Symmetry Classification for Alternating Excitons in Two-Dimensional Altermagnets

Excitons, bound electron-hole 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. By focusing on a growing class of collinear antiferromagnets with a nonrelativistic spin splitting, referred to also as altermagnets (AMs), we propose a theoretical framework based on the spin space group to elucidate their resulting excitons. Our approach is illustrated on 2D AMs with spin-polarized valleys, where we classify the combination of conduction and valence bands by the spin space group representations into two cases that hosts bright s-like and p-like excitons, respectively. This analysis is further supported by effective Hamiltonians and the Bethe-Salpeter equation. We identify the excitonic optical selection rules from the calculated absorption spectra and the symmetry of bright excitons from their momentum-space envelope functions. Together with first-principles calculations, several material candidates are predicted for realizing excitons in 2D AMs. Our framework provides optical fingerprints for various cases of AMs, while their tunability, such as the strain-induced valley splitting, is also transferred to excitons allowing, additionally, valley-polarized photocurrent generation.