For composite complexes - quasi-two-dimensional (2D) charged magneto-excitons X-- we propose a new exact classification of states, which is based on magnetic translations. We consider implications of this symmetry for magneto-optical transitions. It is shown, in particular, that in a translationally invariant system with a simple valence band, the ground triplet Xt-state is dark in interband transitions at finite magnetic fields B. This exact result calls for the re-interpretation of several previous theoretical studies. We consider the symmetry-breaking effects of spatial lateral confinement on internal transitions of charged complexes.
Dzyubenko, A. B., & Sivachenko, A. Y. (2000). Two-dimensional charged magneto-excitons: Magnetic translations and localization. Physica E: Low-Dimensional Systems and Nanostructures, 6(1), 226–229. https://doi.org/10.1016/S1386-9477(99)00119-8