Impurity Effects on the Nodal Structure of Anisotropic Superconductors

TL;DR

This paper investigates how impurities affect the nodal structure of anisotropic superconductors, revealing that nonmagnetic impurities do not alter the nodes and providing methods to determine the nodes for various crystal symmetries.

Contribution

It introduces a comprehensive perturbation approach that considers all series terms, showing that impurity effects do not change the nodal structure in anisotropic superconductors.

Findings

Nonmagnetic impurities do not alter the nodal structure.

Method to determine gap nodes for specific crystal symmetries.

List of nodes for $O_{h}$, $D_{4h}$, and $D_{6h}$ symmetries.

Abstract

For anisotropic superconductors, the gap function belongs to an irreducible representation of the point group of crystals, which determines the nodal structure of the gap function. Impurity effects on anisotropic superconductors have been treated by the Born or T-matrix approximation by which only a partial sum of the pertutbation series is calculated. Instead, we take into acount all terms of the perturbation series. As a result, we find that the introduction of nonmagnetic impurities does not change the nodal structure in all cases. We also find how to obtain nodes of the gap function and show the list for $O_{h}$, $D_{4h}$, and $D_{6h}$.