Theory of one-phonon resonant Raman scattering in a magnetic field

A theory of one-phonon resonant Raman scattering in diamond- and zinc-blende-type semiconductors in a magnetic field is developed. We consider the deformation-potential and Fr\"ohlich interactions for the electron--one-phonon coupling. Explicit expressions for the Raman efficiency as a function of the laser energy {}ωₗ and the applied magnetic field H are given. The Landau levels and the spin splitting are considered in the framework of the envelope-function approximation using a three-band parabolic model. In both types of electron-phonon interaction, the Raman intensity as a function of {}ωₗ and H shows a set of incoming and outgoing resonances corresponding to different interband magneto-optical transitions. Selection rules and conditions for double resonance are deduced for different scattering configurations with circularly polarized light. An extension of the theory to consider an admixed-valence-level structure is outlined. On these grounds the essential features of recent magneto-Raman experiments discussed in the following paper can be explained.