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/τT) 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 ωτ, 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 ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ single crystals.