Magnetophonon-resonance theory of the two-dimensional electron gas in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs single heterostructures

The theory of the transverse magnetophonon effect in ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$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 ${\omega }_c$ and ${\omega }_0$, the cyclotron and optical-phonon frequencies, as Δρ∼ for the case of a Lorentzian-type density of states, where the damping parameter γ is determined by the Landau-level broadening and given by γ=2Γ/ħ${\omega }_c$ with the Landau-level broadening Γ. 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 2πγ proportional to ${\omega }_0$/${\omega }_c$ 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 ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$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.