BCS theory of driven superconductivity

TL;DR

This paper investigates how external time-dependent phonon driving can enhance the critical temperature of BCS superconductors, providing analytic expressions and demonstrating universal applicability.

Contribution

It introduces a theoretical framework showing that parametric phonon driving and anharmonicities can increase $T_c$ in BCS superconductors, with simple analytic formulas.

Findings

Parametric phonon driving can elevate $T_c$.

Dipolar phonon drive has no effect on $T_c$.

Phonon anharmonicities further amplify $T_c$.

Abstract

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 $T_c$, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of $T_c$. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify $T_c$. Our results hold universally for the large class of normal BCS superconductors.