Eur. Phys. J. B (2016) 89: 244
https://doi.org/10.1140/epjb/e2016-70528-1

Regular Article

BCS theory of driven superconductivity

¹ Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
² I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstr. 9, 20355 Hamburg, Germany
³ The Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany

^a e-mail: michael.thorwart@physik.uni-hamburg.de

Received: 9 September 2016
Published online: 9 November 2016

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.