Unified Symmetry Framework for Excitons in two-dimensional Materials: Monolayer and Bilayer Transition-Metal Dichalcogenides and Altermagnets

Excitons, bound electron-holes states, often dominate the optical response of two-dimensional (2D) materials and reflect their inherent properties, including spin-orbit coupling, magnetic ordering, or band topology. A unified symmetry framework for excitons provides a transparent model of exciton beyond the hydrogen picture. Such a framework predicts resonant mixing of 1s and 2p excitons when the exciton Hamiltonian commutes with a total angular momentum made possible by broken mirror symmetry in monolayer TMD or inter-layer hopping in 3R-stacked bilayer TMD[1]. In 2D Altermagnets, the symmetry of excitons is described by spin-space-group (SSG) representation theory. These excitons demostrate distinct polarization-dependent optical selection rules and serve as optical fingerprints for detecting altermagnetism. Our framework also unified the description of excitons across different 2D platforms.

[1] J. D. Cao et al., Tunable resonant s–p mixing of excitons in van der Waals Heterostructures, Phys. Rev. B 112, L161405 (2025).

[2] J. D. Cao et al., Symmetry classification for alternating excitons in two-dimensional altermagnets, arXiv: 2506.05753