Spin-triplet superconductivity from intervalley Goldstone modes in magic-angle graphene

We consider magic-angle graphene in the doping regime around charge neutrality, and we study the connection between a recently proposed intervalley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The intervalley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes that couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and we study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the p-wave channel.