Structure of the dipole tensor and influence of the dipole-dipole interaction on dielectric properties and long-wavelength optical lattice vibrations in crystalline insulators and semiconductors

A new approach is proposed to the description of the influence of dipole forces on the spectrum of long-wavelength optical lattice vibrations in crystals having complex lattices. It is shown that subtraction of the dipole tensor for a crystal's Bravais lattice from the dipole tensor for a complex lattice leaves a residue which depends on the relative positions of the sublattices and, in the long-wavelength limit, is equivalent to a short-range interaction that falls off at least as fast as R −5 outside the limits of a primitive cell. In the case of the long-range part of the dipole-dipole interaction, therefore, it is possible to reduce the problem to that (solved earlier by the present author) of crystals having a simple lattice and to obtain an explicit expression for the contribution of the long-range dipole forces to the dispersion frequencies of polar optical lattice vibrations that contain only the experimentally determinable quantities [tensors E∞ and dipole oscillator strengths f(a) for the a model] and a matrix of dipole structure constants for the Bravais lattice of the investigated crystal