Cyclotron effective mass in wide parabolic quantum wells

Cyclotron-resonance measurements are reported for wide (100–300 nm) modulation-doped ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As graded parabolic quantum wells for electron areal densities ${\mathit{N}}_{\mathit{S}}$=${10}^9$/${\mathrm{cm}}^2$ –2.5×${10}^{11}$/${\mathrm{cm}}^2$. A clear dependence of the cyclotron frequency on ${\mathit{N}}_{\mathit{S}}$ is observed in the extreme quantum limit which is understood in terms of alloy effects. Self-consistent calculations that include the x dependence of the local effective mass and exchange-correlation effects in a local-density approximation are in quantitative agreement with the measurements for high densities. At low densities a pinning of the cyclotron frequency is observed that is not predicted by the model.