Exciton Photoemission Tomography Reveals Correlated Electron-Hole Wave Functions in 2D Systems

Excitons, quasiparticles formed from bound electron-hole pairs, represent a fundamental element in understanding the optical and electronic properties of materials, and scientists are now able to directly observe their momentum-space characteristics. Siegfried Kaidisch, Amir Kleiner, Sivan Refaely-Abramson, and colleagues develop a new computational framework, exciton photoemission orbital tomography (exPOT), which simulates and interprets experimental observations of these particles within complex materials. This method connects established theoretical approaches with photoemission tomography, allowing researchers to accurately model how excitons behave when probed with light, and crucially, captures the effects of electron-hole interactions. Demonstrating the power of their approach with hexagonal boron nitride, the team reveals how exciton behaviour depends on the polarization of the light used to observe it, and provides a means to study even those excitons that are normally invisible to conventional techniques, offering valuable new insights into these fundamental particles.

DFT and GW Calculations for 2D Materials

Researchers extensively utilize density functional theory (DFT) and many-body perturbation theory (GW) to investigate the electronic structure, optical properties, and quasiparticle energies of two-dimensional materials like graphene and transition metal dichalcogenides. Accurate descriptions of electron behavior require careful consideration of basis sets and pseudopotentials, methods for representing the complex interactions within materials. Studies explore the behavior of stacked 2D materials, known as heterostructures, and how defects and doping influence their properties, as well as how external stimuli like strain and electric fields can tune material characteristics. Investigations cover a wide range of materials, including graphene, transition metal dichalcogenides (like MoS2 and WS2), and hexagonal boron nitride. Researchers continually refine computational methods, focusing on improving the convergence of GW calculations, developing more efficient algorithms, and utilizing real-space methods for calculating dielectric functions. These studies demonstrate that accurate calculations of 2D material properties require going beyond standard DFT and incorporating many-body perturbation theory, addressing the unique challenges and opportunities presented by the reduced dimensionality and strong excitonic effects in these materials.

Exciton Photoemission Tomography via Many-Body Perturbation Theory

Scientists developed a novel computational framework, exciton photoemission orbital tomography (exPOT), to simulate and interpret time-resolved photoelectron spectroscopy experiments on periodic systems. This method overcomes limitations of previous approaches by explicitly incorporating the effects of the probe pulse on photoemission matrix elements and capturing the correlated behavior of electrons and holes within many-body perturbation theory. By connecting the Bethe-Salpeter Equation (BSE) approach to photoemission tomography, researchers enable detailed analysis of exciton photoemission in crystalline solids and two-dimensional semiconductors. Researchers implemented exPOT in frequency space, utilizing exciton wave functions obtained from GW+BSE calculations.

The photoemission signal is expressed using Fourier-transformed single-particle Bloch functions, weighted by BSE eigenvectors to reflect the entangled many-body character of electron-hole correlations. Crucially, the method extends to excitons with finite center-of-mass momentum, enabling the study of optically dark excitons, which are prevalent in transition metal dichalcogenides and other layered materials, bridging the gap between theoretical many-body wave functions and experimental momentum-resolved spectra. To demonstrate the method, researchers applied exPOT to monolayer hexagonal boron nitride, revealing that photoelectron angular distributions depend on both the exciton character and the pump pulse polarization. This work establishes a powerful new tool for understanding exciton phenomena and interpreting experimental results from advanced spectroscopic techniques.

Exciton Photoemission Mapped by Orbital Tomography

Scientists developed a theoretical framework, exciton photoemission orbital tomography (exPOT), for understanding how excitons, bound electron-hole pairs, emit photoelectrons in materials. The core achievement lies in connecting the Bethe-Salpeter Equation, a sophisticated approach for describing correlated electron-hole interactions, with photoemission tomography, a technique for mapping electronic structure. The team demonstrated that the correlated nature of electrons and holes significantly influences exciton photoemission, revealing a dependence on the polarization of the pump pulse used to excite the material. Using hexagonal boron nitride as a model system, researchers showed that the framework extends to excitons with finite center-of-mass momentum, enabling the study of “momentum-dark” excitons.

This is accomplished by formulating the photoemission process within many-body perturbation theory, allowing for a detailed description of the electronic structure and the resulting photoelectron spectra. Measurements confirm that the calculated photoelectron angular distributions depend not only on the intrinsic character of the exciton but also on the polarization of the pump pulse, providing a richer understanding of exciton behavior. The method utilizes a Dyson orbital-like construction for Bloch functions, effectively reducing the complex many-electron problem to an effective one-electron description, providing valuable insights into the microscopic nature of excitonic phenomena and opening new avenues for exploring the properties of materials with complex electronic structures.

Exciton Photoemission Mapping via Tomography

Scientists developed a computational framework, exciton photoemission orbital tomography (exPOT), for simulating and interpreting experimental observations of excitons in periodic systems. By connecting the Bethe-Salpeter Equation approach to photoemission tomography, researchers have developed a method that accurately captures exciton photoemission, explicitly accounting for the effects of the probe pulse on photoemission matrix elements. The framework demonstrates that the correlated nature of electrons and holes significantly influences excitonic photoemission, introducing a dependence on the polarization of the pump pulse used to excite the system. Researchers successfully applied this framework to hexagonal boron nitride, demonstrating its ability to model excitons with finite center-of-mass momentum, including those that are typically difficult to observe, known as momentum-dark excitons. Furthermore, the study details how the initial state of the exciton impacts the observed photoemission intensity, revealing the importance of considering the superposition of exciton states when interpreting experimental results.