Signatures of superconducting gap inhomogeneities in optical properties

TL;DR

This study investigates how nanoscale inhomogeneities in the superconducting gap affect optical properties, finding that d-wave superconductors' optical conductivity remains robust despite such variations.

Contribution

The paper provides the first analysis of optical signatures of gap inhomogeneities in high-$T_c$ cuprates using an effective medium approximation, considering both s-wave and d-wave symmetries.

Findings

Gap inhomogeneities significantly affect s-wave superconductors' optical properties.

D-wave superconductors' optical conductivity is robust against gap inhomogeneities.

Optical measurements may not detect inhomogeneities in d-wave superconductors.

Abstract

Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has revealed significant spatial inhomogeneity on the nanoscale. Regions on the order of a coherence length in size show variations of the magnitude of the superconducting gap of order $\pm20%$ or more. An important unresolved question is whether or not these variations are also present in the bulk, and how they influence superconducting properties. As many theories and data analyses for high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude, this is a pressing question. We consider the far-infrared optical conductivity and evaluate, within an effective medium approximation, what signatures of spatial variations in gap magnitude are present in various optical quantities. In addition to the case of d-wave superconductivity, relevant to the high-$T_c$ cuprates, we have also considered s-wave gap symmetry in order to provide expected signatures of inhomogeneities for superconductors in general. While signatures of gap inhomogeneities can be strongly manifested in s-wave superconductors, we find that the far-infrared optical conductivity in d-wave is robust against such inhomogeneity.