Collective mode and peak splitting in phonon sidebands from interaction of degenerate exciton states with longitudinal optical phonons

By solving the Schrodinger equation for degenerate exciton states identically interacting with LO phonons we are able to analytically show that the composite states can be grouped into collective and individual sets with two different energies. The optical transition for the individual set is prohibited but this prohibition can be partially removed by spreading of off-diagonal exciton-phonon coupling in a system with many exciton states. As a result, every satellite peak in the phonon sidebands of photoluminescence is split into a two-peak structure corresponding to these two sets. The model can be associated with excitons bound to deep donor centers in wide-gap semiconductors and provides a natural explanation for the peak splitting observed in the phonon sidebands of these materials.