Ballistic Electron Transport in AlAs Quantum Wells

We report the observation of commensurability oscillations in an AlAs two-dimensional electron system where two conduction-band valleys with elliptical in-plane Fermi contours are occupied. The Fourier power spectrum of the oscillations shows two frequency components consistent with those expected for the Fermi contours of the two valleys. From an analysis of the spectra we deduce $m_l/m_t=5.2\pm 0.5$ for the ratio of the longitudinal and transverse electron effective masses, a fundamental parameter that cannot be directly measured from other transport experiments.

Figure 1

(a) Schematic cross section of the device used to measure COs. Application of a bias to the Ti/Au surface gate with respect to the 2DES produces a potential modulation which is periodic in the [100] direction and has period $a$. (b) The AlAs in-plane valleys $X$ and $Y$ in $k$ space (left), and their corresponding first two resonant CO orbits in real space (right) [13]. The Fermi wave vectors $k_{F,X}$ and $k_{F,Y}$ relevant for the COs of the $X$ and $Y$ valley are also indicated.

Figure 2

(a) Magnetoresistance trace showing COs at low fields ($-1<B<1\mathrm{T}$) and SdHOs at high fields ($B>1.7\mathrm{T}$) for a device with 400 nm grating period. Inset: numerically determined second derivative $d^2{\rho }_{xx}/d{B}^2$. (b) Fourier power spectra of COs from both ${\rho }_{xx}$ (solid curve) and $d^2{\rho }_{xx}/d{B}^2$ (dotted curve). (c) Fourier power spectrum of SdHOs.

Figure 3

Density dependence of the CO frequencies for the $Y$ (circles) and $X$ valleys (squares). The line through the circles is a least-squares fit to the data; its slope determines the ratio $m_l/m_t$ and its intercept the density difference $\Delta n$ of the two valleys. The dashed line is described in the text.

Figure 4

Results of the inverse Fourier decomposition of the COs of Fig. 2 for the $Y$ and $X$ valleys. The dotted curves show the best fits of Eq. (7) using the indicated parameters. The fits are done only for fields smaller than those marked by squarewhich indicate the positions of the first CO resonant orbits. The arrows indicate where the first two CO resonance occur.