Impurity states and the absence of quasiparticle localization in disordered d-wave superconductors

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) proportional to e(-c/nimp), with n(imp) the impurity density and c a positive constant.