Unified First-Principles Formula for Time-Resolved ARPES Spectra of Coherent and Incoherent Excitons

Abstract

Despite major experimental progresses in time-resolved and angle-resolved photoemission spectroscopy, a quantitative, microscopic framework for interpreting exciton-induced modifications of electronic band structures -- applicable even beyond the low-density limit -- is still lacking. Here we close this gap by introducing a unified approach that links the dynamics of coherent and incoherent excitons to distinct and experimentally observable excitonic sidebands. Our central result is a general, first-principles formula for time-resolved photoemission spectra, applicable across a broad range of temperatures, excitation densities, and pump-probe delays. This advance provides a predictive tool for quantitatively tracking excitonic dynamics in complex materials.

Figures (3)

• Figure 1: TX self-energy for the Green's function in the incoherent regime. We represent Green's functions $G$ with solid lines, bare interactions $v$ with wiggly lines, screened interactions $W$ with wiggly lines and the xc function $L$ with a gray circle.
• Figure 2: (a) First Brillouin zone and location of a few high symmetry points. (b) Exciton band structure of the equilibrium WSe$_{2}$ ML along the red path illustrated in panel (a) -- curves are colored according to the thermal occupation of excitons at temperature $T=70$ K and excitation density $n_{c}=10^{13}$ cm$^{-2}$. (c,f) Illustration of conduction band and replica of valence band at low [panel (c)] and moderate [panel (f)] excitation densities. (d,e,g,h) TR-ARPES spectrum (in arbitrary units) for low [panels (d,e)] and high [panels (g,h)] excitation densities at different temperatures: $n_{c}=10^{11}$ cm$^{-2}$ and $T=0$ K [panel (d)]; $n_{c}=10^{11}$ cm$^{-2}$ and $T=70$ K [panel (e)]; $n_{c}=4\times 10^{12}$ cm$^{-2}$ and $T=0$ K [panel (g)]; $n_{c}=10^{13}$ cm$^{-2}$ and $T=70$ K [panel (h)].
• Figure 3: Equilibrium and nonequilibrium [excitation density $n\simeq 10^{13}$ cm$^{-2}$] exciton dispersions (a) and quasiparticle energies (b). To highlight the band crossing between the conduction bands and the replica of the valence bands, dashed horizontal lines have been superimposed in correspondence of the energy of the lowest exciton with vanishing momentum.