depth, the quantum melting of the CIAF and density-wave (DW) Mott states (which are also realized in these systems) leads to supersolid (SS) phases of the atoms. We provide analytical expressions for the phase boundaries and collective excitations of these phases in the hardcore limit within mean-field theory and discuss possible experiments to test our theory.
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Bethe ansatz description of edge-localization in the open-boundary XXZ spin chain

2013-10-24
Vincenzo Alba , Kush Saha , Masudul Haque
At large values of the anisotropy Δ, the open-boundary Heisenberg spin- chain has eigenstates displaying localization at the edges. We present a Bethe ansatz description of this 'edge-locking' phenomenon in … At large values of the anisotropy Δ, the open-boundary Heisenberg spin- chain has eigenstates displaying localization at the edges. We present a Bethe ansatz description of this 'edge-locking' phenomenon in the entire Δ > 1 region. We focus on the simplest spin sectors, namely the highly polarized sectors with only one or two overturned spins, i.e., one-particle and two-particle sectors.
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Study of low dimensional lattice systems

2013-01-01
Kush Saha

Superfluid-insulator transition of two-species bosons with spin-orbit coupling

2012-10-01
Saptarshi Mandal , Kush Saha , K. Sengupta
Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional … Motivated by recent experiments [Y. J. Lin et al., Nature (London) 471, 83 (2011)], we study Mott phases and superfluid-insulator (SI) transitions of two-species ultracold bosonic atoms in a two-dimensional square optical lattice with nearest-neighbor hopping amplitude $t$ and in the presence of a spin-orbit coupling characterized by a tunable strength $\ensuremath{\gamma}$. Using both strong-coupling expansion and Gutzwiller mean-field theory, we chart out the phase diagrams of the bosons in the presence of such spin-orbit interaction. We compute the momentum distribution of the bosons in the Mott phase near the SI transition point and show that it displays precursor peaks whose position in the Brillouin zone can be varied by tuning $\ensuremath{\gamma}$. Our analysis of the critical theory of the transition unravels the presence of unconventional quantum critical points at $t/\ensuremath{\gamma}=0$, which are accompanied by emergence of an additional gapless mode in the critical region. We also study the superfluid phases of the bosons near the SI transition using a Gutzwiller mean-field theory that reveals the existence of a twisted superfluid phase with an anisotropic twist angle which depends on $\ensuremath{\gamma}$. Finally, we compute the collective modes of the bosons and point out the presence of reentrant SI transitions as a function of $\ensuremath{\gamma}$ for nonzero $t$. We propose experiments to test our theory.
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GRAPHENE: JUNCTIONS AND STM SPECTRA

2012-07-18
Moitri Maiti , Kush Saha , K. Sengupta
The presence of low-energy Dirac-like quasiparticles is one of the central features responsible for plethora of recent theoretical and experimental studies on graphene. In this review, we focus on the … The presence of low-energy Dirac-like quasiparticles is one of the central features responsible for plethora of recent theoretical and experimental studies on graphene. In this review, we focus on the effect of the Dirac nature of these quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness d and arbitrary gate voltages V 0 applied across the barrier region. The second aspect involves study of the presence of localized magnetic impurities in graphene in which we discuss the unconventional nature of Kondo physics in graphene and the tunablity of Kondo effect with a gate voltage. We also chart out the nature of scanning tunneling conductance spectra for both doped and undoped graphene in the presence of impurities and discuss the effect of Dirac nature of graphene quasiparticles on such spectra. In particular, we provide a detailed analysis of the phenomenon that that the position of the impurity in the graphene matrix plays a crucial role in determining the nature of the STM specta.
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Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field

2011-11-28
Tobias Graß , Kush Saha , K. Sengupta +1 more
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a … We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2) hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a non-monotonic dependence on the gauge field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at non-zero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
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Spin-polarized STM spectra of Dirac electrons on the surface of a topological insulator

