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

Abstract

We have systematically studied the cyclotron resonance (CR) of high-mobility two-dimensional electrons in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As heterostructures at T=4.2 and 2.3 K in low densities ranging from ${n}_{s}$=1.55\ifmmode\times\else\texttimes\fi{}${10}^{10}$ to 1.03\ifmmode\times\else\texttimes\fi{}${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, in the extreme quantum limit from filling factor \ensuremath{\nu}\ensuremath{\simeq}0.6 to \ensuremath{\nu}\ensuremath{\simeq}0.08. For 0.4<\ensuremath{\nu}<0.6, the effect of level crossing dominates the CR and its linewidth. The effective mass, after nonparabolicity correction, is constant to better than 0.025% from \ensuremath{\nu}=0.4 to 0.14 and decreases by \ensuremath{\Delta}${m}_{0}^{\mathrm{*}}$\ensuremath{\simeq}7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$${m}_{0}$ from \ensuremath{\nu}=0.14 to 0.08. The CR lifetime ${\ensuremath{\tau}}_{\mathrm{CR}}$ is 104 ps at \ensuremath{\nu}=0.4, which is 15 times the dc scattering time and the longest CR lifetime reported. In the range 0.08<\ensuremath{\nu}<0.4 the dependence of ${\ensuremath{\tau}}_{\mathrm{CR}}$ on ${n}_{s}$ follows a power law, ${\ensuremath{\tau}}_{\mathrm{CR}\mathrm{\ensuremath{\propto}}{n}_{s}^{1.9\ifmmode\pm\else\textpm\fi{}0.1}}$. We attribute this ${n}_{s}$-dependent ${\ensuremath{\tau}}_{\mathrm{CR}}$ 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 \ensuremath{\nu}.