Resonant states and order-parameter suppression near pointlike impurities in d-wave superconductors

We examine the role of order-parameter suppression in the development of lo w-energy peaks (i.e., resonances) in the tunneling density of states near a nonmagnetic impurity in a d-wave superconductor. Without order-parameter s uppression, the zero-energy resonance appears only in the unitary (i.e., st rong impurity) limit. However, suppression makes the resonance appear even when the impurity is much weaker. To model this situation, we make the phys ical hypothesis that the order parameter is reduced whenever one electron o f a Cooper pair encounters the impurity, a hypothesis that retains the exac t solvability of the problem. In this way, we determine that suppression of the order parameter drives the effective strength of the impurity towards the unitary limit. We determine the order-parameter reduction variationally , and show that the ratios between the main energy scales-the bandwidth and superconducting gap-strongly affect this reduction and, in consequence, th e position and width of the resonance. [S0163-1829(99)11033-6].