Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at non-zero magnetic fields, or when spin-orbit coupling is induced in BBG by coupling to a substrate. We present detailed functional renormalization group and random-phase approximation calculations that provide a unified explanation for the superconducting mechanism in both cases. Both calculations yield a purely electronic $p$-wave instability of the Kohn-Luttinger (KL) type. The latter can be enhanced either by magnetic fields or Ising spin-orbit coupling, naturally explaining the behaviour seen in experiments.