Localized states in a d-wave superconductor

Impurity scatterers, particularly in the unitary limit, produce low energy quasiparticles in a two-dimensional d-wave superconductor. We argue that even if the impurity concentration is small so that the wave functions in the normal state are essentially extended, the quasiparticles in the superconducting state become strongly localized for a short coherence length d-wave superconductor. An effective mobility gap then leads to thermally activated behavior for the microwave conductivity and possibly for the London penetration depth. We argue that this observation allows some puzzling data on oxide superconductors to be reconciled with the hypothesis of d-wave pairing.