Dielectric theory of elementary excitations in crystals

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Abstract
The microscopic theory of dielectric response and its application to elementary excitations is discussed with particular emphasis on periodic solids for which the free-electron description is not valid. The discussion is based on a solution of Maxwell's equations which is achieved in a local wavefunction representation. Many-body effects are included within the self-consistent field approximation. The resulting dielectric-response function presents a practical scheme for a microscopic calculation of elementary excitations and their interaction in conducting as well as non-conducting crystals. As an example, the linear response of crystal electrons to a perturbing photon field is studied in detail. Results of a calculation of the optical absorption in diamond establish the importance of including both local-field and continuum excition effects. These effects are important for the identification of structures in the experimental optical spectrum with electronic inter-band transitions, and quite generally for calculating dielectric response in covalent crystals. Other examples deal with phonons and the electron-phonon interaction in transition metals and their compounds. Various results of the theory such as phonon renormalization due to local-field and exchange-correlation effects are discussed and compared with experiment. A microscopic explanation for phonon softening and its interrelation with high-T c superconductivity is given in terms of incipient lattice instabilities which are driven by dielectric response.