Odd-Integer Quantum Hall Effect in Graphene: Interaction and Disorder Effects

Abstract

We study the competition between the long-range Coulomb interaction, disorder scattering, and lattice effects in the integer quantum Hall effect (IQHE) in graphene. By direct transport calculations, both $\nu =1$ and $\nu =3$ IQHE states are revealed in the lowest two Dirac Landau levels. However, the critical disorder strength above which the $\nu =3$ IQHE is destroyed is much smaller than that for the $\nu =1$ IQHE, which may explain the absence of a $\nu =3$ plateau in recent experiments. While the excitation spectrum in the IQHE phase is gapless within numerical finite-size analysis, we do find and determine a mobility gap, which characterizes the energy scale of the stability of the IQHE. Furthermore, we demonstrate that the $\nu =1$ IQHE state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet, while the $\nu =3$ state is an $xy$ plane polarized pseudospin ferromagnet.