Microscopic theory of correlated states in Bernal bilayer graphene

The recent discovery of spin- and valley polarized states as well as superconductivity has established Bernal bilayer graphene (BBG) as a highly tunable platform to study the interplay of various strongly correlated states. The emergence of spin-polarized superconductivity close to spin(/valley magnetic states hints towards an unconventional mechanism. Using the supercell Wannierization technique presented in [arXiv:2407.02576], we build an ab-initio effective low-enery model for BBG at low electron/hole densities. We apply the functional renormalization group (FRG) to this model and characterize particle-hole and particle-particle instabilities emerging from repulsive Coulomb interactions in an unbiased way. By adding self-energies to the FRG flow and flowing into symmetry broken phases, we find spin/valley magnetism in line with experimental observations. Additionally, the FRG analysis predicts strong spin/valley fluctuations in vicinity to the magnetic states that drive spin-triplet superconductivity. Our results reinforce the picture of an electronic pairing glue in BBG.