Role of quantum dipole fluctuations in the theory of excitons and of the dielectric constant of crystals

Abstract

A general expression for the frequency-dependent dielectric constant of a molecular-crystal model, which has been derived in a previous paper by the author, is analyzed in an improved two-state model for the individual atoms or molecules. This expression includes explicitly the effect of quantum dipole fluctuations and is used to perform a detailed study of their role in various other properties. First, we obtain a simple expression for the correction in the polarizability of an individual atom arising from these fluctuations. This result agrees roughly with dielectric-constant measurements for the rare-gas crystals. Secondly, we derive detailed expressions for the effect of the dipole fluctuations on the energies of the long-wavelength tight-binding exciton modes. In addition to the usual longitudinal and transverse single-exciton states, a new class of cooperative double excitons is found, and their oscillator strength is determined. The double-exciton modes result directly from the dipole-fluctuation mechanism. All the effects which are calculated corrections in the polarizability and in the exciton energies and oscillator strength of the transverse double excitation appear to be quadratic in the refractivity. Except for the correction in the polarizability, these fluctuation effects are all fairly large. For example, the oscillator strength of the transverse double-exciton mode ranges between 1 and 15% of that of the single-exciton mode in the case of the rare-gas solids. © 1969 The American Physical Society.