2011-10-24
Kush Saha , Sourin Das , K. Sengupta +1 more
We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low … We provide a theory for the tunneling conductance $G(V)$ of Dirac Fermions on the surface of a topological insulator as measured by a spin-polarized scanning tunneling microscope tip for low bias voltages $V$. We show that $G(V)$ exhibits an unconventional dependence on the direction of magnetization of the tip and can be used to measure the magnitude of the local out-of-plane spin orientation of the Dirac Fermions on the surface. We also demonstrate that if the in-plane rotational symmetry on the surface of the topological insulator is broken by an external field, then $G(V)$ acquires a dependence on the azimuthal angle of the magnetization of the tip. We explain the role of the Dirac Fermions in this unconventional behavior and suggest experiments to test our theory.
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Ultracold bosons in a synthetic periodic magnetic field: Mott phases and reentrant superfluid-insulator transitions

2010-11-29
Kush Saha , K. Sengupta , Koushik Ray
We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector … We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the non-interacting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields $q$ energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying $p$ for a given $q$. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the $p$ and $q$ dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several re-entrant field-induced SI transitions for any fixed period $q$. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in real space for odd (even) $q$ and suggest experiments to test our theory.
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Unconventional scanning tunneling conductance spectra for graphene

2010-04-30
Kush Saha , I. Paul , K. Sengupta
We compute the tunneling conductance of graphene as measured by a scanning tunneling microscope (STM) with a normal/superconducting tip. We demonstrate that for undoped graphene with zero Fermi energy, the … We compute the tunneling conductance of graphene as measured by a scanning tunneling microscope (STM) with a normal/superconducting tip. We demonstrate that for undoped graphene with zero Fermi energy, the first derivative of the tunneling conductance with respect to the applied voltage is proportional to the density of states of the STM tip. We also show that the shape of the STM spectra for graphene doped with impurities depends qualitatively on the position of the impurity atom in the graphene matrix and relate this unconventional phenomenon to the pseudospin symmetry of the Dirac quasiparticles in graphene. We suggest experiments to test our theory.
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Casimir force on an interacting Bose–Einstein condensate

2010-04-06
Shyamal Biswas , Jayanta K. Bhattacharjee , Dwipesh Majumder +2 more
We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the … We have presented an analytic theory for the Casimir force on a Bose-Einstein condensate (BEC) which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wave function as well as for the phonon field. We have shown that, the condensate wave function (which obeys the Gross-Pitaevskii equation) is responsible for the mean field part of Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.
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Coauthor Papers Together
K. Sengupta 8
Arko Roy 5
Ion Garate 5
Soumya Bera 4
Sourin Das 3
S. D. Mahanti 3
Snehasish Nandy 3
Ivan Dutta 3
Sarbajit Mazumdar 3
Roderich Moessner 3
Abhishek Kumar 2
Katherine Légaré 2
Debamalya Dutta 2
S. A. Parameswaran 2
Ipsita Mandal 2
Sthitadhi Roy 2
Abhishek Kumar 2
Vincenzo Alba 1
Shyamal Biswas 1
Sai Satyam Samal 1
P. V. Sriluckshmy 1
Diptiman Sen 1
Jayanta K. Bhattacharjee 1
Dwipesh Majumder 1
Subhadip Pradhan 1
Biplab Pal 1
Anamitra Mukherjee 1
Kartik Samanta 1
Kevin Singh 1
A. Taraphder 1
Piotr Surówka 1
Francisco Peña-Benítez 1
David Weld 1
Somsubhra Ghosh 1
Subhajyoti Pal 1
Ashis Nandy 1
Akash Dey 1
Ivan Dutta 1
Rahul Nandkishore 1
Moitri Maiti 1
Saptarshi Mandal 1
Tobias Graß 1
Abhirup Roy Karmakar 1
I. Paul 1
Sumanta Tewari 1
Aditya Prakash 1
Nabajit Chakravarty 1
G. P. Das 1
Ashis Nandy 1
Rahul Ghosh 1

