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Superconducting diode effect in selectively grown topological insulator based Josephson junctions

Gerrit Behner*, Abdur Rehman Jalil, Detlev Grützmacher, and Thomas Schäpers†

  • *Contact author: g.behner@fz-juelich.de
  • †Contact author: th.schaepers@fz-juelich.de

Phys. Rev. B 113, 035440 – Published 28 January, 2026

DOI: https://doi.org/10.1103/gc7k-rn8q

Abstract

The Josephson diode effect, where the switching current magnitude depends on its direction, arises when both time-reversal and inversion symmetries are broken, often achieved by a combination of spin-orbit interaction and applied magnetic fields. Taking advantage of the strong spin-orbit coupling inherent in three-dimensional topological insulators, we study this phenomenon in Nb/Bi0.8Sb1.2Te3/Nb Josephson weak-link junctions. Under an in-plane magnetic field perpendicular to the current direction, we observe a pronounced Josephson diode effect with efficiencies up to 7%. A crucial component of this behavior is the nonsinusoidal current-phase relationship and an anomalous phase shift, which we attribute to the presence of a ballistic supercurrent component due to the surface states. These findings open up new avenues for harnessing and controlling the Josephson diode effect in topological material systems.

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References (79)

  1. M. Nadeem, M. S. Fuhrer, and X. Wang, The superconducting diode effect, Nat. Rev. Phys. 5, 558 (2023).
  2. J. Ma, R. Zhan, and X. Lin, Superconducting diode effects: Mechanisms, materials and applications, Adv. Phys. Res. 4, 2400180 (2025).
  3. A. I. Braginski, Superconductor electronics: Status and outlook, J. Supercond. Novel Magn. 32, 23 (2018).
  4. R. Bairamkulov and G. De Micheli, Superconductive electronics: A 25-year review [feature], IEEE Circuits Syst. Mag. 24, 16 (2024).
  5. J. Linder and J. W. A. Robinson, Superconducting spintronics, Nat. Phys. 11, 307 (2015).
  6. R. Cai, I. Žutić, and W. Han, Superconductor/ferromagnet heterostructures: A platform for superconducting spintronics and quantum computation, Adv. Quantum Technol. 6, 2200080 (2022).
  7. G. Wendin, Quantum information processing with superconducting circuits: A review, Rep. Prog. Phys. 80, 106001 (2017).
  8. X. Liu and M. C. Hersam, 2D materials for quantum information science, Nat. Rev. Mater. 4, 669 (2019).
  9. M. Davydova, S. Prembabu, and L. Fu, Universal Josephson diode effect, Sci. Adv. 8, eabo0309 (2022).
  10. K. Misaki and N. Nagaosa, Theory of the nonreciprocal Josephson effect, Phys. Rev. B 103, 245302 (2021).
  11. Y. Zhang, Y. Gu, P. Li, J. Hu, and K. Jiang, General theory of Josephson diodes, Phys. Rev. X 12, 041013 (2022).
  12. Y. Tanaka, B. Lu, and N. Nagaosa, Theory of giant diode effect in d-wave superconductor junctions on the surface of a topological insulator, Phys. Rev. B 106, 214524 (2022).
  13. A. Daido, Y. Ikeda, and Y. Yanase, Intrinsic superconducting diode effect, Phys. Rev. Lett. 128, 037001 (2022).
  14. N. F. Q. Yuan and L. Fu, Supercurrent diode effect and finite-momentum superconductors, Proc. Natl. Acad. Sci. USA 119, e2119548119 (2022).
