Density of States of a d-wave Superconductor in the Presence of Strong Impurity Scatterers: a Non Perturbative Result

We present a method to compute the density of states induced by N non magnetic impurities in a d-wave superconductor, in the unitary limit of very strong scatering centers. For frequencies very small as compared to the superconducting gap ($\omega \ll {\mathrm{\Delta }}_0$) the additional density of states has the leading divergence ${\displaystyle \delta \rho (\omega) \simeq n_i / [ | 2 \omega | (\ln^2 |\omega/\Delta_0| + (\pi/2)^2)]}$. This result is non perturbative.