Fermi contour anisotropy of GaAs electron-flux composite fermions in parallel magnetic fields

In high-quality two-dimensional electrons confined to GaAs quantum wells, near Landau level filling factors $\nu =1/2$ and 1/4, we observe signatures of the commensurability of the electron-flux composite fermion cyclotron orbits with a unidirectional periodic density modulation. Focusing on the data near $\nu =1/2$, we directly and quantitatively probe the shape of the composite fermions' cyclotron orbit, and therefore their Fermi contour, as a function of magnetic field ($B_{\parallel }$) applied parallel to the sample plane. The composite fermion Fermi contour becomes severely distorted with increasing $B_{\parallel }$ and appears to be elliptical, in sharp contrast to the electron Fermi contour which splits as the system becomes bilayerlike at high $B_{\parallel }$. We present a simple, qualitative model to interpret our findings.

Figure 1

Inset: An L-shaped Hall bar with periodic superlattices of negative electron-beam resist. (a) Magnetoresistance trace from the [110] Hall bar of the 40-nm-wide QW sample with $n=1.78\times {10}^{11}$ cm${}^{-2}$. (b) and (c) Prominent commensurability resistance minima are seen near $\nu =1/2$ and 1/4. The positions of the resistance minima expected for fully spin-polarized CFs with a circular Fermi contour are marked with indexed vertical lines (see text).

Figure 2

Evolution of the magnetoresistance near $\nu =1/2$ for the 40-nm-wide QW sample measured along the [110] and [$\overline{1}10$] Hall bars. The tilt angle $\theta$ is given for each trace, and the traces are shifted vertically for clarity. The vertical green dashed lines mark the expected positions of the primary commensurability resistance minima if the CF cyclotron orbit were circular. In both panels, the scale for the applied external field $B_{\perp }$ is shown on top while the bottom scale is the effective magnetic field $B_{\perp }^{*}$ felt by the CFs.

Figure 3

(a) Deduced values of the CF Fermi wave vectors $k_F^{*}$ from the $B_{\perp }^{*}>0$ positions of the $i=1$ commensurability minima along the [$\overline{1}10$] and [110] directions, normalized to $k_{F0}^{*}$ (see text). Data shown with open circles (blue), filled squares (red), and open squares (black) are from the 30-, 40-, and 50-nm-wide QWs, respectively. Representative error bars are included for each data set. (b) Solid lines: Relative anisotropy of the CF Fermi contours in each QW deduced from dividing the (interpolated) measured values of $k_F^{*}$ along [$\overline{1}10$] by those along [110]. Dashed lines: Theoretical estimate of the anisotropy using Eq. (1) (see text). Inset: Geometric mean of the measured values of $k_F^{*}$ along the two directions normalized to $k_{F0}^{*}$ for each QW.

Figure 4

(a)–(c) Calculated electron Fermi contours for a 40-nm-wide GaAs QW with density $n=1.7\times {10}^{11}$ cm${}^{-2}$ at $B_{\parallel }=0,10,25$ T. The solid and dotted contours correspond to the majority- and minority-spin electrons, respectively. (d)–(f) Evolution of the distortion of the CF Fermi contour with $B_{\parallel }$ measured in the 40-nm-wide QW.