Two-fluid interpretation of the conductivity of clean BCS superconductors

The temperature and frequency dependence of the microwave and optical conductivity are studied for a BCS superconductor with weak elastic scattering [1/{τ}2{Δ}(0), where {τ} is the scattering time and {Δ}(T) is the BCS energy gap]. The results are interpreted in terms of a two-fluid model in which the combined oscillator strength of the {δ} function at the origin and the thermally excited free-carrier conductivity is found to be only weakly temperature dependent. The low-frequency conductivity is shown to be a function of {ω}{τ}, in the clean limit, with a characteristic logarithmic divergence at {ω}=0. The frequency dependence of the microwave surface resistance is discussed and comparison is made to the recent experimental results of Bonn, Hardy, and co-workers on YBa₂{Cu}₃O_7-δ single crystals.