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We study the competition between the long-range Coulomb interaction, disorderscattering, and lattice effects in the integer quantum Hall effect (IQHE) ingraphene. By direct transport calculations, both $\nu=1$ and $\nu=3$ IQHEstates are revealed in the lowest two Dirac Landau levels. However, thecritical disorder strength above which the $\nu=3$ IQHE is destroyed is muchsmaller 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 theIQHE phase is gapless within numerical finite-size analysis, we do find anddetermine a mobility gap, which characterizes the energy scale of the stabilityof the IQHE. Furthermore, we demonstrate that the $\nu=1$ IQHE state is a Diracvalley and sublattice polarized Ising pseudospin ferromagnet, while the $\nu=3$state is an $xy$ plane polarized pseudospin ferromagnet.

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