Spatial inhomogeneities in disordered d-wave superconductors

We study a short coherence length d-wave superconductor with a finite density of unitary scatterers using the Bogoliubov-deGennes technique. We find that the low-energy density of states is reduced, the superfluid stiffness is significantly larger, and off-diagonal long-range order is more robust than the conventional self-consistent T-matrix prediction. These results are a consequence of the inhomogeneous pairing amplitude in the ground state and of the low-lying excitations formed by hybridized impurity resonances. This inhomogeneous response accounts for the insensitivity of high-$T_c$ superconductors to impurities.