Magnetic field dependence of the energy of negatively charged excitons in semiconductor quantum wells

We present a variational calculation of the spin-singlet and spin-triplet states of a negatively charged exciton (trion) confined to a single quantum well in the presence of a perpendicular magnetic field. We calculated the probability density and the pair correlation function of the singlet and triplet trion states. The dependence of the energy levels and of the binding energy on the well width and on the magnetic field strength was investigated. We compared our results with the available experimental data on GaAs/AlGaAs quantum wells and find that in the low-magnetic-field region $(B<\mathrm{}18\mathrm{}\hspace{0.5em}\mathrm{T})$ the observed transitions are those of the singlet and the dark triplet trion (with angular momentum $L_z=-1),$ while for high magnetic fields $(B>\mathrm{}25\mathrm{}\hspace{0.5em}\mathrm{T})$ the dark trion becomes optically inactive and possibly a transition to a bright triplet trion (angular momentum $L_z=0)$ state is observed.