Phonon-assisted magneto-optical transitions in two-dimensional systems

We have calculated the phonon-assisted dielectric response of p-type two-dimensional systems in the presence of a magnetic field. This permits us to calculate the magneto-optical absorption at the mixed cyclotron resonance in which absorption or emission of a boson accompanies a cyclotron transition. We use the Luttinger-Kohn Hamiltonian to represent the hole carriers and through a canonical transformation eliminate the carrier-boson interaction to first order. The expression for the phonon-assisted cyclotron-resonance absorption coefficient is obtained using linear-response theory. The calculation is valid in the weak-coupling limit when only a one-boson process needs to be considered. From the above formulation we have calculated the line shape for the usual cyclotron resonance and a phonon-assisted sideband in the Faraday configuration for left and right circularly polarized light. An additional peak in the absorption coefficient due to phonon-assisted transition is predicted in p-type GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells.