Probing excitons with time-resolved momentum microscopy

TL;DR

This review surveys time-resolved momentum microscopy as a powerful approach to study excitons across two-dimensional and organic semiconductors. It outlines how fs momentum microscopy and trARPES access the energy and momentum of excitons, including bright and dark states, and how photoemission orbital tomography enables reconstruction of real-space exciton wavefunctions. The article presents experimental fingerprints for intralayer, interlayer, and hybrid excitons, as well as moiré-induced miniband effects, and discusses multi-orbital excitons with characteristic multi-peak photoemission spectra. Overall, the framework unifies energy-minto-momentum mapping with real-space imaging, enabling detailed insight into exciton energetics, spatial distribution, and their underlying orbital structure.

Abstract

Excitons -- two-particle correlated electron-hole pairs -- are the dominant low-energy optical excitation in the broad class of semiconductor materials, which range from classical silicon to perovskites, and from two-dimensional to organic materials. Recently, the study of excitons has been brought on a new level of detail by the application of photoemission momentum microscopy -- a technique that has dramatically extended the experimental capabilities of time- and angle-resolved photoemission spectroscopy (trARPES). Here, we review how the energy- and momentum-resolved photoelectron detection scheme enables direct access to the energy landscape of bright and dark excitons, and, more generally, to the momentum-coordinate of the exciton that is fundamental to its wavefunction. Focusing on two-dimensional materials and organic semiconductors as two tuneable platforms for exciton physics, we first discuss the typical photoemission fingerprint of excitons in momentum microscopy and highlight that is is possible to obtain information not only on the electron- but also hole-component of the former exciton. Second, we focus on the recent application of photoemission orbital tomography to such excitons, and discuss how this provides a unique access to the real-space properties of the exciton wavefunction. Throughout the review, we detail how studies performed on two-dimensional transition metal dichalcogenides and organic semiconductors lead to very similar conclusions, and, in this manner, highlight the strength of time-resolved momentum microscopy for the study of optical excitations in semiconductors.

Figures (11)

• Figure 1: Description of excitons and their detection in a time- and angle-resolved photoemission spectroscopy experiment. a Schematic illustration of the exciton formation, thermalization and detection process. A pump laser pulse (red) is used to excite optically bright excitons that reside in a single TMD layer. Interlayer charge-transfer can lead to the formation of interlayer excitons where the exciton's electron and hole reside in different layers. In the photoemission process, the Coulomb correlation between the electron and the hole is broken, the single-particle electron is detected with the photoelectron analyzer and the single-particle hole remains in the sample. b Schematic energy level diagram indicating the single-particle valence band maximum (or HOMO) and conduction band minimum (or LUMO) at binding energies $E_{\rm VBM}$ and $E_{\rm CBM}$ that are separated by the single-particle band gap energy E$_g$, respectively. In this picture, the binding energy $E_{\rm bin}$ of a two-particle excitons can be defined by comparing the exciton energy E$_{\rm exc}$ with the single-particle band gap E$_g$. c In the exciton picture (shown for $\boldsymbol{w}=0$), Coulomb correlated electron-hole pairs are described based on equation (\ref{['eq:excitonenergy']}) and have a parabolic dispersion with regard to their center-of-mass momentum $Q$. Within the light cone (orange area, vanishing $Q$), excitons are labeled to be optically bright because they can be excited by light and can decay in a radiative process. In contrast, excitons with a finite $Q$ are termed optically dark. d A related pictorial description of excitons can be drawn in the electron-hole picture. Here, in addition, momentum-indirect excitons are sketched where the electron- and the hole-component are separated by momentum $\boldsymbol{w}$ and reside in different valleys of the Brillouin zone. Panel a is reproduced from ref. bange24SciAdv under Creative Commons Attribution License 4.0 (CC BY). Panels c,d are adopted from ref. Werner23ma.
• Figure 2: Schematic illustration of the momentum microscopy setup and the accessible multi-dimensional photoemission data. a Momentum microscopes are a novel type of photoelectron analyzers that are assembled by a microscope type electronic lens system, a time-of-flight drift tube or a hemisphere-based energy filter, and a position sensitive photoelectron detector. By projecting either the Fourier or the real-space plane onto the detector, spectrally-resolved momentum maps (b) or real-space maps of the sample (c) can be collected. By inserting an aperture into the real-space plane, a region-of-interest with a diameter of approximately 10 $\mu$m can be selected on the sample. d If the momentum microscope is equipped with a time-of-flight detector, it is possible to simultaneously collect three-dimensional data sets that contain information on the kinetic energy $E$ and two in-plane momenta (k$_x$, k$_y$) of the photoelectrons. The 3-dimensional data representation shows the occupied bands of homobilayer MoS$_2$ and excitonic photoemission signal at a pump-probe delay of 140 fs. Panels a, b, and c are reproduced from ref. Schmitt22nat (Copyright by Springer Nature). The data in panel d was taken in the Göttingen photoemission laboratory.
• Figure 3: The photoemission signature from excitons is affected by the joint electron-hole nature of the compound quasiparticle. a For cold, $Q=0$ excitons in TMDs, it was found that the dispersion of the hole state is directly imprinted on the trARPES data. b For hot excitons including a wider range of momenta $Q$ (see insets), the trARPES signature is broadened and the hole-dispersion is no longer apparent. Figure reproduced from ref. Rustagi18prb. Copyright 2018 by the American Physical Society
• Figure 4: The multi-orbital nature of excitons can be identified in the photoemission spectroscopy experiment. Kern et al. (a) and Meneghini et al. (b) found that multi-orbital excitons lead to more complex trARPES fingerprints, with one peak for each unique final-state binding energy of the hole. Panel a is reproduced from ref. Kern23prb. Copyright 2023 by the American Physical Society. Panel b is reproduced with permission from ref. Meneghini23ACSPhotonics. Copyright 2023 American Chemical Society.
• Figure 5: Energy- and momentum-resolved photoemission spectra collected on exfoliated a monolayer WSe$_2$ and b monolayer WS$_2$. a Photoemission spectral weight originating from the breakup of excitons is detected at the K and the $\Sigma$ (Q) valley within the single-particle band gap. b Pump-probe delay dependent momentum-maps indicating the optical excitation of K excitons at the K valley and the subsequent formation of dark $\Sigma$ excitons at the $\Sigma$ valley. Panel a from ref. Madeo20sci. Reprinted with permission from AAAS. Panel b reprinted with permission from ref. Wallauer21nanolett. Copyright 2021 American Chemical Society.