Charged Magnetoexcitons in Two-Dimensions: Magnetic Translations and Families of Dark States

We show that optical transitions of charged excitons in semiconductor heterostructures are governed in magnetic fields by a novel exact selection rule, a manifestation of magnetic translations. It is shown that the spin-triplet ground state of the quasi-two-dimensional charged exciton $X^{-}$—a bound state of two electrons and one hole—is optically inactive in photoluminescence at finite magnetic fields. Internal bound-to-bound $X^{-}$ triplet transition has a specific spectral position, below the electron cyclotron resonance, and is strictly prohibited in a translationally invariant system. These results allow one to discriminate between free and disorder-affected charged excitons.