  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.
