Supercurrent Interference in Few-Mode Nanowire Josephson Junctions

Kun Zuo, Vincent Mourik, Daniel B. Szombati, Bas Nijholt, David J. van Woerkom, Attila Geresdi, Jun Chen, Viacheslav P. Ostroukh, Anton R. Akhmerov, Sebastién R. Plissard, Diana Car, Erik P. A. M. Bakkers, Dmitry I. Pikulin, Leo P. Kouwenhoven, and Sergey M. Frolov

Phys. Rev. Lett. 119, 187704 – Published 3 November 2017

Abstract

Junctions created by coupling two superconductors via a semiconductor nanowire in the presence of high magnetic fields are the basis for the potential detection, fusion, and braiding of Majorana bound states. We study $NbTiN / InSb$ $nanowire / NbTiN$ Josephson junctions and find that the dependence of the critical current on the magnetic field exhibits gate-tunable nodes. This is in contrast with a well-known Fraunhofer effect, under which critical current nodes form a regular pattern with a period fixed by the junction area. Based on a realistic numerical model we conclude that the Zeeman effect induced by the magnetic field and the spin-orbit interaction in the nanowire are insufficient to explain the observed evolution of the Josephson effect. We find the interference between the few occupied one-dimensional modes in the nanowire to be the dominant mechanism responsible for the critical current behavior. We also report a strong suppression of critical currents at finite magnetic fields that should be taken into account when designing circuits based on Majorana bound states.

Received 7 June 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.187704

Physics Subject Headings (PhySH)

Josephson effect Quantum interference effects Spin-orbit coupling Topological superconductors

Nanowires

Josephson junctions Tight-binding model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Kun Zuo^1,2, Vincent Mourik^1,2,3, Daniel B. Szombati^1,2,4,5, Bas Nijholt², David J. van Woerkom^1,2,6, Attila Geresdi^1,2, Jun Chen⁷, Viacheslav P. Ostroukh⁸, Anton R. Akhmerov², Sebastién R. Plissard^2,9, Diana Car^1,2,9, Erik P. A. M. Bakkers^1,2,9, Dmitry I. Pikulin^10,11,12, Leo P. Kouwenhoven^1,2,13, and Sergey M. Frolov^2,7

¹QuTech, Delft University of Technology, 2600 GA Delft, Netherlands
²Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands
³Centre for Quantum Computation and Communication Technologies, School of Electrical Engineering and Telecommunications, UNSW Sydney, Sydney, New South Wales 2052, Australia
⁴Australian Research Council Centre of Excellence for Engineered Quantum Systems, St Lucia, Queensland 4072, Australia
⁵School of Mathematics and Physics, University of Queensland, St Lucia, Queensland 4072, Australia
⁶Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
⁷Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
⁸Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands
⁹Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
¹⁰Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
¹¹Department of Physics and Astronomy, University of British Columbia, Vancouver British Columbia, Canada V6T 1Z1
¹²Quantum Matter Institute, University of British Columbia, Vancouver British Columbia, Canada V6T 1Z4
¹³Station Q Delft, Microsoft Research, 2600 GA, Delft, Netherlands

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Vol. 119, Iss. 18 — 3 November 2017

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Images

Figure 1
(a) Schematic superconductor ( $S$ )-nanowire- $S$ Josephson junction. The cross section shows cartoon wave functions of $n = 3$ transverse modes and the flux $Φ$ penetrating the area of the nanowire. The blue arrows indicate spin-resolved modes; the black dashed arrows are same-spin scattering events within the wire. All modes are coupled at the contacts. The directions of $B$ and the spin-orbit effective field $B_{SO}$ are indicated. (b) Differential resistance $d V / d I$ vs $B$ and $I_{bias}$ . The current bias sweep direction is from negative to positive. Data from device 1. Inset: SEM image of a typical device similar to those studied here. $S$ labels the superconducting contacts while $B$ indicates the in-plane magnetic field for device 2.
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Figure 2
(a)–(d) $d V / d I$ vs $B$ and $I_{bias}$ for different gate voltage settings $V_{g}$ indicated above each panel. Data from device 2; see the Supplemental Material [25]for the scanning electron micrograph of the device with the tuned gate marked.
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Figure 3
(a)–(e) $d V / d I$ vs $V_{g}$ and $I_{bias}$ at different $B$ (indicated within each panel). Data from device 2. The gate used for tuning is different from that used in Fig. 2, see the Supplemental Material [25]
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Figure 4
Critical current and corresponding ground state phase difference for different combinations of terms in the Hamiltonian. The Zeeman effect ( $g = 50$ ) is present in all of the curves. Only the system corresponding to the red curve labeled with $l_{mfp} = 250 nm$ includes disorder, for which the critical current is multiplied by a factor of 6. The simulation is performed at $T = 100 mK$ . The curves in panels (a) and (b) are for a single spinful transverse mode ( $μ = 10 meV$ ). Panels (c) and (d) are for the multimode (three transverse or six spin-full modes) regime ( $μ = 20 meV$ ). The vertical thick dashed light blue lines in (a) and (c) indicate the positions of $0 - π$ transitions in the absence of disorder and with $α = 0$ , $A = 0$ . Where not specified, the other constant simulation parameters are $α = 20 nm$ , $m_{eff} = 0.015 m_{e}$ , $Δ_{ind} = 0.250 meV$ ; the lattice constant $a = 8 nm$ , the nanowire diameter $d_{1} = 104 nm$ , the outer diameter (with superconductor) $d_{2} = 120 nm$ , and the superconductor coverage angle (see the Supplemental Material [25], Fig. 6) $ϕ = 135 °$ . For plots of corresponding current-phase relationships, Josephson energies, and numerical geometry, see the Supplemental Material [25], Figs. 6–9.
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Figure 5
Comparison between experimental (a) and numerical (b) results. The parameters for the numerical simulations are the same as in Figs. 4 and 4, red curve. The range of the chemical potential in the gated region ( $μ_{gate}$ ) is chosen using Ref. [56]. The experimental data are taken with device 2.
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