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

TL;DR

This paper provides an exact theoretical analysis of time-resolved ARPES spectra in a two-band semiconductor model, revealing how exciton formation and phonon interactions influence spectral features during out-of-equilibrium dynamics.

Contribution

It introduces an exactly solvable model to interpret time-resolved ARPES spectra, emphasizing phonon effects and exciton dynamics, which are often approximated in prior studies.

Findings

Resonant excitations produce a valence band replica shifted by the exciton energy.

Phonon interactions cause decoherence, shifting and broadening spectral features.

Nonresonant excitations lead to a conduction band replica within the gap, reflecting exciton formation.

Abstract

We calculate the {\em 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. {\em Resonant} excitations initially yield a replica of the {\em 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. {\em 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 {\em 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 wavefunction 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.