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Impurity scattering and localization in $d$-wave superconductors

M. Franz·C. Kallin·A. J. Berlinsky
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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.

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M. Franz, C. Kallin, A. J. Berlinsky. 1996-04-30. Impurity scattering and localization in $d$-wave superconductors. https://doi.org/10.1103/physrevb.54.r6897

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