Dielectric Screening and the Phonon Spectra of Metallic and Nonmetallic Crystals

Abstract

A quantum theory of the phonon excitation spectrum of a general crystal in the harmonic approximation is presented. Many-body perturbation theory is used to (i) generalize a result obtained by Baym relating the dielectric and lattice dynamical properties of a monoatomic metal to a general crystal, and (ii) show that Phillips's recent doubts regarding the applicability of linear screening theory to covalent crystals can be allayed. It is shown that a correct, "dressed" inverse screening tensor can be defined so as to make the linear-screening approach rigorous in the harmonic approximation and for wavelengths short enough so that relativisitic effects are not important. An identity is also derived which allows the elimination of divergent self-interaction terms and provides an explicit demonstration that the acoustic-mode frequencies vanish in the long-wavelength limit.