Ultrafast Excited State Dynamics of Coupled Carriers and Phonons from Ab Initio Calculations

The out-of-equilibrium dynamics and equilibration processes of excited states in materials are crucial to understanding time-resolved spectroscopies. Several ultrafast phenomena occurring on a sub-picosecond time scale are governed by the coupled dynamics of electrons and atomic vibrations (phonons), including transient structural distortions and excited electron thermalization due to the competing electron-phonon (e-ph) and phonon-phonon (ph-ph) interactions. Here, we show ab initio calculations of the coupled ultrafast dynamics of carriers and phonons. We develop an efficient algorithm to time-step the coupled electron and phonon Boltzmann transport equations, which include both the e-ph and ph-ph scattering on the same footing. Our approach allows us to study the time evolution of the excited electron populations as well as the out-of-equilibrium phonons together with the transient structural distortions they induce. We apply our method to silicon and graphene, and compare the results with time-resolved spectroscopies probing both the structural and the electron dynamics, such as free-electron laser and time-resolved electron diffraction experiments.