Electron–Phonon Interaction and Optical Spectra of Metals

Abstract

Observed optical reflectivity in the infrared spectral region is compared with theoretical predictions in a strongly coupled electron–phonon system. Starting from a Fröhlich Hamiltonian, the spectral functions and their temperature dependence are derived. A full analysis including vertex corrections leads to an expression for the optical conductivity σ(ω) that 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, shows little difference over a wide range of coupling constants. Normal-state optical spectra for the high-T _c superconductors YBa₂Cu₃O₇ and La_{2 − x} Sr _x CuO₄ at optimal doping are compared with the results of model calculations. Taking the plasma frequency and ∈_∞ from band structure calculations, the model has only one free parameter, the electron–phonon coupling constant λ. In both materials the overall behavior 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.