Energy levels of an anisotropic three-dimensional polaron in a magnetic field

In the context of the improved Wigner-Brillouin theory, the energy levels are found of a Frohlich polaron in a uniaxial anisotropic polar semiconductor with complex structure, placed in a magnetic field directed either along the optical axis or orthogonal to it. All sources of anisotropy that are contained in the shape of constant-energy surfaces of the bare electron, the electron - optical-phonon interaction, and the frequency spectrum of the extraordinary phonon modes are considered. Analytical results for the electron-phonon interaction correction to the Landau levels below the optical-phonon continuum are given and, numerical results for the magnetic-field dependence of the cyclotron resonance frequency at low temperature are presented for the particular case of the layered semiconductors InSe and GaSe. Although the interaction between the bare electron and quasitransverse optical-phonon modes is weak, these modes play an important role in the pinning of Landau levels. The results given by Das Sarma for a two-dimensional isotropic magnetopolaron are generalized to the anisotropic uniaxial case by taking formally m#parallel→infinity# in the expression of the perturbed Landau levels found when the magnetic field is directed along the optical axis, m#parallel# being the component of the bare-electron effective-mass tensor along the optical axis