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Evidence for chiral supercurrent in quantum Hall Josephson junctions

Nature volume 624, pages 545–550 (2023)Cite this article

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Abstract

Hybridizing superconductivity with the quantum Hall (QH) effect has notable potential for designing circuits capable of inducing and manipulating non-Abelian states for topological quantum computation1,2,3. However, despite recent experimental progress towards this hybridization4,5,6,7,8,9,10,11,12,13,14,15, concrete evidence for a chiral QH Josephson junction16—the elemental building block for coherent superconducting QH circuits—is still lacking. Its expected signature is an unusual chiral supercurrent flowing in QH edge channels, which oscillates with a specific 2ϕ0 magnetic flux periodicity16,17,18,19 (ϕ0 = h/2e is the superconducting flux quantum, where h is the Planck constant and e is the electron charge). Here we show that ultra-narrow Josephson junctions defined in encapsulated graphene nanoribbons exhibit a chiral supercurrent, visible up to 8 T and carried by the spin-degenerate edge channel of the QH plateau of resistance h/2e2 ≈ 12.9 kΩ. We observe reproducible 2ϕ0-periodic oscillations of the supercurrent, which emerge at a constant filling factor when the area of the loop formed by the QH edge channel is constant, within a magnetic-length correction that we resolve in the data. Furthermore, by varying the junction geometry, we show that reducing the superconductor/normal interface length is crucial in obtaining a measurable supercurrent on QH plateaus, in agreement with theories predicting dephasing along the superconducting interface19,20,21,22. Our findings are important for the exploration of correlated and fractional QH-based superconducting devices that host non-Abelian Majorana and parafermion zero modes23,24,25,26,27,28,29,30,31,32.

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Fig. 1: Josephson effect through QH edge channels.
Fig. 2: The 2ϕ0-periodic chiral supercurrent oscillations.
Fig. 3: Edge-state wavefunction shrinkage.
Fig. 4: Aharonov–Bohm interferometry with CAES.

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Data availability

All data described here are available at Zenodo49.

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Acknowledgements

We thank D. Basko, C. Beenakker, M. Feigelman, L. Glazman, M. Houzet, V. Kurilovich, J. Meyer, Y. Nazarov, K. Snizhko and A. Stern for valuable discussions. We thank F. Blondelle for technical support on the experimental apparatus, and P. David for the MoGe deposition. The samples were prepared at the Nanofab facility of the Néel Institute. This work has received funding from the Horizon 2020 research and innovation programme of the European Union under the ERC grant SUPERGRAPH no. 866365. This study is also supported by a French government grant managed by the ANR agency under the France 2030 plan, with reference to ANR-22-PETQ-0003. B.S., H.S. and W.Y. acknowledge support from the QuantERA II Program that has received funding from the Horizon 2020 research and innovation program of the European Union under grant agreement no. 101017733. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos 20H00354, 21H05233 and 23H02052) and the World Premier International Research Center Initiative (WPI), MEXT, Japan.

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  1. These authors contributed equally: Hadrien Vignaud, David Perconte

Authors and Affiliations

  1. Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Hadrien Vignaud, David Perconte, Wenmin Yang, Bilal Kousar, Edouard Wagner, Frédéric Gay, Hervé Courtois, Zheng Han, Hermann Sellier & Benjamin Sacépé

  2. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  3. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  4. State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan, People’s Republic of China

    Zheng Han

  5. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China

    Zheng Han

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Contributions

H.V. and D.P. fabricated the samples. H.V. and D.P. performed the measurements. H.V., D.P., H.S. and B.S. analysed the data. K.W. and T.T. supplied the hBN crystals. E.W. and F.G. provided technical support for the experiment. W.Y., B.K., H.C. and Z.H. contributed to the discussions. B.S. conceived the project and wrote the paper with inputs from all the authors.

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Correspondence to Benjamin Sacépé.

