Disorder effects in two-dimensionald-wave superconductors

Abstract

We show that weak nonmagnetic impurities in a two-dimensional d-wave superconductor introduce a nontrivial exponent in the energy dependence of the single-particle density of states: ρ(ω)∼‖ω${\mathrm{\Vert }}^{\mathrm{\alpha }}$. The exponent α>0 is exactly calculated for two types of disorder. We argue that the appearance of a finite ρ(0) would be equivalent to breaking of a continuous symmetry, prohibited in two dimensions. The method we use is based on the Abelian and non-Abelian bosonization of the effective model of 1D interacting fermions.