Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires

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Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires

Jouri D. S. Bommer, Hao Zhang, Önder Gül, Bas Nijholt, Michael Wimmer, Filipp N. Rybakov, Julien Garaud, Donjan Rodic, Egor Babaev, Matthias Troyer, Diana Car, Sébastien R. Plissard, Erik P. A. M. Bakkers, Kenji Watanabe, Takashi Taniguchi, and Leo P. Kouwenhoven

Phys. Rev. Lett. 122, 187702 – Published 9 May 2019

Abstract

Spin-orbit interaction (SOI) plays a key role in creating Majorana zero modes in semiconductor nanowires proximity coupled to a superconductor. We track the evolution of the induced superconducting gap in InSb nanowires coupled to a NbTiN superconductor in a large range of magnetic field strengths and orientations. Based on realistic simulations of our devices, we reveal SOI with a strength of 0.15–0.35 eV Å. Our approach identifies the direction of the spin-orbit field, which is strongly affected by the superconductor geometry and electrostatic gates.

Received 26 November 2018
Revised 5 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.187702

Physics Subject Headings (PhySH)

Proximity effect Quantum transport Spin-orbit coupling Superconductivity Topological superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jouri D. S. Bommer^1,2,*, Hao Zhang^1,2,3,†, Önder Gül^1,2,‡, Bas Nijholt², Michael Wimmer^1,2, Filipp N. Rybakov⁴, Julien Garaud⁵, Donjan Rodic⁶, Egor Babaev⁴, Matthias Troyer^6,7, Diana Car⁸, Sébastien R. Plissard^8,§, Erik P. A. M. Bakkers^1,2,8, Kenji Watanabe⁹, Takashi Taniguchi⁹, and Leo P. Kouwenhoven^1,2,10

¹QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
²Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
³State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
⁴Department of Physics, KTH-Royal Institute of Technology, SE-10691 Stockholm, Sweden
⁵Laboratoire de Mathématiques et Physique Théorique CNRS/UMR 7350, Institut Denis Poisson FR2964, Université de Tours, Parc de Grandmont, 37200 Tours, France
⁶Institut für Theoretische Physik, ETH Zürich, 8093 Zürich, Switzerland
⁷Microsoft Quantum, Redmond, Washington 98052, USA
⁸Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
⁹Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki, Tsukuba, 305-0044, Japan
¹⁰Microsoft Station Q Delft, 2600 GA Delft, Netherlands

^*Corresponding author. JouriBommer@gmail.com
^†Corresponding author. HaoZhangDelft@gmail.com
^‡Present address: Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
^§Present address: CNRS-Laboratoire d’Analyse et d’Architecture des Systèmes (LAAS), Université de Toulouse, 7 avenue du colonel Roche, F-31400 Toulouse, France.

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Vol. 122, Iss. 18 — 10 May 2019

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Images

Figure 1
(a) False-color scanning electron micrograph of Majorana nanowire device $A$ . An InSb nanowire (blue) is contacted by a normal metal contact ( $N$ , yellow) and a NbTiN superconducting contact ( $S$ , purple). The additional contact (gray) is kept floating. The nanowire is isolated from the barrier gate (red) and the super gate (green) by $\sim 30 nm$ thick boron nitride. (b) Differential conductance $d I / d V$ as a function of bias voltage $V$ and barrier gate voltage $V_{barrier}$ at $B = 0 T$ . (c) Schematic of the nanowire device and definition of the axes. (d) Band diagram of a Majorana nanowire at an externally applied magnetic field $B$ perpendicular to the spin-orbit field $B_{SO}$ . The arrows indicate the total magnetic field $B_{T} = B + B_{SO}$ along which the spin eigenstates are directed. At $k = 0$ the spin always aligns with $B$ . At increasing $k$ , $B_{SO}$ increases, tilting the spin more towards $B_{SO}$ . (e) $d I / d V$ as a function of $V$ at $B$ along $x$ , $y$ , $z$ (left, middle, right) for super gate voltage $V_{SG} = 0 V$ . The white dashed lines indicate a fit to the gap closing corresponding to $α = 0.15 \pm 0.05 eV Å$ . (f) Horizontal line cuts of (e) at $B$ indicated by the colored arrows in (e).
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Figure 2
(a) Numerical simulations of $d I / d V$ as a function of $V$ and $B$ , including the Zeeman and the orbital (Lorentz) effect of the magnetic field. (b) Same as (a), but including Zeeman and SOI instead of the orbital effect, reproducing the anisotropy in Fig. 1. (c) Same as (b), but including the Zeeman, SOI and orbital effect. The parameters used in (a)–(c) are $μ = 5.6 meV$ and $Δ V_{G} = - 8 meV$ .
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Figure 3
(a) Measured $d I / d V$ as a function of $V$ upon rotation of $B$ at 0.3 T over angles $Θ$ between $z$ and $y$ in device $B$ (see Fig. S5 [26] for the same behavior in device $A$ ). The voltage $V_{SG}$ on the super gate (see insets) is varied in the three panels. (b) Simulated $d I / d V$ as a function of $Θ$ and $V$ at 0.25 T. The top panel includes the Zeeman effect and SOI. The middle and bottom panels additionally include the orbital effect at two values of the potential difference $Δ V_{G}$ between the top and middle of the wire. (c) Horizontal line cuts of (a) averaged over $| V | < 0.2 V$ at $V_{SG} = - 3$ , 2.25, and 3.75 V (black, orange, blue). Dashed lines indicate the $z$ axis ( $Θ = 0 °$ ). (d) Vertical line cuts of (a) at $Θ = 0 °$ (left) and $Θ = 90 °$ (right).
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Figure 4
(a) Tilted view electron micrograph of Majorana nanowire device $E$ , which is partially covered with NbTiN. In this device, the electric field $E$ (and the associated spin-orbit field $B_{SO}$ ) can rotate away from the $z$ axis ( $y$ axis), as illustrated in the inset. (b) Measured $d I / d V$ as a function of $V$ and angle $Θ$ in the $z y$ plane at $| B | = 75 mT$ and $V_{SG} = 5.6 V$ , with a horizontal line cut averaged over $| V | < 0.25 mV$ in the lower panel. The gap is maximum at $Θ_{\max} = 32 °$ as indicated by the dashed line. (c) Same as (b), but at $V_{SG} = - 1.9 V$ and $| B | = 0.15 T$ . $Θ_{\max}$ is gate tuned to 22°. (d)–(f) Simulated $d I / d V$ at 0.25 T at various $Δ V_{G}$ (see inset) with the superconductor rotated to the side by 45° and including the Zeeman effect, SOI, and the orbital effect. The illustrations in the insets indicate the direction of $E$ , which is rotated by 45° from $z$ in (d).
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