Half-Metallic Semi-Dirac-Point Generated by Quantum Confinement in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>TiO</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>VO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>Nanostructures

2009-04-22
Víctor Pardo , Warren E. Pickett
Multilayer ${\mathrm{VO}}_{2}/{\mathrm{TiO}}_{2}$ nanostructures (${d}^{1}\mathrm{\text{\ensuremath{-}}}{d}^{0}$ interfaces with no polar discontinuity) are studied with first-principles density functional methods including structural relaxation. Quantum confinement of the half-metallic ${\mathrm{VO}}_{2}$ slab within insulating ${\mathrm{TiO}}_{2}$ produces … Multilayer ${\mathrm{VO}}_{2}/{\mathrm{TiO}}_{2}$ nanostructures (${d}^{1}\mathrm{\text{\ensuremath{-}}}{d}^{0}$ interfaces with no polar discontinuity) are studied with first-principles density functional methods including structural relaxation. Quantum confinement of the half-metallic ${\mathrm{VO}}_{2}$ slab within insulating ${\mathrm{TiO}}_{2}$ produces an unexpected and unprecedented two-dimensional new state, with a (semi-Dirac) point Fermi surface: spinless charge carriers are effective-mass-like along one principal axis but are massless along the other. Effects of interface imperfection are addressed.
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<i>Colloquium</i>: Topological insulators

2010-11-08
M. Zahid Hasan , C. L. Kane
Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is … Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.
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Topological Insulators in Three Dimensions

2007-03-07
Liang Fu , C. L. Kane , E. J. Melé
We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants … We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel "topological metal" surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.
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Cold Bosonic Atoms in Optical Lattices

1998-10-12
Dieter Jaksch , Christoph Bruder , J. I. Cirac +2 more
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. … The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap, and in optical superlattices are presented.
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Topological phases and the quantum spin Hall effect in three dimensions

2009-05-21
Rahul Roy
The $Z_2$ invariant for filled bands in the ground states of systems with time reversal invariance characterizes the number of stable pairs of edge states. Here we study the $Z_2 … The $Z_2$ invariant for filled bands in the ground states of systems with time reversal invariance characterizes the number of stable pairs of edge states. Here we study the $Z_2 $ invariant using band touching methods discussed in a recent previous work \cite{roy2006zcq} and extend the study to three dimensions. Band collisions preserve the $Z_2 $ invariant both in two and three dimensions, but there are crucial differences in the two cases. In three dimensions,we find a novel fourth $Z_2 $ invariant which is characterized by a "trapped monopole" in momentum space. If the monopole charge in half the Brillouin zone is odd, then atleast one of the monopoles cannot recombine with another monopole and vanish unlike the case when the monopole charge is even. We also point out the possibility of a three dimensional quantum spin Hall effect and discuss the connection of various topological invariants to such an effect.
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The electronic properties of graphene

2009-01-14
A. H. Castro Neto , F. Guinea , N. M. R. Peres +2 more
This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external … This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
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Topological insulators and superconductors

2011-10-14
Xiao-Liang Qi , Shou-Cheng Zhang
Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk … Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi$_2$Te$_3$ and Bi$_2$Se$_3$ crystals. We review theoretical models, materials properties and experimental results on two-dimensional and three-dimensional topological insulators, and discuss both the topological band theory and the topological field theory. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. We review the theory of topological superconductors in close analogy to the theory of topological insulators.
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Tight-Binding Modeling and Low-Energy Behavior of the Semi-Dirac Point

2009-07-01
S. Banerjee , Rajiv R. P. Singh , Víctor Pardo +1 more
We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of VO$_2$/TiO$_2$ nano-heterostructures. We contrast their … We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of VO$_2$/TiO$_2$ nano-heterostructures. We contrast their spectral properties with the well known Dirac points on the honeycomb lattice relevant to graphene layers and the spectra of bands touching each other in zero-gap semiconductors. We also consider the lowest order dispersion around one of the semi-Dirac points and calculate the resulting electronic energy levels in an external magnetic field. We find that these systems support apparently similar electronic structures but diverse low-energy physics.
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New Magnetic Field Dependence of Landau Levels in a Graphenelike Structure

