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

Abstract

The absence of localization of impurity-induced low-energy quasiparticle states in a 2D d-wave superconductor is shown for any amount of disorder in the limit of unitary scatterers. This 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 ${\omega }_c\propto e^{{-c/n}_{\mathrm{imp}}}$, with $n_{\mathrm{imp}}$ the impurity density and c a positive constant.