Strain-Induced Fermi Contour Anisotropy of GaAs 2D holes

We report measurements of magnetoresistance commensurability peaks, induced by a square array of antidots, in GaAs (311)A two-dimensional holes as a function of applied in-plane strain. The data directly probe the shapes of the Fermi contours of the two spin subbands that are split thanks to the spin-orbit interaction and strain. The experimental results are in quantitative agreement with the predictions of accurate energy band calculations, and reveal that the majority spin subband has a severely distorted Fermi contour whose anisotropy can be tuned with strain.

Figure 1

(a) Calculated Fermi contours for the HHh and HHl bands of GaAs (311)A 2D holes at $p=2.45\times {10}^{11}{\mathrm{cm}}^{-2}$ at the indicated strain ($ϵ$) values. (b) The primary commensurate orbits for the HHh and HHl bands for $ϵ=5\times {10}^{-4}$ for current along $[\overline{2}33]$ (see text).

Figure 2

The solid curve shows $\Delta f(=f_{+}-f_{-})$, determined from the calculated magneto-oscillations, as a function of strain. The circles are the experimentally measured $\Delta f$. The square is the $\Delta f$ measured on a sample from the same wafer not mounted on a piezoelectric actuator. The inset shows the Fourier power spectra (F.P.S.) of the measured and calculated magneto-oscillations at $ϵ=5.3\times {10}^{-4}$.

Figure 3

(a), (b), and (c) Low-field magnetoresistance traces for the indicated 2D hole density ($p$), antidot lattice period ($a$), and current direction. In each figure traces are shown for the indicated strain values from $6.9\times {10}^{-4}$ (top trace) to $4.5\times {10}^{-4}$ (bottom trace) in steps of $4\times {10}^{-5}$. The resistance scale is for the lowest trace and the other traces are offset vertically for clarity. (a′), (b′), and (c′) Comparison of the expected magnetoresistance peak positions ($B_P$) based on Fermi contour calculations and the positions of the experimentally observed peaks A and B.

Figure 4

Low-field MR traces for the 600 nm AD region for different densities at $ϵ=5.7\times {10}^{-4}$. Traces are offset, except for the bottom one. Theoretically expected MR peak positions are shown by filled circles on each trace.