Probing excitons with time-resolved momentum microscopy

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. 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 capabilities of time- and angle resolved photoemission spectroscopy. Here, we review how the 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 wavefunction. Focusing on two-dimensional materials and organic semiconductors, we first discuss the typical photoemission fingerprint of excitons in momentum microscopy and highlight that it is possible to obtain information not only on the electron- but also hole-component. 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. 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 momentum microscopy for the study of optical excitations in semiconductors.