Supercurrent-induced resonant optical response

Abstract

The optical conductivity encodes the current response to a time dependent electric field. We develop a theory of the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in the presence of a dc supercurrent. Current induced optical response is prohibited when current is conserved, an illustrative example of which is Galilean invariant systems. However, we show that lattice effects give rise to a pronounced current dependent peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ at the gap edge $\ensuremath{\omega}=2\mathrm{\ensuremath{\Delta}}$, which diverges in the clean limit. We demonstrate this in a model of a multiband superconductor. Our theory predicts the current induced peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ to scale quadratically with the super-current density, as was recently reported in experiments on NbN by Nakamura et al. [Phys. Rev. Lett. 122, 257001 (2019)]. This provides the potential for a new mechanism for direct activation of the Higgs mode with light.