Isotropic and Anisotropic $g$-Factor Corrections in GaAs Quantum Dots

Isotropic and Anisotropic $g$ -Factor Corrections in GaAs Quantum Dots

Leon C. Camenzind, Simon Svab, Peter Stano, Liuqi Yu, Jeramy D. Zimmerman, Arthur C. Gossard, Daniel Loss, and Dominik M. Zumbühl

Phys. Rev. Lett. 127, 057701 – Published 29 July 2021

Abstract

We experimentally determine isotropic and anisotropic $g$ -factor corrections in lateral GaAs single-electron quantum dots. We extract the Zeeman splitting by measuring the tunnel rates into the individual spin states of an empty quantum dot for an in-plane magnetic field with various strengths and directions. We quantify the Zeeman energy and find a linear dependence on the magnetic field strength that allows us to extract the $g$ factor. The measured $g$ factor is understood in terms of spin-orbit interaction induced isotropic and anisotropic corrections to the GaAs bulk $g$ factor. Experimental detection and identification of minute band-structure effects in the $g$ factor is of significance for spin qubits in GaAs quantum dots.

Received 25 October 2020
Revised 29 April 2021
Accepted 17 June 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.057701

Physics Subject Headings (PhySH)

Quantum transport Spintronics

Quantum dots

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Leon C. Camenzind^1,*, Simon Svab^1,*, Peter Stano ^2,3, Liuqi Yu ^1,†, Jeramy D. Zimmerman^4,‡, Arthur C. Gossard⁴, Daniel Loss ^1,2, and Dominik M. Zumbühl ^1,¶

¹Department of Physics, University of Basel, Basel 4056, Switzerland
²Center for Emergent Matter Science, RIKEN, Saitama 351-0198, Japan
³Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia
⁴Materials Department, University of California, Santa Barbara, California 93106, USA

^*These authors contributed equally to this work.
^†Present address: Laboratory for Physical Sciences, 8050 Greenmead Drive, College Park, Maryland 20740, USA.
^‡Present address: Physics Department, Colorado School of Mines, Golden, Colorado 80401, USA.
^¶Corresponding author. dominik.zumbuhl@unibas.ch

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Vol. 127, Iss. 5 — 30 July 2021

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Images

Figure 1
(a) Electron micrograph of a cofabricated device with dot position (solid ellipse) and sensor dot (dashed ellipse). The sensor conductance $G_{sensor}$ reads the real-time charge state of the dot. (b) A two-step pulse—(I) ionize and (II) load—is applied on the dot gate $C_{P}$ to measure the tunneling rate $Γ$ into the empty dot for detuning $Δ E$ from the reservoir chemical potential $μ$ . The sensor plunger $C_{SP}$ is compensated to maintain readout sensitivity. A magnetic field splits the dot states $| ↑ ⟩$ , $| ↓ ⟩$ as well as the conduction band (blue and green) by the Zeeman energy $Δ$ . (c) Sensor conductance $G_{sensor}$ for two cycles (dashed pulses). Low (high) $G_{sensor}$ indicates an empty (occupied) dot, respectively. The ionization rate during (I) is faster than the sensor bandwidth. The electron loading times $t_{L}$ , appearing as clear steps (red traces), are histogrammed to extract the tunnel rate $Γ$ via exponential fit, shown in (d) for two examples, with typical error bars $\pm 10 Hz$ .
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Figure 2
(a) Examples of the normalized tunnel rate $Γ$ into the empty quantum dot for different detunings $Δ E$ and magnetic field strengths. Each trace exhibits two resonances, identified as the two spin states due to their behavior in the magnetic field (yellow arrows). The fits shown here are according to a phenomenological model described in Sec. 3 of Ref. [26]. In the trace taken at 4 T, the dashed line shows $Γ_{g} (Δ E)$ , the contribution of the spin ground state to the total tunnel rate, and $Δ$ indicates the Zeeman splitting. (b) Zeeman splittings $Δ$ in device 1, measured for different magnetic field strengths $B$ and directions as indicated by the labels. The error bars reflect the statistical uncertainty from the fits. The slope is the absolute value of the $g$ factor $| g | = Δ / (μ_{B} | B |)$ and differs from the GaAs bulk $g$ factor due to spin-orbit interaction induced corrections. A distinct $g$ -factor anisotropy is observed in the data. The inset shows the direction of the applied magnetic fields with respect to the crystal axes.
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Figure 3
(a) Cumulative $g$ -factor corrections $δ g$ to $g_{bulk}$ as labeled. The isotropic terms are due to penetration into the AlGaAs, $δ g_{p}$ , due to the $H_{43}$ term, $δ g_{43}$ , and the Rashba correction, $δ g_{R}$ . The magnetic field dependence of $δ g_{R}$ arises from an interference of the Rashba term and orbital effects. The Dresselhaus correction, $δ g_{D}$ , is anisotropic and given for a field along $Y$ ( $ϕ = 315 °$ ), the same direction for which the data are shown (black device 1, yellow device 2). Here, the $g$ -factor corrections at the respective magnetic fields are directly obtained from the individual measured Zeeman splitting. The green curve shows the total theoretical $g$ -factor correction for this field direction. (b) The anisotropic corrections to the $g$ factor are dominated by $δ g_{D}$ , while $δ g_{R}$ and $δ g_{43}$ give insignificant anisotropic corrections. The gray band indicates the $1 σ$ confidence interval of a sine fit to the data of device 2 with a fixed period of 180°. Note that the blue trace ( $δ g_{D}$ ) is a plot of the model, not a fit.
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