Despite the large number of papers devoted to the magnetoluminescence from CdTe/(Cd,Mg)Te quantum wells, there have been no attempts to analyze it on the basis of band-structure calculations. This has been proposed in the present paper. Samples containing one or ten CdTe quantum wells with ${\mathrm{Cd}}_{0.7}{\mathrm{Mg}}_{0.3}\mathrm{Te}$ barriers are grown by molecular beam epitaxy on a semi-insulating GaAs substrate. Each well is modulation-doped with iodine donors, which leads to the creation of a two-dimensional electron gas in the wells. Polarization-resolved (${\sigma }^{+}/{\sigma }^{-}$) photoluminescence spectra are measured at liquid helium temperatures and magnetic fields up to 9 T. The results are interpreted on the basis of calculations of the energy of Landau levels in conduction and valence bands. In the latter case, we use the Luttinger Hamiltonian while the conduction band is described within a three-level $\mathbf{k}·\mathbf{p}$ model. Both models, originally formulated for bulk materials, are adapted for two-dimensional structures. We have found that the majority of all observed transitions is well-reproduced by this theory. However, some strong transitions are not, which allows us to propose an enlarged scheme of selection rules of the photoluminescence transitions resulting from mixing of the conduction and valence bands. We observe transitions involving Landau levels in the valence band with the index up to 7. To understand the origin of occupation with photoexcited holes of these levels, lying deep in the valence band, we carry out time-resolved measurements, which show that the photoexcited barrier is a source of long-lived holes tunneling into quantum wells. Calculations of the conduction-band electron effective $g$-factor show its strong variation with the electron's energy and the external magnetic field.

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• Landau levels
• Magneto-optics
• Quantum wells
• Luminescence
• k dot p method