2008-06-13
Petra Dietl , Frédéric Piéchon , Gilles Montambaux
We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic … We consider a tight-binding model on the honeycomb lattice in a magnetic field. For special values of the hopping integrals, the dispersion relation is linear in one direction and quadratic in the other. We find that, in this case, the energy of the Landau levels varies with the field $B$ as ${ϵ}_{n}(B)\ensuremath{\sim}[(n+\ensuremath{\gamma})B{]}^{2/3}$. This result is obtained from the low-field study of the tight-binding spectrum on the honeycomb lattice in a magnetic field (Hofstadter spectrum) as well as from a calculation in the continuum approximation at low field. The latter links the new spectrum to the one of a modified quartic oscillator. The obtained value $\ensuremath{\gamma}=1/2$ is found to result from the cancellation of a Berry phase.
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Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor α-(BEDT-TTF)<sub>2</sub>I<sub>3</sub>Salt

2006-05-12
Shinya Katayama , Akito Kobayashi , Yoshikazu Suzumura
We show a zero-gap semiconducting (ZGS) state in the quasi-two-dimensional organic conductor α-(BEDT-TTF) 2 I 3 salt, which emerges under uniaxial pressure along the a -axis (the stacking axis of … We show a zero-gap semiconducting (ZGS) state in the quasi-two-dimensional organic conductor α-(BEDT-TTF) 2 I 3 salt, which emerges under uniaxial pressure along the a -axis (the stacking axis of the BEDT-TTF molecule). The ZGS state is the state in which a Dirac cone with the band spectrum of a linear dispersion exists around the Fermi point connecting an unoccupied (electron) band with an occupied (hole) band. The spectrum exhibits a large anisotropy in velocity, which depends on the direction from the Fermi point. By varying the magnitude of several transfer energies of a tight-binding model with four sites per unit cell, it is shown that the ZGS state exists in a wide pressure range, and is attributable to the large anisotropy of the transfer energies along the stacking axis.
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Merging of Dirac points in a two-dimensional crystal

2009-10-27
Gilles Montambaux , Frédéric Piéchon , Jean-Noël Fuchs +1 more
We study under which general conditions a pair of Dirac points in the electronic spectrum of a two-dimensional crystal may merge into a single one. The merging signals a topological … We study under which general conditions a pair of Dirac points in the electronic spectrum of a two-dimensional crystal may merge into a single one. The merging signals a topological transition between a semimetallic phase and a band insulator. We derive a universal Hamiltonian that describes the physical properties of the transition, which is controlled by a single parameter, and analyze the Landau-level spectrum in its vicinity. This merging may be observed in the organic salt $\ensuremath{\alpha}\ensuremath{-}{(\text{BEDT-TTF})}_{2}{\text{I}}_{3}$ or in an optical lattice of cold atoms simulating deformed graphene.

A semi-Dirac point and an electromagnetic topological transition in a dielectric photonic crystal

2014-01-21
Ying Wu
A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic … A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic crystal consisting of a square array of elliptical dielectric cylinders is able to produce this particular dispersion relation in the Brillouin zone center. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. Effective medium parameters calculated from a boundary effective medium theory not only explain the unexpected topological transition in the iso-frequency surfaces occurring at the semi-Dirac point, they also offer a perspective on the property at that point, where the photonic crystal behaves as a zero-refractive-index material along the symmetry axis but functions like at a photonic band edge in the perpendicular direction.
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A universal Hamiltonian for motion and merging of Dirac points in a two-dimensional crystal

2009-11-07
Gilles Montambaux , Frédéric Piéchon , Jean-Noël Fuchs +1 more
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Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates

