Electronic Ordered States in Bernal Bilayer Graphene

We present the results for the evolution of the Fermi surfaces in the spin and valley ordered states in Bernal bilayer graphene (BBG) using a realistic form of the electronic dispersion. We consider variation of both number density and displacement field. We determine the evolution of the Fermi surfaces in these scenarios and compare the results to quantum oscillation data. We find that, at low densities, there is a first order transition to a state that is both spin and valley polarized. We find that this state is a perfect quarter-metal, which matches well with the experimental data. Then, at large densities, there is another first order transition to a state that is only spin (or only valley) polarized. This state is "almost" half-metal, with a large, but still non-complete polarization, with two large and two small Fermi pockets, in another agreement with experimental data. We also discuss the effects of spin-orbit coupling on the system.