Lattice theory of pseudospin ferromagnetism in bilayer graphene: Competing interaction-induced quantum Hall states

In mean-field theory, bilayer graphene's massive Dirac fermion model has a family of broken-inversion-symmetry ground states with charge gaps and flavor-dependent spontaneous interlayer charge transfers. We use a lattice Hartree-Fock model to explore the lattice scale physics of graphene bilayers, which has a strong influence on ordering energy scales and on the competition between distinct ordered states. We find that inversion symmetry is still broken in the lattice model and estimate that the transferred areal densities are ~10^-5 electrons per carbon atom, that the associated energy gaps are ~10^-2eV, that the ordering condensation energies are ~10^-7 eV per carbon atom, and that the differences in energy between competing ordered states is ~10^-9 eV per carbon atom. We find that states with a quantized valley Hall effect are lowest in energy, but that the coupling of an external magnetic field to spontaneous orbital moments favors the broken-time-reversal-symmetry states that have quantized anomalous Hall effects. Our theory predicts nonmonotonic behavior of the band gap at neutrality on the potential difference between layers, in qualitative agreement with recent experiments.