2011-05-02
Xiangang Wan , Ari M. Turner , Ashvin Vishwanath +1 more
We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, … We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, and argue that it may be realized in a class of pyrochlore iridates (such as ${\mathrm{Y}}_{2}$Ir${}_{2}$O${}_{7}$) based on calculations using the $\text{LDA}+U$ method. This state is a three-dimensional analog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. For intermediate correlation strengths, we find this to be the ground state of the pyrochlore iridates, coexisting with noncollinear magnetic order. A narrow window of magnetic ``axion'' insulator may also be present. An applied magnetic field is found to induce a metallic ground state.
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Mott-insulator–to–superfluid transition in the Bose-Hubbard model: A strong-coupling approach

2005-03-25
K. Sengupta , N. Dupuis
We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive … We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.
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Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

2006-12-14
B. Andrei Bernevig , Taylor L. Hughes , Shou-Cheng Zhang
We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride semiconductor … We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an “inverted” type at a critical thickness d c . We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.
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Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter "Moth" to Lattice Gauge Theory

2005-06-28
Klaus Osterloh , M. Baig , L. Santos +2 more
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive … We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary k x k matrices. The single-particle dynamics in the case of intense U2 vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
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Quantum Spin Hall Effect in Graphene

2005-11-23
C. L. Kane , E. J. Melé
We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime … We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.
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Diffusion of Dirac fermions across a topological merging transition in two dimensions

2016-03-08
Pierre Adroguer , David Carpentier , Gilles Montambaux +1 more
A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In … A continuous deformation of a Hamiltonian possessing at low energy two Dirac points of opposite chiralities can lead to a gap opening by merging of the two Dirac points. In two dimensions, the critical Hamiltonian possesses a semi-Dirac spectrum: linear in one direction but quadratic in the other. We study the transport properties across such a transition, from a Dirac semi-metal through a semi-Dirac phase towards a gapped phase. Using both a Boltzmann approach and a diagrammatic Kubo approach, we describe the conductivity tensor within the diffusive regime. In particular, we show that both the anisotropy of the Fermi surface and the Dirac nature of the eigenstates combine to give rise to anisotropic transport times, manifesting themselves through an unusual matrix self-energy.
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Two-dimensional gas of massless Dirac fermions in graphene

2005-11-01
Kostya S. Novoselov , A. K. Geǐm , С. В. Морозов +5 more
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Theory of the Topological Anderson Insulator

2009-11-06
Christoph Groth , Michael Wimmer , Anton Akhmerov +2 more
We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of … We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic corrections proportional to p^2 sigma_z to the Dirac Hamiltonian that can drive an ordinary band insulator into a topological insulator (having an inverted band gap). We calculate the location of the phase boundary at weak disorder and show that it corresponds to the crossing of a band edge rather than a mobility edge. Our mechanism for the formation of a topological Anderson insulator is generic, and would apply as well to three-dimensional semiconductors with strong spin-orbit coupling.
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Topological invariants of time-reversal-invariant band structures

2007-03-26
Joel E. Moore , Leon Balents
The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the ${\mathbb{Z}}_{2}$ invariant found by Kane and Mele. Such invariants protect the ``topological insulator'' phase … The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the ${\mathbb{Z}}_{2}$ invariant found by Kane and Mele. Such invariants protect the ``topological insulator'' phase and give rise to a spin Hall effect carried by edge states. Each pair of bands related by time reversal is described by one ${\mathbb{Z}}_{2}$ invariant, up to one less than half the dimension of the Bloch Hamiltonians. In three dimensions, there are four such invariants per band pair. The ${\mathbb{Z}}_{2}$ invariants of a crystal determine the transitions between ordinary and topological insulators as its bands are occupied by electrons. We derive these invariants using maps from the Brillouin zone to the space of Bloch Hamiltonians and clarify the connections between ${\mathbb{Z}}_{2}$ invariants, the integer invariants that underlie the integer quantum Hall effect, and previous invariants of $\mathcal{T}$-invariant Fermi systems.
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Semi-Dirac point in the Hofstadter spectrum

