Correlation energy in bernal bilayer graphene under strong displacement field

The discovery of spin-valley symmetry-broken states in graphene multilayers in a strong displacement field raises many questions about the phase diagram and the nature of electronic correlations in this system. While mean-field theory can often correctly explain the onset of symmetry-breaking and the order in which spin-valley symmetries are broken, it completely fails to describe some parts of the experimental phase diagram. In particular in bernal bilayer graphene, experiments found that the low-hole-density paramagnetic state (“Sym-12”) generally survives to much larger hole densities than predicted in mean-field theory. The discrepancies are particularly stark in some parts of the phase diagram; for example the paramagnetic state seems to be exceptionally stable on the low-density side of the van Hove singularity. In an effort to explain the systematic deviations from Hartree-Fock theory, we study the correlation energy contribution to the total energy using the time-dependent Hartree-Fock method, paying special attention to its relationship to the shape and the topology of the Fermi surface.