Odd-integer quantum hall effect in graphene: Interaction and disorder effects

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 ν=1 and ν=3 IQHE states are revealed in the lowest two Dirac Landau levels. However, the critical disorder strength above which the ν=3 IQHE is destroyed is much smaller than that for the ν=1 IQHE, which may explain the absence of a ν=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 ν=1 IQHE state is a Dirac valley and sublattice polarized Ising pseudospin ferromagnet, while the ν=3 state is an xy plane polarized pseudospin ferromagnet.