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 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 (cid:12)nite density of impurities, the impurity-induced states are coupled by long-range overlaps yielding extended quasiparticle states below a characteristic energy scale !c. Simple scaling arguments suggest that !c / e (cid:0)c=nimp , where nimp is the impurity density and c is a positive constant.