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 from the quasi-classical limit of Kadanoff-Baym-Keldysh formalism (also called NEGF) of many-body perturbation theory (MBPT) utilizing the Density Functional Theory (DFT) simulation output. Here we present an approach to phonon-mediated relaxation in a nanomaterials that includes exciton effects, and does not rely on perturbation theory in coupling of electrons to individual phonon modes and harmonic approximation. The method is based on the observation that the nonadiabatic couplings of the DFT-based non-adiabatic molecular dynamics (NAMD) play the role of a time-dependent external potential coupled to the electrons. This allows application of the Keldysh approach of MBPT resulting in the exciton-phonon BE collision integral, which incorporates exciton wave functions and energies obtained from 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 (PL) spectrum. Also, we include carrier multiplication and exciton transfer terms into BE from exisitng methods to compute internal quantum efficiency. We present results for several 1.5-nm semiconductor chalcogenide nanocrystals, such as Cd₃₇Pb₃₁Se₆₈, Cd₃₁Pb₃₇Se₆₈, which are Janus-type, and for Pb₆₈Se₆₈.