(pi)a la Node: Disordered d Wave Superconductors in Two Dimensions for the Random Masses

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 ((pi), (pi)) 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.