Coulomb interactions, Dirac sea polarization, and SU(4) symmetry breaking of the integer quantum Hall states of graphene

We investigate effects of the filled Dirac sea on the SU(4) symmetry breaking for the integer quantum Hall states of graphene with long-ranged electrostatic Coulomb interactions. Our model also includes Hubbard and nearest-neighbor repulsive interactions with strengths U and V, respectively. We find the symmetry breaking of n = 0 Landau level is accompanied by an SU(4) polarization of the filled Dirac sea. We compute the phase diagram for filling factor v = 0,+/- 1 in the U-V space at magnetic fields relevant to experiments. The Dirac sea polarization significantly influences the phase diagram. It suppresses the Kekule ordering at v = 0 and induces it at v = +/- 1. We also calculate the excitation gaps at small tilted magnetic fields. This enables us to conclude that the ground state is a charge density wave at v = 0 and valley-spin polarized at v = +/- 1. We delineate a region in the U-V space consistent with the experiments.