Non-local dielectric screening and electric fields associated with optical vibrations in superlattices

Abstract

We develop a simple and straightforward technique for extracting information about the electrostatic fields created by optical phonons in superstructures directly from microscopic three-dimensional lattice dynamics calculations. Local fields with a mesoscopic scale of variation associated with long-wavelength phonons in superlattices are derived using an 11-parameter rigid-ion force-field model. The classification of local fields, their connection to and distinctions from those obtained from the conventional dielectric continuum approaches is discussed. We also develop an alternative approach based on spatially dependent non-local microscopic dielectric screening in semiconducting superstructures. The analytical properties of long-wavelength phonon frequencies and associated electric fields find an explanation in terms of an eigenvalue problem for the non-local frequency-dependent microscopic dielectric matrix. Rigorous expressions for eigenfields and eigenpotentials are derived in the exactly solvable model of the dispersionless continuum. A simple and practical approximation with a short-range (elastic) dispersion included shows an excellent agreement with lattice dynamical calculations for .