BCS theory of driven superconductivity

We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature Tc, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of Tc. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify Tc. Our results hold universally for the large class of normal BCS superconductors.