  15. S. Ilić and F. S. Bergeret, Theory of the supercurrent diode effect in Rashba superconductors with arbitrary disorder, Phys. Rev. Lett. 128, 177001 (2022).
  16. T. Karabassov, I. V. Bobkova, A. A. Golubov, and A. S. Vasenko, Hybrid helical state and superconducting diode effect in superconductor/ferromagnet/topological insulator heterostructures, Phys. Rev. B 106, 224509 (2022).
  17. B. Zinkl, K. Hamamoto, and M. Sigrist, Symmetry conditions for the superconducting diode effect in chiral superconductors, Phys. Rev. Res. 4, 033167 (2022).
  18. C. Baumgartner, L. Fuchs, A. Costa, S. Reinhardt, S. Gronin, G. C. Gardner, T. Lindemann, M. J. Manfra, P. E. Faria Junior, D. Kochan, et al., Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions, Nat. Nanotechnol. 17, 39 (2022).
  19. B. Turini, S. Salimian, M. Carrega, A. Iorio, E. Strambini, F. Giazotto, V. Zannier, L. Sorba, and S. Heun, Josephson diode effect in high-mobility InSb nanoflags, Nano Lett. 22, 8502 (2022), .
  20. A. Costa, C. Baumgartner, S. Reinhardt, J. Berger, S. Gronin, G. Gardner, T. Lindemann, M. Manfra, J. Fabian, D. Kochan, et al., Sign reversal of the Josephson inductance magnetochiral anisotropy and 0–π-like transitions in supercurrent diodes, Nat. Nanotechnol. 18, 1266 (2023).
  21. N. Lotfizadeh, W. F. Schiela, B. Pekerten, P. Yu, B. H. Elfeky, W. M. Strickland, A. Matos-Abiague, and J. Shabani, Superconducting diode effect sign change in epitaxial Al-InAs Josephson junctions, Commun. Phys. 7, 120 (2024).
  22. B. Pal, A. Chakraborty, P. K. Sivakumar, M. Davydova, A. K. Gopi, A. K. Pandeya, J. A. Krieger, Y. Zhang, M. Date, S. Ju, et al., Josephson diode effect from Cooper pair momentum in a topological semimetal, Nat. Phys. 18, 1228 (2022).
  23. B. Lu, S. Ikegaya, P. Burset, Y. Tanaka, and N. Nagaosa, Tunable Josephson diode effect on the surface of topological insulators, Phys. Rev. Lett. 131, 096001 (2023).
  24. A. A. Reynoso, G. Usaj, C. A. Balseiro, D. Feinberg, and M. Avignon, Spin-orbit-induced chirality of Andreev states in Josephson junctions, Phys. Rev. B 86, 214519 (2012).
  25. T. Yokoyama, M. Eto, and Y. V. Nazarov, Josephson current through semiconductor nanowire with spin–orbit interaction in magnetic field, J. Phys. Soc. Jpn. 82, 054703 (2013).
  26. T. Yokoyama, M. Eto, and Y. V. Nazarov, Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires, Phys. Rev. B 89, 195407 (2014).
  27. F. Dolcini, M. Houzet, and J. S. Meyer, Topological Josephson ϕ0 junctions, Phys. Rev. B 92, 035428 (2015).
  28. Z. Liu, L. Huang, and J. Wang, Josephson diode effect in topological superconductors, Phys. Rev. B 110, 014519 (2024).
  29. J. S. Meyer and M. Houzet, Josephson diode effect in a ballistic single-channel nanowire, Appl. Phys. Lett. 125, 022603 (2024).
  30. R. S. Souto, M. Leijnse, and C. Schrade, Josephson diode effect in supercurrent interferometers, Phys. Rev. Lett. 129, 267702 (2022).
  31. E. Nikodem, J. Schluck, M. Geier, M. Papaj, H. F. Legg, J. Feng, M. Bagchi, L. Fu, and Y. Ando, Tunable superconducting diode effect in a topological nano-SQUID, Sci. Adv. 11, eadw4898 (2025).
  32. Y. V. Fominov and D. S. Mikhailov, Asymmetric higher-harmonic SQUID as a Josephson diode, Phys. Rev. B 106, 134514 (2022).
