Cyclotron resonance of high-mobility two-dimensional electrons at extremely low densities

We have systematically studied the cyclotron resonance (CR) of high-mobility two-dimensional electrons in GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures at T=4.2 and 2.3 K in low densities ranging from $n_s$=1.55×${10}^{10}$ to 1.03×${10}^{11}$ ${\mathrm{cm}}^{\mathrm{-}2}$, in the extreme quantum limit from filling factor ν≃0.6 to ν≃0.08. For 0.4<ν<0.6, the effect of level crossing dominates the CR and its linewidth. The effective mass, after nonparabolicity correction, is constant to better than 0.025% from ν=0.4 to 0.14 and decreases by Δ$m_0^{\mathrm{*}}$≃7×${10}^{\mathrm{-}4}$ $m_0$ from ν=0.14 to 0.08. The CR lifetime ${\tau }_{\mathrm{CR}}$ is 104 ps at ν=0.4, which is 15 times the dc scattering time and the longest CR lifetime reported. In the range 0.08<ν<0.4 the dependence of ${\tau }_{\mathrm{CR}}$ on $n_s$ follows a power law, ${\tau }_{\mathrm{CR}\mathrm{\propto }{n}_s^{1.9\pm 0.1}}$. We attribute this $n_s$-dependent ${\tau }_{\mathrm{CR}}$ in the extreme quantum limit to scattering by screened residual ionized impurities in GaAs. Our studies also resolve the existing experimental discrepancies concerning the oscillatory behavior of the CR linewidth as a function of ν.