- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Probing the topological protection of edge states in multilayer tungsten ditelluride with the superconducting proximity effect

X. Ballu1,*, Z. Dou1,†, L. Bugaud1, R. Delagrange1, A. Bernard1,‡, Ratnadwip Singha2,§, L. M. Schoop2, R. J. Cava2, R. Deblock1 et al.

Sophie Guéron1,∥, H. Bouchiat1, and M. Ferrier1,¶

  • *Present address: Laboratoire National de Métrologie et d’Essais, 29 avenue Roger Hennequin, 78197 Trappes, France.
  • †Present address: Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
  • ‡Present address: Walter Schottky Institute and Physics Department, Technical University of Munich, Garching 85748, Germany.
  • §Present address: Department of Physics, Indian Institute of Technology Guwahati, Guwahati, Assam 781039, India.
  • ∥Contact author: sophie.gueron@universite-paris-saclay.fr
  • Contact author: meydi.ferrier@universite-paris-saclay.fr
PDF

Phys. Rev. Research 8, 023034 – Published 10 April, 2026

DOI: https://doi.org/10.1103/jxks-s35x

Abstract

The topology of WTe2, a transition-metal dichalcogenide with large spin-orbit interactions, is thought to combine type II Weyl semimetal and second-order topological insulator (SOTI) character. The SOTI character should endow WTe2 multilayer crystals with topologically protected helical states at their hinges, and, indeed, one-dimensional states have been detected thanks to Josephson interferometry. However, the immunity to backscattering conferred to those states by their helical nature has so far not been tested. To probe the topological protection of WTe2 edge states, we have fabricated superconducting quantum interference devices (SQUIDs) in which the supercurrent through a junction on the crystal edge interferes with the supercurrent through a junction in the bulk of the crystal. We find behaviors ranging from a symmetric SQUID to asymmetric SQUID patterns, including one in which the modulation by magnetic field reveals a sawtoothlike supercurrent versus phase relation for the edge junction, demonstrating that the supercurrent at the edge is carried by ballistic channels over 600 nm, a telltale sign of the SOTI character of multilayer WTe2.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (58)

