Infrared conductivity in superconductors with a finite mean free path

Abstract

We discuss the form of the infrared conductivity and reflectivity in strong-coupling superconductors with a finite mean free path. We restrict attention to the local limit, in which the London penetration depth is much larger than the coherence length. We further assume that the fluctuations responsible for electronic pairing may be treated within a conventional Eliashberg approximation. The conductivity typically exhibits two onsets: one at 2${\mathrm{\Delta }}_0$ and another at 2${\mathrm{\Delta }}_0$+${\mathrm{\omega }}_0$, with ${\mathrm{\omega }}_0$ a typical fluctuation energy. The strength of the latter onset relative to the one at 2${\mathrm{\Delta }}_0$ increases as the ratio of the mean free path to the coherence length increases, and in an extremely clean system (2${\mathrm{\Delta }}_0$≫${\mathrm{\tau }}^{\mathrm{-}1}$) becomes the dominant feature in both the conductivity and reflectivity.