Microscopic theory of dielectric screening and lattice dynamics. I. Local-field corrections and dielectric constants

Abstract

We show how local-field corrections in solids may be treated by a very general factorization scheme for $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}}^{\ensuremath{'}})$ from which practically all existing models of dielectric screening and lattice dynamics may be derived as special cases, including the shell model, the breathing-shell model, and the bond-charge model, as well as generalizations of these models which result from the introduction of a "screening medium." The latter arise naturally in our formalism from a portion of $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}},{\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}}^{\ensuremath{'}})$ which is purely diagonal. It is shown that the formalism also allows for charge-transfer and multipole effects. In this first paper we derive explicit expressions for the elements of $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}},\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}+{\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}}^{\ensuremath{'}})$ and its inverse and show that they have the correct analytic behavior as $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}\ensuremath{\rightarrow}0$. For insulators of cubic and tetrahedral symmetry, explicit microscopic expressions are derived for the high-frequency dielectric constant ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ thus realizing a generalization of the Lorentz-Lorenz formula, and for the local field produced by an applied field.