  1. Z. Fei, T. Palomaki, S. Wu, W. Zhao, X. Cai, B. Sun, P. Nguyen, J. Finney, X. Xu, and D. H. Cobden, Edge conduction in monolayer WTe2, Nat. Phys. 13, 677 (2017).
  2. S. Wu, V. Fatemi, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, and P. Jarillo-Herrero, Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal, Science 359, 76 (2018).
  3. L. Peng, Y. Yuan, G. Li, X. Yang, J.-J. Xian, C.-J. Yi, Y.-G. Shi, and Y.-S. Fu, Observation of topological states residing at step edges of WTe2, Nat. Commun. 8, 659 (2017).
  4. S. Tang, C. Zhang, D. Wong, Z. Pedramrazi, H.-Z. Tsai, C. Jia, B. Moritz, M. Claassen, H. Ryu, S. Kahn, et al., Quantum spin Hall state in monolayer 1T′-WTe2, Nat. Phys. 13, 683 (2017).
  5. Y. Shi, J. Kahn, B. Niu, Z. Fei, B. Sun, X. Cai, B. A. Francisco, D. Wu, Z.-X. Shen, X. Xu, D. H. Cobden, and Y.-T. Cui, Imaging quantum spin Hall edges in monolayer WTe2, Sci. Adv. 5, eaat8799 (2019).
  6. Y. Maximenko, Y. Chang, G. Chen, M. R. Hirsbrunner, T. L. Hughes, L. K. Wagner, and V. Madhavan, Nanoscale studies of electric field effects on monolayer 1T-WTe2, npj Quantum Mater. 7, 29 (2022).
  7. C.-H. Hsu, X. Zhou, Q. Ma, N. Gedik, A. Bansil, V. M. Pereira, H. Lin, L. Fu, S.-Y. Xu, and T.-R. Chang, Purely rotational symmetry-protected topological crystalline insulator α-Bi4Br4, 2D Mater. 6, 031004 (2019).
  8. K.-S. Lin, G. Palumbo, Z. Guo, Y. Hwang, J. Blackburn, D. P. Shoemaker, F. Mahmood, Z. Wang, G. A. Fiete, B. J. Wieder, and B. Bradlyn, Spin-resolved topology and partial axion angles in three-dimensional insulators, Nat. Commun. 15, 550 (2024).
  9. F. Tang, H. C. Po, A. Vishwanath, and X. Wan, Efficient topological materials discovery using symmetry indicators, Nat. Phys. 15, 470 (2019).
  10. C. Yoon, C.-C. Liu, H. Min, and F. Zhang, Quasi-one-dimensional higher-order topological insulators, arXiv:2005.14710.
  11. Z. Wang, B. J. Wieder, J. Li, B. Yan, and B. A. Bernevig, Higher-order topology, monopole nodal lines, and the origin of large Fermi arcs in transition metal dichalcogenides XTe2 (X = Mo, W), Phys. Rev. Lett. 123, 186401 (2019).
  12. Z. Song, T. Zhang, Z. Fang, and C. Fang, Quantitative mappings between symmetry and topology in solids, Nat. Commun. 9, 3530 (2018).
  13. B. J. Wieder, B. Bradlyn, Z. Wang, and J. Cano, Wallpaper fermions and the nonsymmorphic Dirac insulator, Science 361, 246 (2018).
  14. B. J. Wieder, Y. Kim, A. M. Rappe, and C. L. Kane, Double Dirac semimetals in three dimensions, Phys. Rev. Lett. 116, 186402 (2016).
  15. J. Lee, J. Kwon, E. Lee, J. Park, S. Cha, K. Watanabe, T. Taniguchi, M.-H. Jo, and H. Choi, Spinful hinge states in the higher-order topological insulators WTe2, Nat. Commun. 14, 1801 (2023).
  16. A. Murani, A. Kasumov, S. Sengupta, Y. Kasumov, V. T. Volkov, I. Khodos, F. Brisset, R. Delagrange, A. Chepelianskii, R. Deblock, H. Bouchiat, and S. Guéron, Ballistic edge states in bismuth nanowires revealed by SQUID interferometry, Nat. Commun. 8, 15941 (2017).
  17. C. Li, A. Kasumov, , , , , , , , , , , , and , Magnetic field resistant quantum interferences in bismuth nanowires based Josephson junctions, Phys. Rev. B 90, 245427 (2014).
  18. S. Hart, H. Ren, T. Wagner, P. Leubner, M. Mühlbauer, C. Brüne, H. Buhmann, L. W. Molenkamp, and A. Yacoby, Induced superconductivity in the quantum spin Hall edge, Nat. Phys. 10, 638 (2014).
  19. C. Li, B. de Ronde, J. de Boer, J. Ridderbos, F. Zwanenburg, Y. Huang, A. Golubov, and A. Brinkman, Zeeman-effect-induced 0−π transitions in ballistic Dirac semimetal Josephson junctions, Phys. Rev. Lett. 123, 026802 (2019).
  20. A. Kononov, G. Abulizi, K. Qu, J. Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger, One-dimensional edge transport in few-layer WTe2, Nano Lett. 20, 4228 (2020).
