Quasi-particle density of states of disordered d-wave superconductors

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We present a numerical study of the quasi-particle density of states (DoS) of two-dimensional d-wave superconductors in the presence of disorder. We find qualitatively different behavior for smooth and short-ranged disorder. In the former case, we find power law scaling of the DoS with an exponent depending on the strength of the disorder and the superconducting order parameter in quantitative agreement with the theory of Nersesyan et al. (Phys. Rev. Lett. 72 (1994) 2628). For strong disorder, a qualitative change to an energy independent DoS occurs. In contrast, for short-ranged disorder of sufficient strength, we find localization and derive the dependence of the localization length on the disorder strength from the system size dependence of the micro gap in the DoS near zero energy.