Anisotropy and Suppression of Spin-Orbit Interaction in a GaAs Double Quantum Dot

The spin-flip tunneling rates are measured in GaAs-based double quantum dots by time-resolved charge detection. Such processes occur in the Pauli spin blockade regime with two electrons occupying the double quantum dot. Ways are presented for tuning the spin-flip tunneling rate, which on the one hand gives access to measuring the Rashba and Dresselhaus spin-orbit coefficients. On the other hand, they make it possible to turn on and off the effect of spin-orbit interaction with a high on/off ratio. The tuning is accomplished by choosing the alignment of the tunneling direction with respect to the crystallographic axes, as well as by choosing the orientation of the external magnetic field with respect to the spin-orbit magnetic field. Spin lifetimes of 10 s are achieved at a tunneling rate close to 1 kHz.

Figure 1

(a) A scanning electron micrograph of DQD1, top gates shown in light gray; zero volts are applied between the source ($S$) and drain ($D$). The current $I_{\mathrm{CD}}$ distinguishes the charge states (1, 1) and (0, 2) of the two electron DQD. (b) Crystallographic orientation of the device in (a) including the direction $\overrightarrow{p}$ of tunneling, the spin-orbit magnetic field ${\overrightarrow{B}}_{\mathrm{SO}}$, and the angle $\phi$ between the externally applied in-plane field ${\overrightarrow{B}}_{\mathrm{ext}}$ and the spin-orbit field. (c) Spin-flip tunneling rate versus the angle between the spin-orbit magnetic field ${\overrightarrow{B}}_{\mathrm{SO}}$ and the external field ${\overrightarrow{B}}_{\mathrm{ext}}$. Points with error bars are experimental data; solid lines are fits to the theory. The fitted values at $\phi =0°,180°$ amount to $(0.20\pm 0.17)$ (black line) and $(0.07\pm 0.17)\mathrm{Hz}$ (red line). (d) Spin-flip tunneling rate measured as a function of the spin-conserving tunneling rate ${\mathrm{\Gamma }}_C$. Inset: Resonant alignment of the $(1,1)T_{-}$ and the $(0,2)S$ DQD states.

Figure 2

The spin-flip rate as a function of the spin-conserving rate at an externally applied magnetic field of 100 mT. The blue circles represent data taken from DQD1 ($\overrightarrow{p}\parallel [110]$), and green squares are used for DQD2 ($\overrightarrow{p}\parallel [\overline{1}10]$). Solid symbols are used for perpendicular alignment of the spin quantization axis and the spin-orbit field and open symbols for the parallel alignment. The suppression of the SOI is visible in the vanishing dependence of the spin-flip rate on the tunnel coupling.

Figure 3

The spin-flip rate normalized to the spin-conserving rate as a function of the in-plane angle $\phi$ between the external field (spin quantization axis) and the spin-orbit field (perturbation). The sinusoidal dependence found in DQD1 (solid blue circles) reflects the anisotropy of the perturbation induced by the SOI. The SOI vanishes for DQD2 (open green squares), leading to an almost isotropic spin-flip rate. The isotropic background (red) is determined by the spin-flip processes within the (1, 1) charge state in the individual DQD devices.

Figure 4

Charge detection. (a) The charge detector current $I_{\mathrm{CD}}$ changes between two values, depending on the charge state of the two-electron DQD. The bunching of tunneling events is visible in the long time trace, and the enlargement shows the fast tunneling events when the electron spins are antiparallel. The waiting time distribution is plotted in (b), where green and blue symbols are used for the (0, 2) and (1, 1) state, respectively. The slow time scale (spin-flip rate) is visible in the main figure and the fast time scales (spin-conserving rates) in the enlargement.