Symmetry-broken metallic orders in spin-orbit-coupled Bernal bilayer graphene

We explore Bernal bilayer graphene in the presence of long-range Coulomb interactions, short-range Hund's coupling, and proximity-induced Ising spin-orbit coupling using self-consistent Hartree-Fock simulations. We show that the interplay between these three ingredients produces an intricate phase diagram comprising a multitude of symmetry-broken metallic states tunable via doping and applied displacement field. In particular, we find intervalley coherent and spin-canted ground states that may hold the key to understanding spin-orbit-enabled superconductivity observed in this platform. We also investigate various phase transitions where a continuous $\mathrm{U}(1)$ symmetry is broken to ascertain the possible role of critical fluctuations on pairing.