Effects of extended impurity perturbation in d-wave superconductor

We describe the effects of electronic perturbation distributed on nearest neighbor sites to the impurity center in a planar $\mathit{\text{d}}$-wave superconductor, in approximation of circular Fermi surface. Alike the behavior previously reported for point-like perturbation and square Fermi surface, the quasiparticle density of states $\rho (ϵ)$ can display a resonance inside the gap (and very weak features from low symmetry representations of non-local perturbation) and asymptotically vanishes at $ϵ\to 0$ as $\rho \sim ϵ\mathrm{/}{\ln }^2ϵ$. The local suppression of SC order parameter in this model is found to be somewhat weaker than for an equivalent point-like (non-magnetic) perturbation and much weaker than for a spin-dependent (extended) perturbation.