Raman scattering in quantum wells in a high magnetic field: Fröhlich interaction

An explicit expression for the Raman-scattering efficiency in quantum wells (QW’s) under high magnetic fields is given for the allowed Fröhlich electron-phonon interaction mechanism. The basic features of the theory are studied with a parabolic band approximation, which allows us to understand the physics involved in the selection rules and the double resonance conditions. Furthermore, a Luttinger Hamiltonian is used to describe the heavy-hole–light-hole admixture in III-V compounds. Selection rules are derived for backscattering configuration and circular polarizations. Phonons can couple via Fröhlich interaction with either light or heavy components of a QW subband, and both intrasubband and intersubband scattering become possible, the selection rule being ΔN=0 for the Landau quantum number. The phonon confinement is studied in thin QW’s and a comparison among the different phonon modes is presented: only even phonon modes couple via Fröhlich interaction for ${\mathit{q}}_{\mathrm{\perp }}$=0. We have calculated the Raman polarizability of a 100-Å GaAs/AlAs multiple quantum well and compared it with recent experimental results.