Mori approach to exciton memories in initially unrelaxed excitonphonon systems: direct and reorganized perturbation expansions

Abstract

Starting from the Mori formalism, memory functions of excitons coupled to harmonic phonons in periodic crystals with linear exciton-phonon coupling are calculated in two limiting cases: that of the narrow unrenormalized exciton band with only site local coupling and that of the weak exciton-phonon coupling. Mutual correspondence as well as that with results of analogous works is discussed. By a mathematical trick, perturbational series for memory kernel of initially unrelaxed excitons interacting locally with harmonic phonons is then reorganized. Using that, full agreement is achieved with previous results obtained by Generalized Master Equations for initially relaxed excitons in case of narrow exciton band width. For the weak exciton-phonon coupling case, appreciable reduction of damping of the quasicoherent channel may be achieved on account of polaron effects. Crucial role of the exciton bandwidth beyond the lowest order is found in both cases for the low-temperature exciton diffusivity. Some predictions on the temperature dependence of the phonon-scattering limited exciton diffusion constant are given