Theory of the cyclotron resonance spectrum of a polaron in two dimensions

Abstract

The magneto-optical absorption spectrum of a two-dimensional polaron is calculated by using a memory-function approach. The cyclotron resonance frequency and the cyclotron resonance mass of the polaron are obtained for weak electron-phonon coupling. The absorption spectrum exhibits peaks around the cyclotron frequency ${\ensuremath{\omega}}_{c}$ and the LO-phonon-assisted harmonics ${\ensuremath{\omega}}_{\mathrm{LO}+\mathrm{n}{\ensuremath{\omega}}_{c}}$ (n=1,2,. . .). The oscillator strength and the position of the peaks are investigated as a function of the magnetic field strength. A Landau-level broadening parameter is introduced phenomenologically in order to remove the divergencies in the magneto-optical absorption spectrum. The effect of the nonzero width of the two-dimensional electron layer is also investigated. After taking into account the effect of the nonparabolic energy band of the electron, the calculated cyclotron resonance masses are compared to the experimental data for GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures and InSb inversion layers. In order to explain the experimental results for GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures with our one polaron theory an effective electron-phonon coupling constant has to be used which is smaller than generally accepted. Many-body effects are expected to be responsible for this reduction.