Extended Gapless Regions in Disordered d_{x^2-y^2}-Wave Superconductors

TL;DR

This paper extends the theoretical framework for disordered d_{x^2-y^2}-wave superconductors by including higher harmonics and momentum-dependent scattering, revealing extended gapless regions that explain experimental doping effects.

Contribution

It introduces a generalized model incorporating higher harmonics and momentum-dependent impurity scattering in unconventional superconductors.

Findings

Momentum-dependent scattering creates extended gapless regions around nodes.

Enhanced residual density of states correlates with decreased T_c.

Model explains doping-dependent changes in cuprate superconductors.

Abstract

A generalization of the Abrikosov-Gorkov equations for non-magnetic impurities in unconventional superconductors is proposed, including higher harmonics in the expansion of the momentum dependent gap function and a momentum dependent impurity scattering potential. This model is treated within a self-consistent calculation to obtain the electronic density of states, the optical conductivity, and the gap function in a two-dimensional d_{x^2-y^2}-wave superconductor. It is argued that momentum dependent scattering from the impurities may lead to extended gapless regions in the gap function centered around the nodes of the pure d_{x^2-y^2}-wave superconductor. The associated enhancement of the residual density of states may be responsible for the rapid decrease of T_c and the increase of the London penetration depth with hole doping observed in overdoped cuprate superconductors.