Impurity scattering and localization in d-wave superconductors

Strong evidence is presented for the localization of low-energy quasiparticle states ih disordered d-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory:applied to the extended Hubbard model with a finite concentration pf nonmagnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to 50x50 sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite-size dependence of inverse participation ratios.