We develop a simple theory of the electromagnetic response of a d-wave superconductor in the presence of potential scatterers of arbitrary s-wave scattering strength and inelastic scattering by antiferromagnetic spin fluctuations. In the clean London limit, the conductivity of such a system may be expressed in ‘‘Drude’’ form, in terms of a frequency-averaged relaxation time. We compare predictions of the theory with recent data on Y-Ba-Cu-O and Bi-Sr-Si-Cu-O crystals and on Y-Ba-Cu-O films. While fits to penetration-depth measurements are promising, the low-temperature behavior of the measured microwave conductivity appears to be in disagreement with our results. We discuss implications for d-wave-pairing scenarios in the cuprate superconductors.

• Received 2 March 1994

DOI:https://doi.org/10.1103/PhysRevB.50.10250