Quasiparticle density of states in dirty high-T-c superconductors

We study the density of quasiparticle states of dirty d-wave superconductor s, We show the existence of singular corrections to the density of states d ue to quantum interference effects. We then argue that the density of state s actually vanishes in the localized phase as \E\ or E-2 depending on wheth er time-reversal is a good symmetry or not. We verify this result for syste ms without time-reversal symmetry in one dimension using supersymmetry tech niques. This simple, instructive calculation also provides the exact univer sal scaling function for the density of states for the crossover from balli stic to localized behavior in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a 2 + e psilon expansion. We discuss consequences of our results for various experi ments on dirty high-T-c materials. [S0163-1829(99)00833-4].