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.