  21. Y.-B. Choi, Y. Xie, C.-Z. Chen, J. Park, S.-B. Song, J. Yoon, B. J. Kim, T. Taniguchi, K. Watanabe, J. Kim, K. C. Fong, M. N. Ali, K. T. Law, and G.-H. Lee, Evidence of higher-order topology in multilayer WTe2 from Josephson coupling through anisotropic hinge states, Nat. Mater. 19, 974 (2020).
  22. M. Endres, A. Kononov, M. Stiefel, M. Wyss, H. S. Arachchige, J. Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger, Transparent Josephson junctions in higher-order topological insulator WTe2 via Pd diffusion, Phys. Rev. Mater. 6, L081201 (2022).
  23. A. Murani, A. Chepelianskii, S. Guéron, and H. Bouchiat, Andreev spectrum with high spin-orbit interactions: Revealing spin splitting and topologically protected crossings, Phys. Rev. B 96, 165415 (2017).
  24. J. Cayao, A. M. Black-Schaffer, E. Prada, and R. Aguado, Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states, Beilstein J. Nanotechnol. 9, 1339 (2018).
  25. A. Bernard, Y. Peng, A. Kasumov, R. Deblock, M. Ferrier, F. Fortuna, V. T. Volkov, Y. A. Kasumov, Y. Oreg, F. von Oppen, H. Bouchiat, and S. Guéron, Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction, Nat. Phys. 19, 358 (2023).
  26. M. Endres, A. Kononov, H. S. Arachchige, J. Yan, D. Mandrus, K. Watanabe, T. Taniguchi, and C. Schönenberger, Current–phase relation of a WTe2 Josephson junction, Nano Lett. 23, 4654 (2023).
  27. M. N. Ali, J. Xiong, S. Flynn, J. Tao, Q. D. Gibson, L. M. Schoop, T. Liang, N. Haldolaarachchige, M. Hirschberger, N. P. Ong, and R. J. Cava, Large, non-saturating magnetoresistance in WTe2, Nature (London) 514, 205 (2014).
  28. M. Ohtomo, R. S. Deacon, M. Hosoda, N. Fushimi, H. Hosoi, M. D. Randle, M. Ohfuchi, K. Kawaguchi, K. Ishibashi, and S. Sato, Josephson junctions of Weyl semimetal WTe2 induced by spontaneous nucleation of PdTe superconductor, Appl. Phys. Express 15, 075003 (2022).
  29. Y. Jia, G. Yu, T. Song, F. Yuan, A. J. Uzan, Y. Tang, P. Wang, R. Singha, M. Onyszczak, Z. J. Zheng, K. Watanabe, T. Taniguchi, S. Wu, Superconductivity from on-chip metallization on 2D topological chalcogenides, Phys. Rev. X 14, 021051 (2024).
  30. M. L. Della Rocca, M. Chauvin, B. Huard, H. Pothier, D. Esteve, and C. Urbina, Measurement of the current-phase relation of superconducting atomic contacts, Phys. Rev. Lett. 99, 127005 (2007).
  31. M. Kayyalha, A. Kazakov, I. Miotkowski, S. Khlebnikov, L. P. Rokhinson, and Y. P. Chen, Highly skewed current–phase relation in superconductor–topological insulator–superconductor Josephson junctions, npj Quantum Mater. 5, 7 (2020).
  32. F. Chiodi, M. Ferrier, S. Guéron, J. C. Cuevas, G. Montambaux, F. Fortuna, A. Kasumov, and H. Bouchiat, Geometry-related magnetic interference patterns in long SNS Josephson junctions, Phys. Rev. B 86, 064510 (2012).
  33. J. C. Cuevas and F. S. Bergeret, Magnetic interference patterns and vortices in diffusive SNS junctions, Phys. Rev. Lett. 99, 217002 (2007).
  34. C. Li, S. Guéron, A. Chepelianskii, and H. Bouchiat, Full range of proximity effect probed with superconductor/graphene/superconductor junctions, Phys. Rev. B 94, 115405 (2016).
  35. F. Wilhelm, A. Zaikin, and G. Schön, Supercurrent in a mesoscopic proximity wire, J. Low Temp. Phys. 106, 305 (1997).
  36. P. Adroguer, C. Grenier, D. Carpentier, J. Cayssol, P. Degiovanni, and E. Orignac, Probing the helical edge states of a topological insulator by Cooper-pair injection, Phys. Rev. B 82, 081303(R) (2010).
  37. H.-J. Kwon, K. Sengupta, and V. M. Yakovenko, Fractional ac Josephson effect in p- and d-wave superconductors, Eur. Phys. J. B 37, 349 (2004).
