Phonon-assisted cyclotron resonance in n-type quantum-well structures

We have calculated the phonon-assisted cyclotron resonance in n-type two-dimensional systems where absorption or emission of an optical phonon accompanies a Landau transition. The expression for the phonon-assisted cyclotron resonance absorption coefficient is obtained using the linear-response theory and Green’s-function method. A canonical transformation is used to eliminate the electron–optical-phonon interaction to first order. From the above formulation we have calculated the line shape for 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 GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum well.