Simulation of time-resolved electron-phonon scattering on a Dirac cone

Ultrafast spectroscopy is a powerful tool for studying the dynamical properties of quantum materials driven out of equilibrium. The relaxation dynamics of the non-equilibrium state can provide insights into the properties of the elementary scattering process and many-body interactions present in equilibrium. Using the Keldysh formalism we simulate time- and angle-resolved photoemission spectroscopy on a Dirac cone to capture the quantized relaxation processes of electrons coupled to optical phonons. Including retarded electron-phonon interactions, the simulation naturally captures the appearance of a direct excitation peak at an energy set by the frequency of the pump pulse and the delayed appearance of a secondary non-thermal peak above the Fermi level due to electron-phonon scattering as observed in an experiment performed on graphite.