Integer quantum Hall effect in gapped single-layer graphene

Abstract

Analytical expressions for the Hall conductivity sigma(yx) and the longitudinal resistivity rho(xx) are derived in gapped, single-layer graphene using linear response theory. The gap 2 Delta, described by a mass term, is induced by a substrate made of hexagonal boron nitride (h-BN) and produces two levels at +/-Delta. It is shown that syx has the same form as for a graphene sample supported by a common substrate without a mass term. The differences are a shift in the energy spectrum, which is not symmetric with respect to the Dirac point for either valley due to the gap, the absence of a zero-energy Landau level, and the nonequivalence of the K and K' valleys. In addition, the dispersion of the energy levels, caused by electron scattering by impurities, modifies mostly plateaus due to the levels at +/-Delta. It is shown that the resistivity rho(xx) exhibits an oscillatory dependence on the electron concentration. The main difference with the usual graphene samples, on SiO2 substrates, occurs near zero concentration, as the energy spectra differ mostly near the Dirac point.