Observation of the Holstein shift in high $T_c$ superconductors with thermal modulation reflectometry

Abstract

We use the experimental technique of thermal modulation reflectometry to study the relatively small temperature dependence of the optical conductivity of superconductors. Due to a large cancellation of systematic errors, this technique is shown to a be very sensitive probe of small changes in reflectivity. We analyze thermal modulation reflection spectra of single crystals and epitaxially grown thin films of YBa$_2$Cu$_3$O$_{7-\delta}$ and obtain the ${\alpha_tr}^2F(\omega)$ function in the normal state, as well as the superconductivity induced changes in reflectivity. We present detailed model calculations, based on the Eliashberg-Migdal extension of the BCS model, which show good qualitative and quantitative agreement with the experimental spectra. VSGD.93.12.th