Exciton-mediated unconventional superconductivity in graphene multilayers

We uncover a purely repulsive mechanism for superconductivity in graphene multilayers relying on interband processes and occurring upon doping a band insulator, mediated by excitons forming between the two bands. The symmetry of the pairing order parameter depends on the quantum geometry of the valence band, is generically non s-wave, and undergoes transitions as a function of applied electric field. The attraction can be attributed, in real space, to fluctuations of the electron lattice representing the filled valence band. We apply our theory to results in Bernal bilayer and rhombohedral trilayer graphene, suggesting the importance of exciton-mediated pairing in these systems.