Zeeman-Effect-Induced $0\text{\ensuremath{-}}\ensuremath{\pi}$ Transitions in Ballistic Dirac Semimetal Josephson Junctions

Zeeman-Effect-Induced $0 − π$ Transitions in Ballistic Dirac Semimetal Josephson Junctions

Chuan Li, Bob de Ronde, Jorrit de Boer, Joost Ridderbos, Floris Zwanenburg, Yingkai Huang, Alexander Golubov, and Alexander Brinkman

Phys. Rev. Lett. 123, 026802 – Published 9 July 2019

Abstract

One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction is $π$ -junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman-effect-induced $0 − π$ transitions in ${Bi}_{1 - x} {Sb}_{x}$ , three-dimensional Dirac semimetal-based Josephson junctions. The large in-plane $g$ factor allows tuning of the Josephson junctions from 0 to $π$ regimes. This is revealed by measuring a $π$ phase shift in the current-phase relation measured with an asymmetric superconducting quantum interference device (SQUID). Additionally, we directly measure a nonsinusoidal current-phase relation in the asymmetric SQUID, consistent with models for ballistic Josephson transport.

Received 19 November 2018

DOI:https://doi.org/10.1103/PhysRevLett.123.026802

Physics Subject Headings (PhySH)

Proximity effect

Dirac semimetal

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Chuan Li^1,*, Bob de Ronde¹, Jorrit de Boer¹, Joost Ridderbos¹, Floris Zwanenburg¹, Yingkai Huang², Alexander Golubov^1,3, and Alexander Brinkman¹

¹MESA+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, The Netherlands
²Van der Waals–Zeeman Institute, IoP, University of Amsterdam, Amsterdam 1098 XH, The Netherlands
³Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region 14170, Russia

^*Corresponding author. chuan.li@utwente.nl

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Vol. 123, Iss. 2 — 12 July 2019

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Figure 1
Ballistic junction in SQUID configuration. (a) The extracted critical current $I_{s}$ of the ${Bi}_{0.97} {Sb}_{0.03}$ junction as a function of the phase across the junction at 20 mK. The sawtooth shape indicates the higher harmonics components in the supercurrent. The dashed blue lines indicate the maximum and the minimum of the critical current, which we used to estimate the skewness of the CPR shape in the main text. (b) Scheme of the sample configuration. The niobium leads are normal to the ${Bi}_{0.97} {Sb}_{0.03}$ flake (orange) edges which are in parallel with a niobium constriction (light blue). $x$ , $y$ , $z$ directions are assigned to vertical (vert.), perpendicular, ( $⊥$ ) and parallel ( $∥$ ) directions, respectively. The crystalline orientations in reciprocal space are indicated in the orange box, which has the same coordinates as that in real space. The contacts are always aligned in such way that the current flow is along the bisectrix axis of the ${Bi}_{0.97} {Sb}_{0.03}$ crystals. (c) Fourier transform of the periodic $I_{s} (B)$ , higher order harmonics are indicated by arrows.
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Figure 2
Current-phase relation at different temperatures. (a) Temperature dependence of the extracted critical current amplitude $I_{c} (T) \equiv Max [| I_{s} (ϕ) |]$ . (b)–(f) Current-phase relation at different temperatures. Data (blue circles) are fitted using the same parameters extracted from (a).
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Figure 3
Zeeman-effect-induced $0 − π$ transition. (a) 2D color plot of the current-phase relation of ${Bi}_{0.97} {Sb}_{0.03}$ junction in a parallel magnetic field. The $π$ shift in phase occurs periodically as the parallel field ( $B_{∥}$ ) increases. The horizontal dashed lines separate the map into different 0 or $π$ regions. (b) CPR curves at different parallel field values (indicated by the arrows). The junction alternates between 0 and $π$ states. For clarity, the data have been shifted vertically by successive increments of $2 μ A$ . (c) Extracted $I_{s}$ as a function of the parallel field $B_{∥}$ . Blue circles: $I_{s} (B_{∥})$ at $B_{⊥} = 0$ ; dashed line: fitting curve, exponential decay; solid line: fitting curve, decay, and oscillation, taking into account of the hole-pocket channel contribution (see main text). (d) Schematic illustration of the Zeeman-effect-induced finite-momentum pairing. At zero field (upper), the Dirac Fermion is spin degenerate (electron pocket at the $L$ point); as an in-plane field is applied along the large $g$ factor direction (lower), the Dirac Fermi surface splits with polarized spin. Consequently, the formed Cooper pairs acquire a finite total momentum, driving the $0 − π$ transition.
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Figure 4
Current-phase relation (CPR) in vertical field. (a) 2D color plot of the CPR in in-plane vertical field ( $B_{vert}$ ). (b) Extracted $I_{s} (B_{vert})$ at $B_{⊥} = 0$ . $I_{s}$ decreases with an increase of $B_{vert}$ , but no change of sign in critical current $I_{s}$ is observed. Circles: experimental data, with error bars; black line: fitting curve.
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Physical Review Letters

Zeeman-Effect-Induced 0−π Transitions in Ballistic Dirac Semimetal Josephson Junctions

Chuan Li, Bob de Ronde, Jorrit de Boer, Joost Ridderbos, Floris Zwanenburg, Yingkai Huang, Alexander Golubov, and Alexander Brinkman

Phys. Rev. Lett. 123, 026802 – Published 9 July 2019

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Zeeman-Effect-Induced $0 − π$ Transitions in Ballistic Dirac Semimetal Josephson Junctions