Enhancement of superconductivity by local inhomogeneity

TL;DR

This paper investigates how local inhomogeneity in pairing interactions or background potential can enhance the superconducting transition temperature, especially when the inhomogeneity scale matches the coherence length, within the weak coupling BCS framework.

Contribution

It demonstrates that inhomogeneity not aligned with Fermi surface nesting can increase T_c, identifying optimal modulation scales for enhancement.

Findings

Inhomogeneity enhances T_c compared to uniform systems.

Maximum T_c occurs when modulation length scale matches coherence length.

Incommensurate inhomogeneity with Fermi surface nesting vectors is beneficial.

Abstract

We study the effect of inhomogeneity of the paring interaction or the background potential on the superconducting transition temperature, T_c. In the weak coupling BCS regime, we find that inhomogeneity which is incommensurate with the Fermi surface nesting vectors enhances T_c relative to its value for the uniform system. For a fixed modulation strength we find that the highest T_c is reached when the characteristic modulation length scale is of the order of the superconducting coherence length.