Electron-phonon interaction and optical spectra of metals

Observed optical reflectivity in the infrared spectral region is compared with theoretical predictions in a strongly coupled electron-phonon system. Starting from a Froehlich Hamiltonian, the spectral functions and their temperature dependence are derived. A full analysis including vertex corrections leads to an expression for the optical conductivity \sigma(\omega) which can be formulated in terms of the well known optical conductivity for a quasi-isotropic system without vertex corrections. A numerical comparison between the full result and the so-called ``extended'' Drude formula, its weak coupling expansion, show little difference over a wide range of coupling constants. Normal state optical spectra for the high-T_c superconductors YBa_2Cu_3O_7 and La_{2-x}Sr_{x}CuO_4 at optimal doping are compared with the results of model calculations. Taking the plasma frequency and \epsilon_\infty from band structure calculations, the model has only one free parameter, the electron-phonon coupling constant \lambda. In both materials the overall behaviour of the reflectivity can be well accounted for over a wide frequency range. Systematic differences exist only in the mid-infrared region. They become more pronounced with increasing frequency, which indicates that a detailed model for the optical response should include temperature dependent mid-infrared bands.