Effect of inhomogeneous coupling on superconductivity

TL;DR

This paper studies how spatial variations in pairing interactions affect superconducting properties like critical temperature, energy gap, and phase fluctuations, revealing significant deviations from homogeneous models especially at larger inhomogeneity scales.

Contribution

It provides a theoretical analysis of inhomogeneous coupling effects on superconductivity, including the impact on $T_c$, $E_g$, and phase fluctuations, explaining experimental anomalies.

Findings

Inhomogeneity reduces the $2E_g/T_c$ ratio when the length scale is large.

Large-scale inhomogeneity can increase the $2E_g/T_{KT}$ ratio beyond BCS predictions.

The results qualitatively explain low $2E_g/T_c$ ratios observed in thin film experiments.

Abstract

We investigate the influence of inhomogeneity in the pairing coupling constant $U(\vec r)$ on dirty BCS superconductors, focusing on $T_c$, the order parameter $\Delta(\vec r)$, and the energy gap $E_g(\vec r)$. Within mean-field theory, we find that when the length-scale of the inhomogeneity is comparable to, or larger than the coherence length, the ratio $2E_g/T_c$ is significantly reduced from that of a homogeneous superconductor, while in the opposite limit this ratio stays unmodified. In two dimensions, when strong phase fluctuations are included, the Kosterlitz-Thouless temperature $T_{KT}$ is also studied. We find that when the inhomogeneity length scale is much larger than the coherence length, $2E_g/T_{KT}$ can be larger than the usual BCS value. We use our results to qualitatively explain recent experimental observation of a surprisingly low value of $2E_g/T_c$ in thin films.