Researchers unlock exciton symmetries across the Brillouin zone using time-reversal and space-group analysis

Excitons, quasiparticles formed when an electron binds to a hole in a material, hold immense promise for next-generation optoelectronic devices, but understanding and predicting their behaviour requires navigating complex quantum mechanical calculations. Robin Bajaj, Namana Venkatareddy, and H. R. Krishnamurthy, along with Manish Jain, all from the Indian Institute of Science, present a new framework that leverages the fundamental principles of symmetry to dramatically simplify the analysis of these crucial particles. Their work demonstrates how time-reversal and spatial symmetries can predict exciton properties across a material’s entire structure, reducing the computational burden of complex calculations and offering a more transparent understanding of exciton behaviour. By classifying excitons according to their symmetry, the team provides a powerful tool for designing materials with tailored optical properties and accelerating the development of advanced technologies, and they validate their approach with calculations on the important material molybdenum disulphide.

of excitonic states, incorporating both time-reversal and space-group symmetries. The research demonstrates that these symmetries allow scientists to determine exciton eigenstates at any point within the Brillouin zone from calculations performed on only a portion of it, significantly reducing computational demands. This approach classifies excitons according to their symmetry properties throughout the Brillouin zone, providing a clear and organized understanding of exciton physics.

Ab Initio Exciton and Optical Properties Calculations

This work details a sophisticated computational workflow for studying how light interacts with materials, focusing on excitons, bound pairs of electrons and holes, and their influence on optical properties. The research primarily investigates 2D materials like molybdenum disulfide, tungsten disulfide, and hexagonal boron nitride. The study employs ab initio methods, meaning calculations based on fundamental physical laws without relying on experimental data. Key techniques include Density Functional Theory (DFT), which determines the electronic structure of the materials; the GW Approximation, which calculates quasiparticle energies more accurately than DFT; and the Bethe-Salpeter Equation (BSE), which calculates exciton binding energies and optical absorption spectra.

Researchers utilize software packages such as BerkeleyGW, Yambo, and VASP to perform these calculations, ensuring accuracy through the use of pseudopotentials, careful selection of exchange-correlation functionals, and appropriate sampling of the Brillouin zone. Techniques to account for periodic image interactions and non-uniform k-point sampling further refine the results. This comprehensive workflow accurately predicts the optical properties of materials, with a strong emphasis on understanding the role of excitons in 2D materials.

Symmetry Simplifies Exciton Calculations and Classification

Researchers have developed a symmetry-based framework for analyzing excitonic states, significantly advancing the understanding and computational efficiency of these crucial semiconductor properties. The team demonstrates that by incorporating both time-reversal and space-group symmetries, exciton eigenstates at any point within the Brillouin zone can be determined from calculations performed only on the irreducible portion of the zone, representing a substantial reduction in computational demand. This approach classifies excitons according to their symmetry properties across the Brillouin zone, providing a rigorous and organized picture of exciton physics. The method involves classifying excitonic eigenstates into irreducible representations and constructing symmetry-adapted linear combinations of electron-hole product states, which effectively block-diagonalize the Bethe-Salpeter Equation (BSE) Hamiltonian at both zero and finite exciton center-of-mass momenta.

This block-diagonalization reduces both the time and memory required for calculations, offering a significant computational advantage. Applying this formalism to monolayer MoS₂, researchers found excellent agreement between the predicted exciton classifications and those derived from group theory, validating the accuracy of the approach. Beyond this specific material, the framework provides a general and conceptually rigorous method for exciton symmetry classification, enabling substantial cost reductions for calculations involving spectra, exciton-phonon interactions, and excitonic band structure across a wide range of materials. This is particularly important for modeling complex phenomena like exciton-phonon scattering, indirect optical transitions, and exciton thermalization dynamics, which require detailed knowledge of excitonic states for a dense momentum grid. The ability to perform these calculations efficiently opens new avenues for designing and optimizing materials for advanced optoelectronic devices and exploring fundamental exciton physics.

Symmetry Simplifies Exciton Brillouin Zone Calculations

This research establishes a symmetry-based framework for understanding excitons, which are fundamental quasiparticles arising from the interaction of electrons and holes in materials. The team demonstrates a method for determining exciton properties across the entire Brillouin zone by leveraging symmetry operations applied to calculations performed within a smaller, irreducible portion of the zone. This approach significantly reduces the computational cost associated with accurately modelling these complex systems, particularly when a detailed understanding of exciton behaviour is required. The framework classifies excitons according to their symmetry properties, enabling the construction of symmetry-adapted linear combinations that simplify calculations of the Bethe-Salpeter Equation. Applying this method to monolayer molybdenum disulfide confirms its accuracy and consistency with established group theory principles, demonstrating a clear correspondence between predicted and observed exciton behaviour. While the method offers substantial computational savings, the complexity of applying symmetry operations can still present challenges for certain materials, and future work may focus on automating these operations or extending the framework to incorporate additional symmetry considerations.