Switching between superconductivity and current density waves in Bernal bilayer graphene

Recent experiments on Bernal-stacked bilayer graphene discovered superconductivity near the van Hove filling only when an in-plane magnetic field or proximate spin-orbit coupling lifts spin degeneracy. Inspired by the experiments, the authors theoretically study here competing ordering instabilities near the van Hove filling of the bilayer graphene with renormalization group methods. The study shows that breaking spin degeneracy would ``switch'' the balance between incommensurate current density wave that breaks translation, time-reversal, and ${C}_{3}$ symmetry, and superconductivity to favor superconductivity.