Symmetry breaking by the sea of Dirac-Landau levels in graphene

The quantum Hall states of graphene have a filled Dirac sea of Landau levels. The short ranged SU(4) symmetry breaking interactions can induce a staggered polarization of the sea of Dirac-Landau levels. We study this effect in the extended Hubbard model on a honeycomb lattice using mean field variational wavefunctions. We find a valley symmetry broken, anti-ferromagnetic spin ordered phase at $\nu =\pm 1$ when the on-site interaction is dominant. Our mean field solution is consistent with the recently reported experimental results of Z. Jiang et. al.\cite{jiang}