Quasiparticle localization in disordered d-wave superconductors

An extensive numerical study is reported on the disorder effect in two-dime nsional d-wave superconductors with random impurities in the unitary limit. It is found that a sharp resonant peak shows up in the density of states a t zero energy and correspondingly the finite-size spin conductance is stron gly enhanced which results in a nonuniversal feature in one-parameter scali ng. However, all quasiparticle states remain localized, indicating that the resonant density peak alone is not sufficient to induce delocalization. In the weak disorder limit, the localization length is so long that the spin conductance at small sample size is close to the universal value predicted by Lee [Phys. Rev. Lett. 71, 1887 (1993)].