2010-07-28
Pierre Delplace , Gilles Montambaux
The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, … The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair of Dirac points may merge into a single one, with a topological transition towards a gapped phase. At the transition, the spectrum is linear in one direction and quadratic in the other one (a spectrum recently named "hybrid" or "semi-Dirac"). This transition is studied in the framework of a general Hamiltonian describing the merging of Dirac points. The possibility of creating gauge fields for cold atoms in optical lattices may offer the first opportunity to observe this merging of Dirac points and the hybrid dispersion relation.
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Topological Anderson Insulator

2009-04-01
Jian Li , Rui-Lin Chu , J. K. Jain +1 more
Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal-insulator transition and the integral and fractional quantum Hall effects. In this Letter, we … Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal-insulator transition and the integral and fractional quantum Hall effects. In this Letter, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions and exhibits the phenomenon of quantum spin Hall effect. We predict an unexpected and nontrivial quantum phase termed "topological Anderson insulator," which is obtained by introducing impurities in a two-dimensional metal; here disorder not only causes metal-insulator transition, as anticipated, but is fundamentally responsible for creating extended edge states. We determine the phase diagram of the topological Anderson insulator and outline its experimental consequences.

Phonon-Induced Topological Transitions and Crossovers in Dirac Materials

2013-01-22
Ion Garate
We show that electron-phonon interactions can alter the topological properties of Dirac insulators and semimetals, at both zero and nonzero temperature. Contrary to the common belief that increasing temperature always … We show that electron-phonon interactions can alter the topological properties of Dirac insulators and semimetals, at both zero and nonzero temperature. Contrary to the common belief that increasing temperature always destabilizes topological phases, our results highlight instances in which phonons may lead to the appearance of topological surface states above a crossover temperature in a material that has a topologically trivial ground state.
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Semi-Dirac dispersion relation in photonic crystals

2013-12-01
Ying Wu
A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic … A semi-Dirac cone refers to a peculiar type of dispersion relation that is linear along the symmetry line but quadratic in the perpendicular direction. Here, I demonstrate that a photonic crystal consisting of a square array of elliptical dielectric cylinders is able to produce this particular dispersion relation in the Brillouin zone center. A perturbation method is used to evaluate the linear slope and to affirm that the dispersion relation is a semi-Dirac type. Effective medium parameters calculated from a boundary effective medium theory not only explain the unexpected topological transition in the iso-frequency surfaces occurring at the semi-Dirac point, they also offer a perspective on the property at that point, where the photonic crystal behaves as a zero-refractive-index material along the symmetry axis but functions like at a photonic band edge in the perpendicular direction.
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Flat-band engineering of mobility edges

2015-06-19
Carlo Danieli , Joshua D. Bodyfelt , Sergej Flach
Properly modulated flat-band lattices have a divergent density of states at the flat-band energy. Quasiperiodic modulations are known to host a metal-insulator transition already in one space dimension. Their embedding … Properly modulated flat-band lattices have a divergent density of states at the flat-band energy. Quasiperiodic modulations are known to host a metal-insulator transition already in one space dimension. Their embedding into flat-band geometries consequently allows for a precise engineering and fine tuning of mobility edges. We obtain analytic expressions for singular mobility edges for two flat-band lattice examples. In particular, we engineer cases with arbitrarily small energy separations of mobility edge, zeroes, and divergencies.
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Mott insulators in strong electric fields

2002-08-30
Subir Sachdev , K. Sengupta , S. M. Girvin
Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient … Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of Rb atoms. This state is stable to a small applied potential gradient (an `electric' field), but a resonant response was observed when the potential energy drop per lattice spacing (E), was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for E close to U via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order, and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions, and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions, and to a variety of lattices, should allow study of numerous other correlated quantum phases.
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Fractional Quantum Hall States at Zero Magnetic Field

2011-06-06
Titus Neupert , Luiz H. Santos , Claudio Chamon +1 more
We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible … We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.
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Mott-Insulator Transition in a Two-Dimensional Atomic Bose Gas

