Electron-phonon interaction in polar solids with application to the tungsten bronzes

We investigate the interaction between electrons and lattice vibrations in polar solids taking into account their microscopic dielectric properties and constructing in a semi-phenomenological manner the nonlocal dielectric function, ?_GG'(q). The results of earlier, phenomenological theories, such as the Clausius-Mossotti formula for the macroscopic screening constant and Fröhlich's electron-phonon coupling parameter α are obtained from the RPA dielectric function when the dipole approximation is used to calculate the screening by the strongly localized valence electrons. For polar metals we also consider the screening by the free conduction electrons. We present and discuss the results of the screened electron-phonon interaction as a function of the phonon wavevector q for the sodium tungsten bronzes.