  33. M. Gupta, G. V. Graziano, M. Pendharkar, J. T. Dong, C. P. Dempsey, C. Palmström, and V. S. Pribiag, Gate-tunable superconducting diode effect in a three-terminal Josephson device, Nat. Commun. 14, 3078 (2023).
  34. G. Behner, A. R. Jalil, A. Rupp, H. Lüth, D. Grützmacher, and T. Schäpers, Superconductive coupling effects in selectively grown topological insulator-based three-terminal junctions, ACS Nano 19, 3878 (2025).
  35. M. Coraiola, A. E. Svetogorov, D. Z. Haxell, D. Sabonis, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, J. C. Cuevas, W. Belzig, and F. Nichele, Flux-tunable Josephson diode effect in a hybrid four-terminal Josephson junction, ACS Nano 18, 9221 (2024).
  36. Z. Zheng, M. Gong, Y. Zhang, X. Zou, C. Zhang, and G. Guo, FFLO superfluids in 2D spin-orbit coupled Fermi gases, Sci. Rep. 4, 6535 (2014).
  37. M. J. Park, J. Yang, Y. Kim, and M. J. Gilbert, Fulde-Ferrell states in inverse proximity-coupled magnetically doped topological heterostructures, Phys. Rev. B 96, 064518 (2017).
  38. A. Q. Chen, M. J. Park, S. T. Gill, Y. Xiao, D. Reig-i Plessis, G. J. MacDougall, M. J. Gilbert, and N. Mason, Finite momentum Cooper pairing in three-dimensional topological insulator Josephson junctions, Nat. Commun. 9, 3478 (2018).
  39. P. Schüffelgen, D. Rosenbach, C. Li, T. W. Schmitt, M. Schleenvoigt, A. R. Jalil, S. Schmitt, J. Kölzer, M. Wang, B. Bennemann, U. Parlak, L. Kibkalo, S. Trellenkamp, T. Grap, D. Meertens, M. Luysberg, G. Mussler, E. Berenschot, N. Tas, A. A. Golubov, et al., Selective area growth and stencil lithography for in situ fabricated quantum devices, Nat. Nanotechnol. 14, 825 (2019).
  40. A. R. Jalil, P. Schüffelgen, H. Valencia, M. Schleenvoigt, C. Ringkamp, G. Mussler, M. Luysberg, J. Mayer, and D. Grützmacher, Selective area epitaxy of quasi-1-dimensional topological nanostructures and networks, Nanomaterials 13, 354 (2023).
  41. T. W. Schmitt, B. Frohn, W. Wittl, A. R. Jalil, M. Schleenvoigt, E. Zimmermann, A. Schmidt, T. Schäpers, J. C. Cuevas, A. Brinkman, D. Grützmacher, and P. Schüffelgen, Anomalous temperature dependence of multiple Andreev reflections in a topological insulator Josephson junction, Supercond. Sci. Technol. 36, 024002 (2023).
  42. J. P. Carbotte, Properties of boson-exchange superconductors, Rev. Mod. Phys. 62, 1027 (1990).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/gc7k-rn8q for additional measurements of JJ1 and for a second dataset obtained from a similar device (JJ2) on another chip, which also includes Refs. [18, 21, 24, 34, 39, 41, 47, 59, 60, 61, 74, 75, 76, 77, 78, 79].
  44. G. Niebler, G. Cuniberti, and T. Novotný, Analytical calculation of the excess current in the Octavio–Tinkham–Blonder–Klapwijk theory, Supercond. Sci. Technol. 22, 085016 (2009).
  45. M. Octavio, M. Tinkham, G. E. Blonder, and T. M. Klapwijk, Subharmonic energy-gap structure in superconducting constrictions, Phys. Rev. B 27, 6739 (1983).
  46. K. Flensberg, J. B. Hansen, and M. Octavio, Subharmonic energy-gap structure in superconducting weak links, Phys. Rev. B 38, 8707 (1988).
  47. D. Rosenbach, A. R. Jalil, T. W. Schmitt, B. Bennemann, G. Mussler, P. Schüffelgen, D. Grützmacher, and T. Schäpers, Ballistic surface channels in fully in situ defined Bi4Te3 Josephson junctions with aluminum contacts, arXiv:2301.03968.
