An explicit expression for the Raman-scattering efficiency in quantum wells (QW's) under high magnetic fields is given for the allowed Fr\"ohlich 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 Fr\"ohlich interaction with either light or heavy components of a QW subband, and both intrasubband and intersubband scattering become possible, the selection rule being {Δ}N=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 Fr\"ohlich interaction for q_⊥=0. We have calculated the Raman polarizability of a 100-A{} GaAs/AlAs multiple quantum well and compared it with recent experimental results.
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Cros et al. (1992) studied this question.
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