2007-02-22
I. B. Spielman , William D. Phillips , J. V. Porto
Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate … Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.
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Novel Electric Field Effects on Landau Levels in Graphene

2007-03-15
Vinu Lukose , Ravi Shankar , G. Baskaran
A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the … A new effect in graphene in the presence of crossed uniform electric and magnetic fields is predicted. Landau levels are shown to be modified in an unexpected fashion by the electric field, leading to a collapse of the spectrum, when the value of electric to magnetic field ratio exceeds a certain critical value. Our theoretical results, strikingly different from the standard 2D electron gas, are explained using a "Lorentz boost," and as an "instability of a relativistic quantum field vacuum." It is a remarkable case of emergent relativistic type phenomena in nonrelativistic graphene. We also discuss few possible experimental consequence.
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Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop

2009-02-26
Nathan Goldman , A. Kubasiak , Pierre Gaspard +1 more
Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties … Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a constant Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analog of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.
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Anderson localization in tight-binding models with flat bands

2010-09-27
J. T. Chalker , Thomas Pickles , Pragya Shukla
We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is … We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localized nor spatially extended. Further, we establish a mapping between this localization problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.
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Many-body physics with ultracold gases

2008-07-18
Immanuel Bloch , Jean Dalibard , W. Zwerger
This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical … This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.
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Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

2012-03-01
Leticia Tarruell , Daniel Greif , Thomas Uehlinger +2 more
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Topological phases for fermionic cold atoms on the Lieb lattice

2011-06-02
Nathan Goldman , Daniel F. Urban , Dario Bercioux
We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum … We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term - a non-Abelian gauge field - and demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold-atoms.
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Topological Surface States in Three-Dimensional Magnetic Insulators

2008-10-31
Joel E. Moore , Ying Ran , Xiao-Gang Wen
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is … An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in three dimensions can have topologically nontrivial properties of the effective band structure. For the simplest case of two bands, these "Hopf insulators" are characterized by a topological invariant as in quantum Hall states and Z2 topological insulators, but instead of a Chern number or parity, the underlying invariant is the Hopf invariant that classifies maps from the three-sphere to the two-sphere. This Letter gives an efficient algorithm to compute whether a given magnetic band structure has nontrivial Hopf invariant, a double-exchange-like tight-binding model that realizes the nontrivial case, and a numerical study of the surface states of this model.
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Bose-Einstein Condensate in a Uniform Light-Induced Vector Potential

2009-03-30
Yu-Ju Lin , R. L. Compton , Abigail R. Perry +3 more
We use a two-photon dressing field to create an effective vector gauge potential for Bose-Einstein-condensed atoms in the hyperfine ground state. These Raman-dressed states are spin and momentum superpositions, and … We use a two-photon dressing field to create an effective vector gauge potential for Bose-Einstein-condensed atoms in the hyperfine ground state. These Raman-dressed states are spin and momentum superpositions, and we adiabatically load the atoms into the lowest energy dressed state. The effective Hamiltonian of these neutral atoms is like that of charged particles in a uniform magnetic vector potential whose magnitude is set by the strength and detuning of the Raman coupling. The spin and momentum decomposition of the dressed states reveals the strength of the effective vector potential, and our measurements agree quantitatively with a simple single-particle model. While the uniform effective vector potential described here corresponds to zero magnetic field, our technique can be extended to nonuniform vector potentials, giving nonzero effective magnetic fields.
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Synthetic magnetic fields for ultracold neutral atoms

2009-12-01
Yu-Ju Lin , R. L. Compton , Karina Jiménez-García +2 more
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Weyl Semimetal in a Topological Insulator Multilayer

2011-09-16
A. A. Burkov , Leon Balents
We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by … We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its bandstructure. This particular type of Weyl semimetal has a finite anomalous Hall conductivity, chiral edge states, and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator with a quantized Hall conductivity, equal to $e^2/h$ per TI layer. We find that the Weyl semimetal has a nonzero DC conductivity at zero temperature and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically-protected edge states.
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Kinetic Ferromagnetism on a Kagome Lattice

