Optical conductivity of a dirty current-carrying superconductor

Abstract

We develop a full microscopic theory for the optical conductivity σ(ω) of a dirty current-carrying superconductor. Within the Keldysh sigma model formalism, we obtain the general analytical expression for σ(ω), applicable for arbitrary frequency ω, temperature T, and dc supercurrent I. In addition to altering the usual Mattis-Bardeen conductivity σ1(ω), a finite supercurrent introduces two new contributions: σ2qp(ω) from quasiparticle redistribution and σ2SH(ω) from the amplitude (Schmid-Higgs) mode excitation by the ac field. We investigate, both analytically and numerically, the main features of the optical conductivity in the presence of a dc supercurrent. They include a peak in Reσ(ω) above the optical gap and a sign change of Imσ(ω), with both effects becoming more pronounced at higher I and lower T. We also elucidate the role of inelastic relaxation, which governs the low-frequency response, leading to a giant microwave absorption and a suppression of the apparent superfluid density at the critical current. The optical conductivity measurement of a superconductor biased by a finite dc supercurrent enables the direct observation of the Schmid-Higgs mode via transport measurements.

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