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Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices

Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices

For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structure of several Dirac systems. In our model, …