Superconductivity from Phonon-Mediated Retardation in a Single-Flavor Metal

We study phonon-mediated pairings in a single-flavor metal with a tunable Berry curvature. In the absence of Berry curvature, we discover an unexpected possibility: p-wave superconductivity emerging purely from the retardation effect, while the static Bardeen-Cooper-Schrieffer (BCS) approximation fails to predict its existence. The gap function exhibits sign-change behavior in frequency (owing to the dynamical structure of the phonon-mediated interaction in the p-wave channel), and T_{c} obeys a BCS-like scaling. We further show that the Berry curvature stabilizes the chiral p-wave superconductivity and can induce transitions to higher-angular-momentum pairings. Our results establish that the phonon-mediated mechanism is a viable pairing candidate in single-flavor systems, such as the quarter-metal superconductivity observed in rhombohedral graphene multilayers.