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 int eraction is shown to provide a bridge among the various traditional ways of description of LT splitting of polarization modes, i.e., the interaction a mong the induced polarization charge, electron-hole exchange interaction (f or excitons), and the interaction of matter polarization with depolarizatio n field. The missing link was the description of polarization energy in ter ms of "induced charge density", which equally applies to excitons and phono ns. Microscopic spatial variation of SCD contributes to (i) the spin single t-triplet splitting and also (ii) the triplet splitting due to non-spherica l symmetry in the case of excitons. Examples of formulation are given for t he "LT" splitting of excitons in a quantum dot, and the spin-triplet splitt ing of excitons in alkali halides due to cubic anisotropy.