How pairing mechanism dictates topology in valley-polarized superconductors with Berry curvature

We investigate how the pairing mechanism influences topological superconductivity in valley-polarized systems with Berry curvature. We demonstrate that short-range attractive interactions, such as those mediated by phonons, favor superconducting states where the Bogoliubov–de Gennes (BdG) Chern number has the same sign as the Berry curvature. In contrast, overscreened repulsive interactions, as in the Kohn–Luttinger mechanism, favor superconducting states where the BdG Chern number has the opposite sign as the Berry curvature. We establish these trends in both a fully controlled limit and in an effective model for rhombohedral multilayer graphene–a system where signatures of chiral superconductivity were recently observed. Our theory provides a concrete experimental criterion for distinguishing between different pairing mechanisms in valley-polarized superconductors.