Theory of internal transitions of charged excitons in quantum wells in magnetic fields

For charged semiconductor complexes in magnetic fields B, we discuss an exact classification of states, which is based on magnetic translations. In this scheme, in addition to the total orbital angular momentum projection $M_z$ and electron and hole spins $S_e$, $S_h$, a new exact quantum number appears. This oscillator quantum number, k, is related physically to the center of the cyclotron motion of the complex as a whole. In the dipole approximation k is strictly conserved in magneto-optical transitions. We discuss implications of this new exact selection rule for internal intraband magneto-optical transitions of charged excitons $X^{-}$ in quantum wells in B.