Electrical control of the sign of the $g$ factor in a GaAs hole quantum point contact

Zeeman splitting of one-dimensional hole subbands is investigated in quantum point contacts fabricated on a (311)-oriented GaAs-AlGaAs heterostructure. Transport measurements can determine the magnitude of the $g$ factor, but cannot usually determine the sign. Here we use a combination of tilted fields and a unique off-diagonal element in the hole $g$ tensor to directly detect the sign of $g^{*}$. We are able to tune not only the magnitude, but also the sign of the $g$ factor by electrical means, which is of interest for spintronics applications. Furthermore, we show theoretically that the resulting behavior of $g^{*}$ can be explained by the momentum dependence of the spin-orbit interaction.

Figure 1

(a) The center panel shows an optical image of the device fabricated on $\left(311\right)A$ GaAs. The left and right panels show electron micrographs of the two orthogonal QPCs along the $\left[\overline{2}33\right]$ and $\left[01\overline{1}\right]$ directions, respectively (red arrows indicate current direction). (b) Schematic diagram showing the orientation of the magnetic fields used in this experiment with respect to the two QPCs. (c) The conductance $G$ vs $V_{SG}$ for $\mathrm{QPC}\left[\overline{2}33\right]$ in a magnetic field applied along $\left[\overline{2}33\right]$, showing characteristic 1D conductance plateaus at $B=0$, which evolve into spin-resolved half plateaus at finite fields (traces offset for clarity).

Figure 2

Top panels show Zeeman splitting in an in-plane magnetic field applied along the $\left[\overline{2}33\right]$ direction for (a) $\mathrm{QPC}\left[01\overline{1}\right]$ and (b) $\mathrm{QPC}\left[\overline{2}33\right]$. Grayscale plots of the transconductance $\partial G/\partial V_{SG}$ are shown, where the dark regions represent the 1D subband edges. Bottom panels show the effective $g$ factors measured for (c) $\mathrm{QPC}\left[01\overline{1}\right]$ and (d) $\mathrm{QPC}\left[\overline{2}33\right]$. $\mathrm{QPC}\left[\overline{2}33\right]$ shows a nonmonotonic trend, indicative of a sign change of $g_{\left[\overline{2}33\right]}^{*}$ at $n=5$.

Figure 3

Grayscale transconductance plot of the Zeeman splitting for both QPCs as a function of $B_{\left[\overline{2}33\right]}$, for $B_{\left[311\right]}=0.2\text{T}$ [(a) and (b)] and $B_{\left[311\right]}=0$ [(c) and (d)]. The dark regions represent the 1D subband edges. The out-of-plane field $B_{\left[311\right]}$ causes an asymmetry around $B_{\left[\overline{2}33\right]}=0$ due to the interplay between $g_{zz}$ and $g_{xz}$. For subband 6, $\mathrm{QPC}\left[\overline{2}33\right]$ shows a reversal of asymmetry due to the sign change of $g_{xz}$, as indicated by the red dashed lines.

Figure 4

(a) Theoretically predicted dependence of $g_{xz}$ on the in-plane momentum for $\mathrm{QPC}\left[01\overline{1}\right]$ (blue) and $\mathrm{QPC}\left[\overline{2}33\right]$ (red). $g_{xz}$ for $\mathrm{QPC}\left[\overline{2}33\right]$ is strongly suppressed as a function of $〈p_{\parallel }^2〉$ and changes sign. (b) Experimentally measured $g_{xz}$ vs subband index for both QPCs. Solid squares correspond to data from this experiment, and open squares are data from Ref. [17] at a higher 2D density.