Shallow donors in magnetic fields in zinc-blende semiconductors. I. Theory

In the weak-field regime (cyclotron energy {} effective Rydberg) the donor associated with the parabolic minimum of the conduction band may be treated as a hydrogen atom in a magnetic field. We review and compare the existing variational and adiabatic models pointing out those which are most useful for the analysis of magneto-optical data. In the high-field regime (cyclotron energy {} effective Rydberg) multiband (``nonparabolic'') calculations are necessary. In this case we develop a new approach (analogue of the adiabatic method in the parabolic case) obtaining simple expressions for the energy levels, the wave functions, the selection rules, and the chemical shifts. In view of the recent high-pressure magneto-optical experiments we discuss the effect of pressure on all determined quantities. We also formulate the generalization of our multiband adiabatic approach.