Two-fluid interpretation of the conductivity of clean BCS superconductors.

Abstract

The temperature and frequency dependence of the microwave and optical conductivity are studied for a BCS superconductor with weak elastic scattering [1/\ensuremath{\tau}2\ensuremath{\Delta}(0), where \ensuremath{\tau} is the scattering time and \ensuremath{\Delta}(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 \ensuremath{\delta} 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 \ensuremath{\omega}\ensuremath{\tau}, in the clean limit, with a characteristic logarithmic divergence at \ensuremath{\omega}=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{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystals.