Disorder Effects in Two-Dimensional d-wave Superconductors

Abstract

Influence of weak nonmagnetic impurities on the single-particle density of states $\rho (\omega )$ 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: $\rho (\omega )\sim |\omega {|}^{\alpha }$. The exponent $\alpha >0$ is calculated for several types of disorder. We demonstrate that the property $\rho (0)=0$ 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 $\rho (0)$ due to breakdown of a {\it discrete} (particle-hole) symmetry.

24 pages, 3 figures upon request, RevTeX

References in corpus (1)

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