2008-04-02
Frank Pollmann , Peter Fulde , Kirill Shtengel
We study strongly correlated electrons on a kagome lattice at 1/6 (and 5/6) filling. They are described by an extended Hubbard Hamiltonian. We are concerned with the limit |t|<<V<<U with … We study strongly correlated electrons on a kagome lattice at 1/6 (and 5/6) filling. They are described by an extended Hubbard Hamiltonian. We are concerned with the limit |t|<<V<<U with a hopping amplitude t, nearest-neighbor repulsion V, and on-site repulsion U. We derive an effective Hamiltonian and show, with the help of the Perron-Frobenius theorem, that the system is ferromagnetic at low temperatures. The robustness of ferromagnetism is discussed and extensions to other lattices are indicated.
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Topological Anderson Insulator in Three Dimensions

2010-11-19
Huaiming Guo , G. Rosenberg , Gil Refael +1 more
We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological "Anderson" insulator, a new topological phase of quantum matter in … We show that disorder, when sufficiently strong, can transform an ordinary metal with strong spin-orbit coupling into a strong topological "Anderson" insulator, a new topological phase of quantum matter in three dimensions characterized by disordered insulating bulk and topologically protected conducting surface states.
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Topological insulators with inversion symmetry

2007-07-02
Liang Fu , C. L. Kane
Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize … Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.
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Flat bands, Dirac cones, and atom dynamics in an optical lattice

2010-10-13
V. Apaja , M. Hyrkäs , M. Manninen
We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed … We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight binding or Hubbard models. In the case of fermions the release of the harmonic confinement removes fast atoms occupying the Dirac cones while those occupying the flat band remain immobile. Using exact diagonalization and dynamics we demonstrate that a similar strong occupation of the flat band does not happen in bosonic case and furthermore that the mean field model is not capable for describing the dynamics of the boson cloud.
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Anderson localization of a non-interacting Bose–Einstein condensate

2008-06-01
G. Roati , Chiara D’Errico , L. Fallani +6 more
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Flatbands under Correlated Perturbations

2014-12-05
Joshua D. Bodyfelt , Daniel Leykam , Carlo Danieli +2 more
Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. … Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $\xi \sim 1 / \ln (E- E_{FB})$, (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), (iv) mobility edge curves show algebraic singularities at $E_{FB}$. Our analytical results are based on perturbative expansions of the CLS, and supported by numerical data in one and two lattice dimensions.
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A topological Dirac insulator in a quantum spin Hall phase

2008-04-01
David Hsieh , Dong Qian , L. Andrew Wray +4 more
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Chiral magnetic effect in ZrTe5

2016-02-08
Qiang Li , Dmitri E. Kharzeev , Cheng Zhang +7 more
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Magnetic-field effects on a two-dimensional Kagomé lattice of quantum dots

2002-02-07
T. Kimura , Hiroyuki Tamura , Kenji Shiraishi +1 more
Magnetic-field effects on the energy spectrum (Hofstadter butterfly) and the flat-band ferromagnetism are studied on a two-dimensional Kagom\'e lattice of quantum dots. Application of a perpendicular magnetic field destroys the … Magnetic-field effects on the energy spectrum (Hofstadter butterfly) and the flat-band ferromagnetism are studied on a two-dimensional Kagom\'e lattice of quantum dots. Application of a perpendicular magnetic field destroys the flat-band ferromagnetism and induces a metal-insulator transition because the flat band has a finite dispersion. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field when the Coulomb interaction is strong. These phenomena can be observed in experiment under reasonable magnetic fields in artificial quantum dot superlattices.
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Observation of a large-gap topological-insulator class with a single Dirac cone on the surface

2009-05-10
Y. Xia , Dong Qian , David Hsieh +7 more
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