  38. I. Babich, A. Kudriashov, D. Baranov, and V. S. Stolyarov, Limitations of the current–phase relation measurements by an asymmetric dc-SQUID, Nano Lett. 23, 6713 (2023).
  39. A. Bernard, Transport signatures of higher-order topology in bismuth nanostructures, Ph.D. thesis, Université Paris Saclay (2022), https://cnrs.hal.science/LPSO/tel-04165403.
  40. W. Zhao, E. Runburg, Z. Fei, J. Mutch, P. Malinowski, B. Sun, X. Huang, D. Pesin, Y.-T. Cui, X. Xu, J.-H. Chu, and D. H. Cobden, Determination of the spin axis in quantum spin Hall insulator candidate monolayer WTe2, Phys. Rev. X 11, 041034 (2021).
  41. C. W. Beenakker, D. I. Pikulin, T. Hyart, H. Schomerus, and J. P. Dahlhaus, Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect, Phys. Rev. Lett. 110, 017003 (2013).
  42. A. A. Golubov and A. Brinkman, Coherence effects in double-barrier Josephson junctions, Phys. Rev. B 61, 11297 (2000).
  43. L. Bugaud and S. Guéron, Probing the topological protection of edge states in multilayer tungsten ditelluride with the superconducting proximity effect, Zenodo (2026), https://doi.org/10.5281/zenodo.18556520.
  44. R. Delagrange, D. J. Luitz, R. Weil, A. Kasumov, V. Meden, H. Bouchiat, and R. Deblock, Manipulating the magnetic state of a carbon nanotube Josephson junction using the superconducting phase, Phys. Rev. B 91, 241401(R) (2015).
  45. R. Delagrange, R. Weil, A. Kasumov, M. Ferrier, H. Bouchiat, and R. Deblock, 0-π quantum transition in a carbon nanotube Josephson junction: Universal phase dependence and orbital degeneracy, Phys. Rev. B 93, 195437 (2016).
  46. M. Houzet (private communication).
  47. D. Sticlet, B. Dóra, and J. Cayssol, Persistent currents in Dirac fermion rings, Phys. Rev. B 88, 205401 (2013).
  48. P. Dubos, Transport électronique dans les nanojonctions supraconducteur - métal normal - supraconducteur, Ph.D. thesis, Université Joseph-Fourier - Grenoble I (2000).
  49. X. Zhang, V. Kakani, J. M. Woods, J. J. Cha, and X. Shi, Thickness dependence of magneto-transport properties in tungsten ditelluride, Phys. Rev. B 104, 165126 (2021).
  50. P. Li, Y. Wen, X. He, Q. Zhang, C. Xia, Z.-M. Yu, S. A. Yang, Z. Zhu, H. N. Alshareef, and X.-X. Zhang, Evidence for topological type-II Weyl semimetal WTe2, Nat. Commun. 8, 2150 (2017).
  51. F. Amet, C. T. Ke, I. V. Borzenets, J. Wang, K. Watanabe, T. Taniguchi, R. S. Deacon, M. Yamamoto, Y. Bomze, S. Tarucha, and G. Finkelstein, Supercurrent in the quantum Hall regime, Science 352, 966 (2016).
  52. V. Ambegaokar and B. I. Halperin, Voltage due to thermal noise in the dc Josephson effect, Phys. Rev. Lett. 22, 1364 (1969).
  53. J. Bardeen and J. L. Johnson, Josephson current flow in pure superconducting-normal-superconducting junctions, Phys. Rev. B 5, 72 (1972).
  54. M. Tinkham, Introduction to Superconductivity (McGraw-Hill, New York, 1996).
  55. L. F. Shatz and C. W. Christensen, Numerical inductance calculations based on first principles, PLoS One 9, e111643 (2014).
  56. A. J. Annunziata, D. F. Santavicca, L. Frunzio, G. Catelani, M. J. Rooks, A. Frydman, and D. E. Prober, Tunable superconducting nanoinductors, Nanotechnology 21, 445202 (2010).
  57. X. Qian, J. Liu, L. Fu, and J. Li, Quantum spin Hall effect in two-dimensional transition metal dichalcogenides, Science 346, 1344 (2014).
  58. F. Zheng, C. Cai, S. Ge, X. Zhang, X. Liu, H. Lu, Y. Zhang, J. Qiu, T. Taniguchi, K. Watanabe, S. Jia, J. Qi, J.-H. Chen, D. Sun, and J. Feng, On the quantum spin Hall gap of monolayer 1T′−WTe2, Adv. Mater. 28, 4845 (2016).

Outline

Information

Phys. Rev. Research 8, 023034– Published 10 April, 2026
  • Received 16 April 2025
  • Accepted 23 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation