  We examine the role of order-parameter suppression in the development of
low-energy peaks (i.e., resonances) in the tunneling density of states near a
non-magnetic impurity in a d-wave superconductor. Without order-parameter
suppression, the zero-energy resonance appears only in the unitary (i.e.,
strong impurity) limit. However, suppression makes the resonance appear even
when the impurity is much weaker. To model this situation, we make the physical
hypothesis that the order parameter is reduced whenever one electron of a
Cooper pair encounters the impurity, a hypothesis that retains the exact
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 band width and
superconducting gap--strongly affect this reduction and, in consequence, the
position and width of the resonance.

Superconductivity