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Extended data figures and tables

Extended Data Fig. 1 hBN-encapsulated graphene nanoribbon samples.

a, Schematic describing the uncertainty in the junction width δW (red lines) and length δL (vertical black dashed lines in the zoom). Horizontal black dashed lines indicate the uncertainty in the graphene width δWAFM from AFM imaging. Blue rectangles represent MoGe electrodes correctly aligned, dashed blue lines indicate the MoGe electrode position with a misalignment (δx, δy), which results in an uncertainty δWal on the graphene edges position. b, AFM picture for sample HV88, the encapsulated graphene is readily visible with contrast enhancement. c, Zoom on the graphene narrow part in (b), with the lithography pattern overlayed (Ti/Au lines in orange and MoGe electrodes in blue). Red lines indicate the total width uncertainty ± δW/2 around the graphene edges. d, AFM picture of the graphene nanoribbon of sample DP24 before hBN encapsulation. Inset: higher resolution AFM picture. The arrows indicate the nanoribbon width of 125 nm. e, AFM picture of sample DP24 after hBN encapsulation. The yellow arrows indicate the nanoribbon position. The lithography pattern is overlayed on the picture. The scale bars are 5 μm (b), 400 nm (c), 2 μm (d), 500 nm (d) inset, 500 nm (e). f, AFM picture of sample DP24 contact fabrication. The scale bar is 1 μm. g, h, Height profiles along the blue and green lines in the AFM image in f. The excess thickness on the contact edge results from the liftoff process of the MoGe.

Extended Data Fig. 2 Shapiro steps of the chiral supercurrent.

I − V characteristics measured at 3.45 T on sample HV88-C, under microwave radiation of frequency f = 1 GHz. The I − V curves are extracted from the data of Fig. 1e at a microwave power of -13.8 dBm. The color-coded arrows indicate the current sweep direction.

Extended Data Fig. 3 Chequerboard patterns.

a–c, Differential resistance modulation with magnetic field and measured voltage showing a characteristic chequerboard pattern. d–f, Fourier transform amplitude at the chequerboard oscillation frequency as a function of the measured voltage. The orange curve is a fit to the data following the same procedure as in ref. 39. a,d, Junction DP24-D with fit parameters ETh = 640 μeV and x = 0. b,e, Junction HV88-C with fit parameters ETh = 240 μeV and x = 0.02. c,f, Junction HV88-F with fit parameters ETh = 140 μeV and x = 0.02.

Extended Data Fig. 4 Wide graphene Josephson junction.

a–d, Top panels show differential resistance maps as a function of back-gate voltage and dc current bias of sample HV88-G (W = 2.3 μm, L = 107 nm). Bottom panels are linecuts of the differential resistance at dc current biases of 0 nA and 26 nA, which show the emergence of supercurrent pockets (zero resistance reached by the blue curve), and the corresponding resistive state (yellow curve). The magnetic field is indicated in each top panel. Supercurrent is visible only when the resistance is not quantized, that is, at filling factors of QH plateaus that are not developed, or in between plateaus. When a QH plateau emerges, as for instance the h/2e2 plateau for B ≥ 4 T or the h/6e2 plateau for B ≥ 6 T, the supercurrent vanishes. This weakness is even more marked in sample HV88-H shown in SI, which is twice longer. Note that the oscillatory behavior of the resistance (see red curve at 26 nA) is characteristic of QH devices in two-terminal configuration with L ≪ W, see ref. 37.

Extended Data Fig. 5 Coulomb blockade on the QH plateau edge.

a, Differential resistance as a function of back-gate voltage for different dc current biases at B = 14 T on sample DP24-D. At low current, Coulomb diamonds appear as high frequency and high amplitude oscillations visible at the transition to the ν = 1 plateau. 2ϕ0-quantum interference gives rise to oscillations with larger period and a very small amplitude on the plateau. The vertical dash line indicates the limit of Coulomb diamonds seen in (b). The horizontal dashed line indicates the resistance value of h/2e2. b, Differential conductance as a function of back-gate voltage and applied voltage across the junction. Measurements are performed in voltage bias configuration. The Coulomb diamonds disappearance coincides with the start of the chequerboard pattern of the Aharonov-Bohm interference. c, Schematics of the scattering process through a compressible island in the bulk49, with the back-gate voltage corresponding to the edge of the plateau, leading to the Coulomb diamonds in (b).

Extended Data Table 1 Device parameters
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Vignaud, H., Perconte, D., Yang, W. et al. Evidence for chiral supercurrent in quantum Hall Josephson junctions. Nature 624, 545–550 (2023). https://doi.org/10.1038/s41586-023-06764-4

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