Spin-Orbit Coupling at the Level of a Single Electron

V. F. Maisi, A. Hofmann, M. Röösli, J. Basset, C. Reichl, W. Wegscheider, T. Ihn, and K. Ensslin

Phys. Rev. Lett. 116, 136803 – Published 30 March 2016

Abstract

We utilize electron counting techniques to distinguish a spin-conserving fast tunneling process and a slower process involving spin flips in $AlGaAs / GaAs$ -based double quantum dots. By studying the dependence of the rates on the interdot tunnel coupling of the two dots, we find that as many as 4% of the tunneling events occur with a spin flip related to spin-orbit coupling in GaAs. Our measurement has a fidelity of 99% in terms of resolving whether a tunneling event occurred with a spin flip or not.

Received 17 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.136803

Physics Subject Headings (PhySH)

Quantum transport Spin-orbit coupling

Heterostructures Quantum dots

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. F. Maisi, A. Hofmann, M. Röösli, J. Basset, C. Reichl, W. Wegscheider, T. Ihn, and K. Ensslin

Solid State Physics Laboratory, ETH Zurich, CH-8093 Zurich, Switzerland

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Vol. 116, Iss. 13 — 1 April 2016

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Images

Figure 1
(a) Scanning electron micrograph of the DQD. The light gray gates deplete the underlying 2DEG and form two quantum dots holding two electrons shown as blue arrows. Letters $S$ and $D$ denote the source and drain reservoirs. Tunnel current $I$ flows through the device when a bias voltage $V_{b}$ is applied. The electrons may tunnel between the dots indicated by the red arrow. The tunneling events are detected via a nearby QPC by measuring the current $I_{QPC}$ through it. (b) The rate of electron tunneling events around the $(2, 0) \leftrightarrow (1, 1)$ transition.
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Figure 2
(a) Tunneling rates as a function of the energy detuning of the levels, changed with the plunger gate voltage $V_{RP}$ , for the transition $(1, 0) \to (0, 1)$ (red circles) and $(0, 1) \to (1, 0)$ (blue squares) with $B = 30 mT$ . Solid lines show Gaussian fits with tunneling rates of $56 \pm 2 Hz$ and $53 \pm 2 Hz$ at the peak. (b) Waiting time distributions for the transitions of panel (a) with zero detuning. Solid lines are fits with average waiting times of $17.4 \pm 0.1 ms$ and $17.8 \pm 0.1 ms$ . (c) Tunneling rates for transition $(2, 0) \leftrightarrow (1, 1)$ similarly as in panel (a). Solid symbols are with $B = 30 mT$ and open ones with $B = 0 mT$ . Tunneling rates at the peak are $256 \pm 4 Hz$ and $63 \pm 2 Hz$ , and $203 \pm 4 Hz$ and $48 \pm 2 Hz$ , respectively. (d) Waiting time distributions of the transitions of panel (c) with zero detuning. The average waiting times obtained from the fits are $4.04 \pm 0.02 ms$ , $7.89 \pm 0.04 ms$ , $216 \pm 3 ms$ , $5.40 \pm 0.04 ms$ , and $21.2 \pm 0.1 ms$ , respectively. (e) The five energetically allowed states around transition $(2, 0) \leftrightarrow (1, 1)$ . The electrons move between the dots with a spin-conserving process with a rate $Γ_{C}$ or a process involving a spin flip with a rate $Γ_{SO}$ . The spins flip within the dots with a rate $Γ_{SI}$ . (f) A time trace of the detector signal $I_{QPC}$ showing bunching of the tunneling events. (g) Histogram of the time trace.
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Figure 3
(a) Spin-flip rate $Γ_{S}$ as a function of the spin-conserving tunneling rate $Γ_{C}$ at various applied fields $B$ . The red straight line presents the linear dependence $Γ_{S} = 0.04 \times Γ_{C}$ and the other lines are $Γ_{S} = 0.04 \times Γ_{C} + 2 Γ_{SI}$ with $Γ_{SI}$ indicated in the figure. (b) Spin-flip rate $Γ_{S}$ for transition $(1, 1) \to (2, 0)$ as a function of $B$ (filled red symbols) for two different tunnel couplings. The tunnel coupling is deduced from the tunneling rate $Γ_{C}$ of the $(2, 0) \to (1, 1)$ transition as presented with the open blue symbols. The solid red lines are guides for the eye with $Γ_{S} = 15 kHz \cdot e^{- B / 3 mT} + 0.15 Γ_{C} \cdot e^{- B / 30 mT}$ .
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Figure 4
Current $I$ through the double dot as function of the detuning $δ V_{RP} - δ V_{LP}$ in the nonblocked direction, $V_{b} = + 200 μ V$ (red dots) and spin blocked direction $V_{b} = - 200 μ V$ (blue squares). Solid lines show fits with rates at the peak of $4.2 \pm 0.6 Hz$ and $0.2 \pm 0.1 Hz$ .
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