Shallow donors in magnetic fields in zinc-blende semiconductors. III. Subtleties of the conduction band and spin doublets in GaAs

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Abstract
We calculate the magnetodonor states within a three-band effective-mass approximation including the interaction with other bands, i.e., we add the donor potential to the complete Hamiltonian of Weiler. We show that the interaction with distant bands can be accurately described with the first-order perturbation theory. This leads to analytical results for Landau states and variational formulas for impurity levels. The energies do not depend on inversion-asymmetry parameters. We compare our results with the experimental data on cyclotron resonance and impurity cyclotron resonance in GaAs, revealing the anisotropy of the conduction band. We also predict a significant magnetic field variation of the g factor in GaAs.