Metastable Photo-Induced Superconductivity far above $T_{\textrm{c}}$

Inspired by the striking discovery of metastable superconductivity in $\mathrm{K}_3\mathrm{C}_{60}$ at 100K, far above $T_{\textrm{c}}=20K$, we discuss possible mechanisms for long-lived, photo-induced superconductivity. Starting from a model of optically-driven Raman phonons coupled to inter-band electronic transitions, we develop a microscopic mechanism for photo-controlling the pairing interaction. Leveraging this mechanism, we first investigate long-lived superconductivity arising from the thermodynamic metastable trapping of the driven phonon. We then propose an alternative route, where the superconducting gap created by an optical drive leads to a dynamical bottleneck in the equilibration of quasi-particles. We conclude by discussing implications of both scenarios for experiments that can be used to discriminate between them. Our work provides falsifiable explanations for the nanosecond-scale photo-induced superconductivity found in $\mathrm{K}_3\mathrm{C}_{60}$, while simultaneously offering a theoretical basis for exploring metastable superconductivity in other quantum materials.