Effects of Impurity Vertex Correction on NMR Coherence Peak in S-Wave Superconductors

TL;DR

This paper investigates how non-magnetic impurity vertex corrections influence the nuclear spin-lattice relaxation rate in s-wave superconductors, revealing that impurity effects can enhance the coherence peak as impurity levels increase.

Contribution

It provides a self-consistent Eliashberg formalism analysis of impurity vertex corrections on $1/T_1$, showing the increase of the coherence peak with impurity concentration, which was not previously understood.

Findings

In the clean limit, $1/(T_1 T)$ remains unaffected by impurity vertex corrections.

Impurity vertex correction enhances the coherence peak in $1/(T_1 T)$ as impurity levels increase.

The results align with experimental observations on conventional superconductors.

Abstract

We study the effects of non-magnetic impurity vertex correction on nuclear spin-lattice relaxation rate $1/{T_1} $ of conventional s-wave superconductors within the Eliashberg formalism. We obtain, with a self-consistent $t-$matrix treatment of impurity scatterings, the expressions for impurity vertex function and nuclear spin-lattice relaxation rate. The $1/T_1$ is evaluated with a simple approximation on angular average, and found to agree in clean limit with the previous result that $1/(T_1 T)$ remains unrenormalized under the impurity vertex correction. As dirtiness is increased, on the other hand, the coherence peak in $1/(T_1 T)$ is found to increase due to the impurity vertex correction. This result is discussed in connection with the experimental observations on conventional superconductors.