Berry-Flux-Controlled Cascade of Chiral Superconducting States

Motivated by recent interest in chiral superconductivity in narrow bands, we develop a general framework to clarify how band topology and quantum geometry affect superconducting pairing and connect to the two-body problem. Berry curvature does not merely favor a chiral pairing channel; it produces a sequence of chiral pairing instabilities indexed by angular momentum, controlled by the Berry flux through the Fermi sea, with a Little-Parks-like periodicity in momentum space. We show that Berry curvature converts a nonchiral attractive interaction into a geometrically frustrated Cooper problem in momentum space. The relevant control parameter is the Berry-curvature flux enclosed by the Fermi sea, $\Phi = b k_F^2$, which acts as an effective Aharonov-Bohm flux for the order parameter defined on the Fermi surface. As $\Phi$ is tuned, the leading pairing instability switches between odd angular-momentum channels $m=1,3,5...$, producing a cascade of first-order transitions and Little-Parks-like oscillations of $T_c$.