Group representations of exciton states and their derivation from first principles*

Excitons play an essential role in the optical properties of semiconductors, especially in reduced-dimensional systems. Their symmetry characters are important ingredients that are relevant to selection rules for optical transition and other interactions. Here, we present a method to derive group representations of exciton states directly from ab initio GW-Bethe-Salpeter-equation calculations without any assumptions on the characters of the envelope functions. This method can be applied to study symmetry properties of Wannier and Frenkel excitons, as well as excitons arising from Mexican-hat quasiparticle bands or parallel valence and conduction bands (e.g. the C exciton in monolayer MoS₂). The method gives definitive conclusion on the exciton-state splitting and degeneracy, mitigating uncertainties from numerical noises.