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Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction

Nature Physics volume 19, pages 358–364 (2023)Cite this article

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Abstract

Second-order topological insulators are characterized by helical, non-spin-degenerate one-dimensional states running along opposite crystal hinges with no backscattering. Injecting superconducting pairs therefore entails splitting Cooper pairs into two families of helical Andreev states of opposite helicity, one at each hinge. Here we provide evidence for such separation via the measurement and analysis of the switching supercurrent statistics of a crystalline nanoring of bismuth. Using a phenomenological model of two helical Andreev hinge modes, we find that pairs relax at a rate comparable to individual quasiparticles, in contrast to the much faster pair relaxation of non-topological systems. This constitutes a unique telltale sign of the spatial separation of topological helical hinges.

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Fig. 1: Comparison of average and distribution of switching currents of the asymmetric bismuth SQUID.
Fig. 2: Andreev spectrum and Josephson current of an intermediate-length Josephson junction with one or two helical hinges between superconducting electrodes.
Fig. 3: Excitation processes in the case of two spatially separated helical Andreev hinge states.
Fig. 4: Comparison of the experimental switching statistics and extracted Andreev hinge state occupation probabilities to the results of the theoretical model in a field region centred at −170 G.
Fig. 5: Comparison of the experimental switching statistics and extracted Andreev hinge state occupation probabilities to the results of the theoretical model in a field region centred at 450 G.

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Data availability

The switching current data are available via Zenodo at https://doi.org/10.5281/zenodo.7119795.

Code availability

The MATLAB files for calculating the joint probabilities and switching histograms are available via GitHub at https://github.com/pengyangraul/BiJunction_Codes.

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Acknowledgements

We acknowledge useful discussions with M. Aprili, C. Girit, M. Houzet, J. Meyer, H. Pothier, P. Simon and C. Urbina, technical help from S. Autier-Laurent and funding from the French programme ANR JETS (ANR-16-CE30-0029-01), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant Ballistop agreement no. 833350), LabEx PALM (ANR-10-LABX-0039-PALM) JosephBismuth, CRC 183 (project C02) of Deutsche Forschungsgemeinschaft (Y.O. and F.v.O.), the European Union’s Horizon 2020 research and innovation programme (grant agreement LEGOTOP no. 788715) (Y.O.), ISF Quantum Science and Technology (grant no. 2074/19) (Y.O.) and a BSF and NSF grant (2018643) (Y.O.). Y.P. is supported by an NSF grant (no. PHY-2216774) and the startup fund from California State University, Northridge.

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Authors and Affiliations

  1. Laboratoire de Physique des Solides, Université Paris-Saclay, CNRS, Orsay, France

    A. Bernard, A. Kasumov, R. Deblock, M. Ferrier, H. Bouchiat & S. Guéron

  2. Department of Physics and Astronomy, California State University, Northridge, Northridge, California, USA

    Y. Peng

  3. Institute of Quantum Information and Matter and Department of Physics, California Institute of Technology, Pasadena, California, USA

    Y. Peng

  4. Institute of Microelectronics Technology and High Purity Materials RAS, Chernogolovka, Moscow Region, Russia

    A. Kasumov, V. T. Volkov & Yu. A. Kasumov

  5. Institut des Sciences Moléculaires d’Orsay, Université Paris-Saclay, CNRS, Orsay, France

    F. Fortuna

  6. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

    Y. Oreg

  7. Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Berlin, Germany

    F. von Oppen

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Contributions

A.K. and V.T.V. grew the Bi nanowires and A.K. deposited them on the substrate. Yu.A.K. characterized the nanowire growth. F.F., A.B. and A.K. selected the nanowires and connected them using focused-ion-beam-assisted deposition. A.B. conducted the low-temperature measurements with input from M.F., R.D., S.G. and H.B. A.B., M.F., R.D., S.G., H.B., Y.P., F.v.O. and Y.O. analysed the data and discussed the results. Y.P., F.v.O. and Y.O. developed the model, and Y.P. wrote the code. S.G., H.B., A.B., R.D., Y.P., F.v.O. and Y.O. wrote the paper.

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Correspondence to S. Guéron.

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Nature Physics thanks Mercedeh Khajavikhan and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections 1–5, Figs. 1–10 and references.

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Bernard, A., Peng, Y., Kasumov, A. et al. Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction. Nat. Phys. 19, 358–364 (2023). https://doi.org/10.1038/s41567-022-01858-8

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