Quantum Hall ferromagnetism in gapped bilayer graphene with trigonal warping effects

The interplay between nontrivial Fermi surface topology and electron-electron interactions often leads to interesting phenomena in the quantum Hall regime. Bilayer graphene provides a unique platform to explore such physics, because the combined effects of trigonal warping and interlayer bias give rise to a nontrivial bandstructure at low energies. In the presence of a small perpendicular magnetic field, the highest valence-band Landau level of gapped bilayer graphene becomes three-fold degenerate excluding the spin degrees of freedom, with the three Landau levels corresponding to semiclassical orbits centered on different points in momentum space. Such a Landau level structure has been observed in a recent experiment [Phys. Rev. Lett. 113, 116602 (2014)]. In this work we construct a theory to show how the electron-electron interactions break this three-fold orbital degeneracy, and give rise to a gapped quantum Hall state at all intermediate integer filling factors. We further demonstrate that the resulting ground state breaks rotational symmetry and discuss some experimental consequences.