Linear response function around a localized impurity in a superconductor

TL;DR

This paper analyzes the linear response function around a localized impurity in a superconductor, extending early Fermi gas work to superconductors with s- and d-wave pairing at zero temperature, relevant for understanding impurity effects.

Contribution

It provides a detailed examination of the linear response function in superconductors with localized impurities, building on and extending classical Fermi gas results to superconducting states.

Findings

Response functions for s-wave superconductors calculated.

Response functions for d-wave superconductors calculated.

Relevance to impurity effects in high-Tc superconductors discussed.

Abstract

Imaging the effects of an impurity like Zn in high-Tc superconductors [Nature 61 (2000) 746] has rekindled interest in defect problems in the superconducting phase. This has prompted us here to re-examine the early work of March and Murray [Phys. Rev. 120 (1960) 830] on the linear response function in an initially translationally invariant Fermi gas. In particular, we present corresponding results for a superconductor at zero temperature, both in the s- and in the d-wave case, and mention their direct physical relevance in the case when the impurity potential is highly localized.