Impurity scattering and localization in $d$-wave superconductors

TL;DR

This paper provides strong evidence that low-energy quasiparticle states in disordered d-wave superconductors become localized due to impurity effects, using self-consistent numerical solutions of the Bogoliubov-de Gennes equations.

Contribution

It demonstrates the localization of quasiparticle states in disordered d-wave superconductors through comprehensive numerical analysis within the BdG framework.

Findings

Localization of low-energy quasiparticle states confirmed

Finite size scaling supports localization evidence

Numerical diagonalization on large clusters performed

Abstract

Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of non-magnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to $50\times 50$ sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite size dependence of inverse participation ratios.