Disorder Effects in Two-Dimensional d-wave Superconductors
Influence of weak nonmagnetic impurities on the single-particle density of states $ρ(ω)$ of two-dimensional electron systems with a conical spectrum is studied. We use a nonperturbative approach, based on replica trick with subsequent mapping of the effective action onto a one-dimensional model of interacting fermions, the latter being treated by Abelian and non-Abelian bosonization methods. It is shown that, in a d-wave superconductor, the density of states, averaged over randomness, follows a nontrivial power-law behavior near the Fermi energy: $ρ(ω) \sim |ω|^α$. The exponent $α>0$ is calculated for several types of disorder. We demonstrate that the property $ρ(0) = 0$ is a direct consequence of a {\it continuous} symmetry of the effective fermionic model, whose breakdown is forbidden in two dimensions. As a counter example, we consider another model with a conical spectrum - a two-dimensional orbital antiferromagnet, where static disorder leads to a finite $ρ(0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.