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

TL;DR

The paper tackles how to access the momentum-space structure of excitons in periodic 2D materials through time-resolved photoemission by developing exciton photoemission orbital tomography (exPOT). It derives a first-principles framework from GW+BSE exciton theory, incorporating plane-wave photoelectron final states and pump-induced superpositions, and provides explicit expressions for exciton- and pump-driven photoemission intensities in terms of Dyson orbitals. The method is demonstrated on monolayer hBN, showing that photoemission maps reflect the hole-dominated energy dispersion while the electron part is encoded in the conduction-band Fourier components, with BSE eigenvectors and pump polarization shaping the patterns and enabling momentum-dark exciton analysis. This exPOT framework offers a predictive tool to interpret and design trARPES experiments in quantum materials, bridging ab initio many-body theory with momentum-resolved spectroscopy.

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 light-matter interaction via the probe pulse. The correlated nature of electrons and holes introduces distinct consequences for excitonic photoemission. Using the prototypical two-dimensional material hexagonal boron nitride, we demonstrate these effects, including a dependence of the photoemission angular distribution on the pump pulse polarization. Moreover, 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.

Figures (6)

• Figure 1: (a) Atomic structure of hBN. Boron and nitrogen atoms are depicted in red and blue, respectively. The vectors $\mathbf{a_1}$ and $\mathbf{a_2}$ span the primitive unit cell, which contains one atom of each kind. (b) $G_0W_0$ band structure of hBN. Quasiparticle energies are shown along the $\Gamma - K - M - \Gamma$ high symmetry path. The calculated band structure exhibits an indirect band-gap, with the valence-band maximum and conduction-band minimum being located at $K$ (and $K'$) and $\Gamma$, respectively.
• Figure 2: Optical excitation of monolayer hBN. (a) Independent-particle spectrum, based on a $G_0W_0$ calculation in dark blue and the BSE spectrum in pink. In the latter, $S_1$ and $S_2$ energies are marked by arrows. Panels (b) and (c) show the $G_0W_0$ band structure with overlays indicating the BSE eigenvector composition of the $S_1$ (blue) and $S_2$ (green) excitations of the system, respectively.
• Figure 3: ARPES bandmap for the $S_1$ exciton in $k_x$ direction (cut of the BZ along $\Gamma-K'-M_2$, see inset with three neighboring BZs). The $G_0W_0$ bandstructure is overlaid in full blue lines, with a duplicate of the valence band, shifted by $\Omega$, as a blue dashed line.
• Figure 4: Momentum maps for three different cases: (a) valence band at $E_b=E_{\mathrm{VBM}}-0.2$ eV ($E_{\mathrm{kin}}=18.6$ eV), (b) conduction band at $E_b=E_{\mathrm{CBM}}+0.6$ eV ($E_{\mathrm{kin}}=26.6$ eV), and (c) $S_1$ exciton at $E_b=E_{\mathrm{VBM}}+\Omega-0.2$ eV ($E_{\mathrm{kin}}=23.9$ eV).
• Figure 5: Decomposition of exciton ARPES maps for $S_1$ in row (a) and $S_2$ in row (b), with black arrows indicating the polarization of the pump laser. First column: Fourier-transformed conduction-band wave functions. Second column: energy-conservation delta-function. Third column: BSE eigenvectors. Fourth column: resulting exciton ARPES maps as products of first to third columns. Each map is individually normalized to one. For $S_1$ in row (a), the horseshoes point away from $\Gamma$, with minor modulations along their contours. For $S_2$ in row (b), four of the six horseshoes are rotated, when compared to the first exciton. This is a direct result of the differences in the momentum-space distribution of their BSE eigenvectors.