Magnetophonon-resonance theory of the two-dimensional electron gas in AlxGa1-xAs/GaAs single heterostructures.

Abstract

The theory of the transverse magnetophonon effect in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As/GaAs single heterostructures is developed by using the Kubo formula and Fang-Howard trial function. The oscillatory magnetoconductivity is evaluated by harmonic analysis including Landau-level broadening. The general oscillatory structure of the magnetoresistivity is shown to depend on ${\ensuremath{\omega}}_{c}$ and ${\ensuremath{\omega}}_{0}$, the cyclotron and optical-phonon frequencies, as \ensuremath{\Delta}\ensuremath{\rho}\ensuremath{\sim} for the case of a Lorentzian-type density of states, where the damping parameter \ensuremath{\gamma} is determined by the Landau-level broadening and given by \ensuremath{\gamma}=2\ensuremath{\Gamma}/\ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$ with the Landau-level broadening \ensuremath{\Gamma}. The Landau-level broadening is evaluated for the electron scattering by optical-phonon, acoustic-phonon, remote-impurity, background-impurity, and interface-roughness scatterings. It is shown that the dominant contribution to the broadening arises from the remote-impurity scattering which results in 2\ensuremath{\pi}\ensuremath{\gamma} proportional to ${\ensuremath{\omega}}_{0}$/${\ensuremath{\omega}}_{c}$ and of the order of unity. With use of the expressions of the Landau-level broadening, the magnetophonon resonance amplitude is calculated as a function of the sheet electron density in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As/GaAs heterostructures, which shows a good agreement with the experimental observations by Brummell et al., indicating that the damping of the magnetophonon resonance in this system is dominated by the remote-impurity scattering.