Feedback Effects in Superconductors

TL;DR

This paper calculates how collective modes in superconductors influence the BCS gap, showing a small effect on the gap but potential significance in type-II superconductors, especially organic ones.

Contribution

It introduces a calculation of feedback effects from collective modes on the BCS gap, highlighting their importance in type-II superconductors and potential experimental relevance.

Findings

Feedback reduces the BCS gap parameter.

Critical temperature remains unchanged.

Effect is significant in type-II superconductors with small Fermi velocities.

Abstract

We calculate corrections to the BCS gap equation caused by the interaction of electrons with the collective phase and amplitude modes in the superconducting state. This feedback reduces the BCS gap parameter, $\Delta$, and leaves the critical temperature, $T_c$, unchanged. The feedback effect is proportional to $(\Delta / {\scriptstyle{\cal E}_F})^2$, where ${\scriptstyle{\cal E}_F}$ is the Fermi energy. This is a negligible correction for type-I superconductors. However in type-II superconductors the feedback effect is greatly enhanced due to smaller Fermi velocities, $v_F$, and may be responsible for effects seen in recent experimental data on organic superconductors.