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

Abstract

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 ($ω\ll Δ_0$) the additional density of states has the leading divergence ${\displaystyle δρ(ω) \simeq n_i / [ | 2 ω| (\ln^2 |ω/Δ_0| + (π/2)^2)]}$. This result is non perturbative.

30 pages, 8 figures