Inter-Landau-level scattering in the valence band of zinc-blende semiconductors induced by the Fröhlich interaction

A calculation of the amplitude for longitudinal-optical phonon scattering between hole Landau levels induced by the Fröhlich interaction is presented. This amplitude, forbidden in the dipole approximation, is proportional to (${\mathit{qR}}_0$ ${)}^2$ in the limit of high magnetic field, where ${\mathit{R}}_0$ is the Landau length and q the phonon wave vector along the magnetic field. The interband Fröhlich scattering brings about double resonances, observable in magneto-Raman spectra, which are comparable to those induced by the deformation-potential interaction. Such resonances have been experimentally studied in GaAs with backscattering Faraday configurations with q along a cubic axis.