Group expansions for impurities in superconductors

TL;DR

This paper introduces a novel algebraic method to calculate impurity interactions in superconductors, revealing that non-magnetic impurities can contribute to the density of states within the s-wave gap at very low concentrations, beyond traditional approximations.

Contribution

The paper presents a new algebraic approach for calculating impurity interactions in superconductors, extending understanding of impurity effects beyond Born and T-matrix approximations.

Findings

Non-magnetic impurities contribute to the density of states within the s-wave gap at order c^3.

The method allows practical calculations of impurity effects using algebraic properties of Nambu matrices.

Impurity interactions can have significant effects even at very low impurity concentrations.

Abstract

A new method is proposed for practical calculation of the effective interaction between impurity scatterers in superconductors, based on algebraic properties of related Nambu matrices for Green functions. In particular, we show that the density of states within the s-wave gap can have a non-zero contribution (impossible either in Born and in T-matrix approximation) from non-magnetic impurities with concentration $c \ll 1$, beginning from $\sim c^{3}$ order.