Density of states of a d-wave superconductor in the presence of strong impurity scatterers: A nonperturbative result

We present a method to compute the density of states induced by a finite density of nonmagnetic impurities in a d-wave superconductor, in the unitary limit of very strong scattering centers. For frequencies very small as compared to the superconducting gap $(\omega \ll {\Delta }_0)$ the additional density of states has the leading divergence $\delta \rho \left(\omega \right)\simeq n_i/(|2\omega |{\ln }^2|\omega /{\Delta }_0|).\mathrm{}$ This result is nonperturbative.