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 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.