Impurity States and the Absence of Quasiparticle Localization in Disordered D-Wave Superconductors

Abstract

The absence of localization of impurity-induced low-energy quasiparticle states in a two-dimensional $d$-wave superconductor is argued for any amount of disorder in the limit of unitary scatterers. This surprising result follows from the fact that a unitary impurity produces a marginally-bound state at zero energy which decays as a power-law along the nodes of the $d$-wave energy gap. Consequently, for finite density of impurities, the impurity-induced states are coupled by long-range overlaps yielding extended quasiparticle states below a characteristic energy scale ${\omega }_c$. Simple scaling arguments suggest that ${\omega }_c\propto e^{-c/n_{\mathrm{imp}}}$, where $n_{\mathrm{imp}}$ is the impurity density and $c$ is a positive constant.

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