Theory of time-resolved optical conductivity of superconductors:comparing two methods for its evaluation

TL;DR

This paper compares two theoretical methods for calculating time-resolved optical conductivity in superconductors, highlighting their differences, advantages, and providing software tools for implementation.

Contribution

It introduces a comparative analysis of two approaches within the non-equilibrium Keldysh formalism for superconductors and offers software to facilitate their application.

Findings

Both methods show similar qualitative features post-pump.

Fixing the gate time removes certain artifacts.

Software is provided for method conversion.

Abstract

Time-resolved optical conductivity is an oft-used tool to interrogate quantum materials driven out of equilibrium. Theoretically calculating this observable is a complex topic with several approaches discussed in the literature. Using a non-equilibrium Keldysh formalism and a functional derivative approach to the conductivity, we present a comparison of two particular approaches to the calculation of the optical conductivity, and their distinguishing features, as applied to a pumped superconductor. The two methods are distinguished by the relative motion of the probe and gate times; either the probe or gate time is kept fixed while the other is swept. We find that both the methods result in same qualitative features of the time-resolved conductivity after pump is over. However, calculating the conductivity by keeping the gate fixed removes artifacts inherent to the other method. We provide software that, based on data for the first method, is able to construct the second approach.