We report on a numerical study of disorder effects in 2D $d$-wave BCS superconductors. We compare exact numerical solutions of the Bogoliubov–de Gennes (BdG) equations for the density of states $\rho \left(E\right)$ with the standard T-matrix approximation. Local suppression of the order parameter near impurity sites, which occurs in self-consistent solutions of the BdG equations, leads to apparent power-law behavior $\rho \left(E\right)\sim |E{|}^{\alpha }$ with nonuniversal $\alpha$ over an energy scale comparable to the single-impurity resonance energy ${\Omega }_0$. We show that the novel effects arise from static spatial correlations between the order parameter and the impurity distribution.

• Received 22 February 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.3922