Effect of Anisotropic Impurity Scattering in D-Wave Superconductors

In dx2-y2-wave superconductors,the effect of s-wave point disorder has been extensively studied in literature.We study the anisotropic disorder in the form of Vkk’imp=Vifkfk’ with fk=cos(2θ)(θ the azimuthal angle of k),as proposed to be caused by apical oxygen vacancies in overdoped La-based cuprate films,under the Born approximation.The disorder self-energy and d-wave pairing affect each other and must be solved simultaneously self-consistently.We find that the self-energy is reduced at low frequencies and thus weakens the pair-breaking effect.This frequency dependence vanishes in the dirty limit for which the disorder is well described by a scattering rate Γk=Γifk2.One consequence of the disorder effect is that the gap-to-Tcratio 2Δ(0)/Tcis greatly enhanced by the d-wave disorder,much larger than the s-wave disorder and the clean BCS value 4.28.Lastly,we generalize the d-wave scattering rate to a general form Γθ=Γα|θ-θ0|αaround each nodal direction θ0.We find the density of states ρ(ω)-ρ(0)∝|ω|(ω2) for all α≥1 (α<1) in the limit of ω→0.As a result,the superfluid density ρsexhibits two and only two possible scaling behaviors:ρs(0)-ρs(T)∝T (T2) for α≥1 (α<1) in the low temperature limit.