Time-resolved optical conductivity and Higgs oscillations in two-band dirty superconductors

TL;DR

This paper investigates how impurity scattering affects the optical Higgs response in dirty superconductors, analyzing time-resolved conductivity and Higgs oscillations in single- and two-band systems using theoretical models.

Contribution

It introduces a comprehensive calculation of time-resolved optical conductivity in dirty superconductors, incorporating impurity effects and comparing two theoretical approaches.

Findings

Good agreement with experimental results on optical conductivity.

Impurity scattering significantly enhances Higgs mode excitation.

Time-dependent models reveal detailed Higgs oscillation dynamics.

Abstract

Recent studies have emphasized the importance of impurity scattering for the optical Higgs response of superconductors. In the dirty limit, an additional paramagnetic coupling of light to the superconducting condensate arises which drastically enhances excitation. So far, most work concentrated on the periodic driving with light, where the third-harmonic generation response of the Higgs mode was shown to be enhanced. In this work, we additionally calculate the time-resolved optical conductivity of single- and two-band superconductors in a two-pulse quench-probe setup, where we find good agreement with existing experimental results. We use the Mattis-Bardeen approach to incorporate impurity scattering and calculate explicitly the time-evolution of the system. Calculations are performed both in a diagrammatic picture derived from an effective action formalism and within a time-dependent density matrix formalism.