Valley-Helical Superconductivity Driven by Repulsion and Quantum Geometry: Applications to Time-Reversal Symmetric Rhombohedral Graphene

Motivated by the recent experimental signatures of chiral superconductivity in valley-polarized graphene- and transition-metal-dichalcogenide-based systems, we investigate the possibility of chiral pairing in the absence of valley polarization or time-reversal symmetry breaking. For systems with opposite Berry curvature in the two valleys, we find that overscreened repulsion (i.e., the Kohn-Luttinger mechanism) can indeed induce pairing of opposite chiralities in each valley, producing a valley-helical state. Moreover, the valley-helical state can outcompete more conventional intervalley paired states at intermediate coupling, despite only the latter having a weak-coupling instability. Using a realistic model of time-reversal-symmetric rhombohedral graphene, we find extended ranges of fillings and displacement fields with dominant valley-helical superconductivity. This occurs for all layer numbers considered here, 4 at most N at most 8. We show that the valley-helical states can display topologically projected edge modes, unusual magnetic responses, and intertwined Kekulé-like bond-order; features that can be used to distinguish them from more conventional superconductors.