Imaginary part of the infrared conductivity of adx2−y2superconductor

We give results for the effect of Born and of resonant impurity scattering on the imaginary part of the infrared conductivity σ(Ω) of a ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$ superconductor. Inelastic scattering is included in our work through an electron-boson spectral density which also causes the pairing. We emphasize the product of Ω times the imaginary past of σ(Ω). Its zero frequency limit gives the penetration depth, while around twice the gap value it shows smooth behavior as is observed in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.95}$, which has ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$ symmetry. This is in sharp contrast to the case of an s-wave superconductor which would display a sharp characteristic dip at this energy as seen in BaKBiO. © 1996 The American Physical Society.