From carriers and virtual excitons to exciton populations: Insights into time-resolved ARPES spectra from an exactly solvable model

We calculate the exact time-resolved ARPES spectrum of a two-band model semiconductor driven out of equilibrium by resonant and nonresonant laser pulses, highlighting the effects of phonon-induced decoherence and relaxation. Resonant excitations initially yield a replica of the valence band shifted upward by the energy of the exciton peak in photoabsorption. This phase is eventually destroyed by phonon-induced decoherence: The valence-band replica lowers in energy by the Stokes shift, locating at the energy of the exciton peak in photoluminescence, and its width grows due to phonon dressing. Nonresonant excitations initially yield a map of the conduction band. Then electrons transfer their excess energy to the lattice and bind with the holes left behind to form excitons. In this relaxed regime a replica of the conduction band appears inside the gap. At fixed momentum the lineshape of the conduction-band replica versus the photoelectron energy is proportional to the exciton wave function in ``energy space'' and it is highly asymmetric. Although the two-band model represents an oversimplified description of real materials, the highlighted features are qualitative in nature; hence they provide useful insights into time-resolved ARPES spectra and their physical interpretation.