Critical temperature and superfluid density suppression in disordered high-T_c cuprate superconductors

We argue that the standard Abrikosov-Gorkov (AG) type theory of $T_c$ in disordered $d$-wave superconductors breaks down in short coherence length high-$T_c$ cuprates. Numerical calculations within the Bogoliubov-de Gennes formalism demonstrate that the correct description of such systems must allow for the spatial variation of the order parameter, which is strongly suppressed in the vicinity of impurities but mostly unaffected elsewhere. Suppression of $T_c$ as measured with respect to the attendant decrease in the superfluid density is found to be significantly weaker than that predicted by the AG theory, in good agreement with experiment.