BCS theory predicts that coherence peaks should occur in both the nuclear-magnetic-resonance (NMR) relaxation rate and the electromagnetic absorption rate as the temperature is lowered below ${\mathit{T}}_{\mathit{c}}$. The former peak has not been observed in the high-${\mathit{T}}_{\mathit{c}}$ oxides while the latter has. We present detailed calculations using BCS theory and its dynamic extension, Eliashberg theory, for the ac conductivity in a superconductor, for arbitrary impurity content. The peak in the conductivity, and hence in the electromagnetic absorption rate, is reduced by damping effects just as in the case of NMR. Furthermore, in the clean limit, no peak is predicted to be present. The observation of a coherence peak in the high-${\mathit{T}}_{\mathit{c}}$ oxides thus places important restrictions on the parameters of any BCS-like theory.

• Received 31 May 1991

DOI:https://doi.org/10.1103/PhysRevB.44.5373