Photoemission tomography of excitons in 2D systems: momentum-space signatures of correlated electron-hole wave functions

Abstract: The momentum-space signatures of excitons can be experimentally accessed through time-resolved (pump-probe) photoelectron spectroscopy. In this work, we develop a computational framework for exciton photoemission orbital tomography (exPOT) in periodic systems, enabling the simulation and interpretation of experimental observables within many-body perturbation theory. By connecting the $GW$+Bethe-Salpeter Equation (BSE) approach to photoemission tomography, our formalism captures exciton photoemission in periodic systems, explicitly incorporating photoemission matrix element effects induced by the probe pulse. The correlated nature of electrons and holes introduces distinct consequences for excitonic photoemission, including a dependence on pump pulse polarization. Using the prototypical two-dimensional material hexagonal boron nitride, we demonstrate these effects and show how our framework extends to excitons with finite center-of-mass momentum, making it well-suited to studying momentum-dark excitons. This provides valuable insights into the microscopic nature of excitonic phenomena in quantum materials.