$Π$ à la node: disordered d-wave superconductors in two dimensions for the random masses

Abstract

We review work on the problem of disorder in the 2D d-wave superconducting state, and show that the symmetries of the normal state and the disorder distribution are vital for understanding the low-energy behavior. Most previous theoretical results for the density of states (DOS) are reconciled by a combination of exact numerical solutions of the Bogoliubov-de Gennes equations and weak localization calculations, which suggest that a novel diffusive mode with momentum $(π,π)$ is responsible for a divergence of the DOS in the globally particle-hole symmetric case. We note briefly that the simple problem of a disordered tight-binding band of normal electrons displays some similar effects, which have been overlooked in the literature. Finally, in the physically realistic case of binary alloy disorder, no particle-hole symmetry, and an order parameter which is supressed around each impurity site, a power law with nonuniversal exponent is predicted.