Ab initio real-time quantum dynamics of charge carriers in momentum space

Application of the nonadiabatic molecular dynamics (NAMD) approach is severely limited to studying carrier dynamics in the momentum space, since a supercell is required to sample the phonon excitation and electron-phonon (e-ph) interaction at different momenta in a molecular dynamics simulation. Here, we develop an ab initio approach for the real-time quantum dynamics for charge carriers in the momentum space (NAMD_k) by directly introducing the e-ph coupling into the Hamiltonian based on the harmonic approximation. The NAMD_k approach maintains the quantum zero-point energy and proper phonon dispersion, and includes memory effects of phonon excitation. The application of NAMD_k to the hot carrier dynamics in graphene reveals the phonon-specific relaxation mechanism. An energy threshold of 0.2eV, defined by two optical phonon modes strongly coupled to the electrons, separates the hot electron relaxation into fast and slow regions with the lifetimes of pico- and nano-seconds, respectively. The NAMD_k approach provides a powerful tool to understand real-time carrier dynamics in the momentum space for different materials.