Two-dimensional charged magneto-excitons: Magnetic translations and localization

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 X- 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.