Instantons and the spectral function of electrons in the half-filled Landau level

Abstract

We calculate the instanton--anti-instanton action ${\mathit{S}}_{\mathit{MM}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}$(\ensuremath{\tau}) in the gauge theory of the half-filled Landau level. It is found that ${\mathit{S}}_{\mathit{MM}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}$(\ensuremath{\tau})=(3-\ensuremath{\eta})[${\mathrm{\ensuremath{\Omega}}}_{0}$(\ensuremath{\eta})\ensuremath{\tau}${]}^{1/(3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}})}$ for a class of interactions v(q)=${\mathit{V}}_{0}$/${\mathit{q}}^{\mathrm{\ensuremath{\eta}}}$ (0\ensuremath{\le}\ensuremath{\eta}2) between electrons. This means that the instanton--anti-instanton pairs are confining so that a well-defined ``charged'' composite fermion can exist. It is also shown that ${\mathit{S}}_{\mathit{MM}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}$(\ensuremath{\tau}) can be used to calculate the spectral function of electrons from the microscopic theory within a semiclassical approximation. The resulting spectral function varies as ${\mathit{e}}_{0}^{\mathrm{\ensuremath{-}}[\mathrm{\ensuremath{\Omega}}}$(\ensuremath{\eta})/\ensuremath{\omega}${]}^{1/(2\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}})}$ at low energies.

Locations

• Physical review. B, Condensed matter - View
• arXiv (Cornell University) - View - PDF
• PubMed - View
• DataCite API - View