Effect of Anisotropic Impurity Scattering in D-Wave Superconductors

In d x 2 – y -wave superconductors, the effect of s-wave point disorder has been extensively studied in literature. We study anisotropic form V k ′ imp = mathvariant="normal">i f with f k = cos(2 θ ) ( azimuthal angle ), as proposed to be caused by apical oxygen vacancies overdoped La-based cuprate films, under Born approximation. The self-energy and d-wave pairing affect each other must solved simultaneously self-consistently. find that is reduced at low frequencies thus weakens pair-breaking effect. This frequency dependence vanishes dirty limit for which well described a scattering rate ${\varGamma }_{k}={\varGamma }_{{\rm{i}}}{f}_{k}^{2}$?> Γ 2 . One consequence gap-to- T c ratio Δ (0)/ greatly enhanced disorder, much larger than clean BCS value 4.28. Lastly, we generalize general }_{\theta }={\varGamma }_{\alpha }|\theta -{\theta }_{0}{|}^{\alpha }$?> θ α | − 0 around nodal direction 0 density states ρ ω )– (0)∝| | all α ≥ 1 < 1) → 0. As result, superfluid s exhibits two only possible scaling behaviors: (0)– )∝ temperature limit.