Influence of Electronic Polarization on the Optical Properties of Insulators

The Toyozawa theory of the electronic polaron and the related Haken-Schottky theory of the optical dielectric function are applied to the alkali and silver halides and to the rare-gas solids. It is found that for most of these crystals the above dynamical theories reduce to a static limit. This in turn indicates that calculations of polarization effects based on the classical approach of Mott and Littleton will be valid. Such calculations are carried out in this paper. It is found that the self-energies due to the interaction of "bare" electrons or holes with the polarization field may be as large as several eV. Furthermore, because of the "inertialess" nature of electronic polarization, these self-energies and other polarization effects must be taken into account in the calculation of states which may be excited optically. Thus, for example, the optical band gap of certain alkali or silver halides may be as much as 5 eV smaller than a "good" one-electron band-structure calculation would yield. The available experimental data on the values of optical band gaps are critically reviewed and comparisons are made with the results of band-structure calculations. The computed $r$ dependence of the optical dielectric function indicates that for small-radius excitations (e.g., $n=1\mathrm{}$ excitons in many substances) electronic polarization should not influence the excitation energy in an important way; the electron and hole are "bare" particles when in the same unit cell. This fact is consistent with the success of a number of calculations in which polarization has been neglected. It is shown how the polarization dependence of the binding energies of these excitations can arise from the self-energies of the conduction electron and the valence-band hole. The use of the effective-mass method for computing binding energies is briefly discussed.