Phonon-mediated relaxation in nanomaterials from combining Density Functional Theory based non-adiabatic molecular dynamics with Kadanoff-Baym-Keldysh technique

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 (KBK) 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 (NAMD) 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 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 for several 1.5-$nm$ semiconductor chalcogenide nanocrystals, such as $Cd_{37}Pb_{31}Se_{68},~Cd_{31}Pb_{37}Se_{68},$ which are Janus-type, and for $Pb_{68}Se_{68}.$