Phonon-mediated relaxation in nanomaterials using Boltzmann transport equation by combining density functional theory based non-adiabatic molecular dynamics with many-body perturbation theory

Boltzmann transport equation (BE) is a potent approach to dynamics of a photoexcited (nano)material. BE collision integrals for different relaxation channels can be systematically computed using the Kadanoff-Baym-Keldysh formalism (also called NEGF) utilizing the density functional theory (DFT) simulation output. However, accurate description of phonon-mediated relaxation in a general class of (nano)materials that includes exciton effects is still an outstanding problem. The approach proposed here is based on the observation that the non-adiabatic couplings of the DFT-based non-adiabatic molecular dynamics play the role of a time-dependent external potential coupled to the electrons. This allows application of the Keldysh approach resulting in the exciton-phonon BE collision integral, which incorporates exciton wave functions and energies obtained from the Bethe-Salpeter equation. As an application, we augment BE with radiative recombination and photon-mediated exciton-exciton transition terms and then use it to calculate photoluminescence spectrum for several 1.5 nm semiconductor chalcogenide nanocrystals, such as Cd37Pb31Se68, Cd31Pb37Se68, which are Janus-type, and for Pb68Se68.