Mechanisms for LT splitting of polarization waves: a link between electron-hole exchange interaction and depolarization shift

SCD (spin-singlet charge density) description of electron-hole exchange interaction is shown to provide a bridge among the various traditional ways of description of LT splitting of polarization modes, i.e., the interaction among the induced polarization charge, electron-hole exchange interaction (for excitons), and the interaction of matter polarization with depolarization field. The missing link was the description of polarization energy in terms of "induced charge density", which equally applies to excitons and phonons. Microscopic spatial variation of SCD contributes to (i) the spin singlet-triplet splitting and also (ii) the triplet splitting due to non-spherical symmetry in the case of excitons. Examples of formulation are given for the "LT" splitting of excitons in a quantum dot, and the spin-triplet splitting of excitons in alkali halides due to cubic anisotropy.