Inelastic Light Scattering from Semiconductor Plasmas in a Magnetic Field

The cross section for the inelastic scattering of light from mobile carriers in semiconductors immersed in a dc magnetic field ${\mathbf{B}}_0$ is calculated approximately in a manner sufficiently general to include directly particle-particle Coulomb interactions (in the random-phase approximation) and energy-band structure of an arbitrary nature. The effect of Coulomb interactions on the momentum matrix elements occurring in the calculation is neglected, but is kept in the evaluation of the correlation function of a generalized electron-pair operator. The results encompass scattering from the various longitudinal magnetoplasma collective modes, and single-particle excitations between Landau levels and spin states. Resonant enhancement factors are automatically included, as are spin-orbit-induced effects such as scattering from spin-density fluctuations and spin waves. Low-temperature electrons in semiconductors of the indium antimonide type are used as a specific example to illustrate general features of the scattering for the two major geometries: q ⊥ ${\mathbf{B}}_0$ and q∥${\mathbf{B}}_0$ where q is the scattering wave vector. For q ⊥ ${\mathbf{B}}_0$ inter-Landau-level scattering is shown to suffer significant screening due to Coulomb interactions. Also, in this geometry it is shown that the strength of the scattering from the Bernstein modes is of the order of the strength for the associated inter-Landau-level excitation, contrary to the conclusions of previous authors.