Gate-Controlled Spin-Orbit Interaction in a Parabolic $\mathrm{GaAs}/\mathrm{AlGaAs}$ Quantum Well

We study the tunability of the spin-orbit interaction in a two-dimensional electron gas with a front and a back gate electrode by monitoring the spin precession frequency of drifting electrons using time-resolved Kerr rotation. The Rashba spin splitting can be tuned by the gate biases, while we find a small Dresselhaus splitting that depends only weakly on the gating. We determine the absolute values and signs of the two components and show that for zero Rashba spin splitting the anisotropy of the spin-dephasing rate vanishes.

Figure 1

(a) False-color image of the sample as seen in an optical microscope: cross-shaped mesa structure covered by a FG (green) and Ohmic contacts on each end (blue). The BG is indicated in red. (b) Schematic conductance-band profile of the grown layer structure including gate electrodes and wave functions of the two occupied subbands. (c) TRKR for $V_{\mathrm{FG}}=V_{\mathrm{BG}}=-0.5$ and 0.1 V, respectively. (d) $g$ factor of the electrons confined in the QW as a function of the gate voltages.

Figure 2

(a) $B_{\mathrm{tot}}$ for $V_{\mathrm{BG}}=-0.375\mathrm{V}$ and different $V_{\mathrm{FG}}$ biases. The magnetic field is applied in the $\theta =180°$ direction. The amplitude of the oscillation in $\phi$, including its sign, is tunable with the FG. (b) Experimentally obtained SO fields as a function of $V_{\mathrm{FG}}$ and $V_{\mathrm{BG}}$. Tuning of the symmetry of the QW allows $B_R$ to be tuned over a large range, including a sign change (dashed line), whereas $B_D$ shows only small variations.

Figure 3

(a) Left panel: $\alpha$ as a function of the FG (BG) voltage with fixed BG (FG) voltage (▵: $V_{\mathrm{FG}}=0.1\mathrm{V}$; ×: $V_{\mathrm{FG}}=-0.5\mathrm{V}$; ○: $V_{\mathrm{BG}}=0.1\mathrm{V}$; □: $V_{\mathrm{BG}}=-0.5\mathrm{V}$). Right panel: $\alpha$ as a function of $E_{\mathrm{ext}}$. The red line represents a least-squares fit as described in the text. (b) Averaged spin-dephasing rate for $\theta =90°$ and $\theta =180°$ (c) In-plane spin-dephasing asymmetry. The dashed line marks the same gate voltage regime as in Fig. 2b.