Valley polarization, magnetization, and superconductivity in bilayer graphene near the van Hove singularity

Abstract: The discovery of Mott insulators and superconductivity in twisted bilayer graphene has ignited intensive research into strong correlation effects in other stacking geometries. Bernal-stacked bilayer graphene (BBG), when subjected to a perpendicular electric field, exhibits phase transitions to a variety of broken-symmetry states. Notably, superconductivity emerges when BBG is in proximity to a heavy transition-metal dichalcogenide, highlighting the role of spin-orbit coupling (SOC). Here we investigate the origin of Ising SOC and its role in the competition between superconductivity and spin- and valley-polarized states in BBG. Starting from strong electron-electron interactions on the BBG lattice, we derive a low-energy effective model near the valleys that incorporates both density-density and spin-spin interactions. Using self-consistent mean-field theory, we map out the BBG phase diagram. Our findings reveal that near the van Hove filling, a mixed spin- and valley-polarized phase dominates over superconductivity. Away from the van Hove filling, a spin-polarized, spin-triplet superconducting state arises, characterized by an in-plane orientation of the magnetic moment and an out-of-plane orientation of the d-vector. Contrary to previous proposals, we find that Ising SOC favours spin-valley order while suppressing superconductivity near the van Hove singularity. We discuss other potential proximity effects and suggest directions for future studies.