Effect of Anisotropic Impurity Scattering in D-Wave Superconductors

Abstract

In d x 2–y 2 -wave superconductors, the effect of s-wave point disorder has been extensively studied in literature. We study the anisotropic disorder in the form of V k k ′ imp = V i f k f k ′ 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 Γ k = Γ i f k 2 . One consequence of the disorder effect is that the gap-to-T c ratio 2Δ(0)/T c is 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 Γ θ = Γ α | θ − θ 0 | α around each nodal direction θ 0. We find the density of states ρ(ω)–ρ(0)∝|ω| (ω 2) for all α ≥ 1 (α < 1) in the limit of ω → 0. As a result, the superfluid density ρ s exhibits two and only two possible scaling behaviors: ρ s(0)–ρ s(T)∝ T (T 2) for α ≥ 1 (α < 1) in the low temperature limit.