  48. A. R. Jalil, T. W. Schmitt, P. Rüßmann, X. Wei, B. Frohn, M. Schleenvoigt, W. Wittl, X. Hou, A. Schmidt, K. Underwood, G. Bihlmayer, M. Luysberg, J. Mayer, S. Blügel, D. Grützmacher, and P. Schüffelgen, Engineering epitaxial interfaces for topological insulator — superconductor hybrid devices with Al electrodes, Adv. Quantum Technol. 8, 2400343 (2024).
  49. J. C. Cuevas and F. S. Bergeret, Magnetic interference patterns and vortices in diffusive SNS junctions, Phys. Rev. Lett. 99, 217002 (2007).
  50. H. Y. Günel, I. E. Batov, H. Hardtdegen, K. Sladek, A. Winden, K. Weis, G. Panaitov, D. Grützmacher, and T. Schäpers, Supercurrent in Nb/InAs-nanowire/Nb Josephson junctions, J. Appl. Phys. 112, 034316 (2012).
  51. L. Bauriedl, C. Bäuml, L. Fuchs, C. Baumgartner, N. Paulik, J. M. Bauer, K.-Q. Lin, J. M. Lupton, T. Taniguchi, K. Watanabe, C. Strunk, and N. Paradiso, Supercurrent diode effect and magnetochiral anisotropy in few-layer NbSe2, Nat. Commun. 13, 4266 (2022).
  52. W.-S. Du, W. Chen, Y. Zhou, T. Zhou, G. Liu, Z. Xiao, Z. Zhang, Z. Miao, H. Jia, S. Liu, Y. Zhao, Z. Zhang, T. Chen, N. Wang, W. Huang, Z.-B. Tan, J.-J. Chen, and D.-P. Yu, Superconducting diode effect and large magnetochiral anisotropy in Td−MoTe2 thin film, Phys. Rev. B 110, 174509 (2024).
  53. T. Ideue, K. Hamamoto, S. Koshikawa, M. Ezawa, S. Shimizu, Y. Kaneko, Y. Tokura, N. Nagaosa, and Y. Iwasa, Bulk rectification effect in a polar semiconductor, Nat. Phys. 13, 578 (2017).
  54. D. C. Marinescu and S. Tewari, Magnetochiral anisotropy induced nonlinear planar Hall effect in topological insulator surface states, Phys. Rev. B 109, 205301 (2024).
  55. H. F. Legg, M. Rößler, F. Münning, D. Fan, O. Breunig, A. Bliesener, G. Lippertz, A. Uday, A. Taskin, D. Loss, et al., Giant magnetochiral anisotropy from quantum-confined surface states of topological insulator nanowires, Nat. Nanotechnol. 17, 696 (2022).
  56. J. J. He, Y. Tanaka, and N. Nagaosa, A phenomenological theory of superconductor diodes, New J. Phys. 24, 053014 (2022).
  57. H. F. Legg, D. Loss, and J. Klinovaja, Superconducting diode effect due to magnetochiral anisotropy in topological insulators and Rashba nanowires, Phys. Rev. B 106, 104501 (2022).
  58. 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).
  59. G. Eilenberger, Transformation of Gorkov's equation for type II superconductors into transport-like equations, Z. Phys. A 214, 195 (1968).
  60. A. V. Galaktionov and A. D. Zaikin, Quantum interference and supercurrent in multiple-barrier proximity structures, Phys. Rev. B 65, 184507 (2002).
  61. K. D. Usadel, Generalized diffusion equation for superconducting alloys, Phys. Rev. Lett. 25, 507 (1970).
  62. G. Behner, A. R. Jalil, D. Heffels, J. Kölzer, K. Moors, J. Mertens, E. Zimmermann, G. Mussler, P. Schüffelgen, H. Lüth, D. Grützmacher, and T. Schäpers, Aharonov-Bohm interference and phase-coherent surface-state transport in topological insulator rings, Nano Lett. 23, 6347 (2023).
  63. A. A. Golubov, M. Y. Kupriyanov, and E. Il'ichev, The current-phase relation in Josephson junctions, Rev. Mod. Phys. 76, 411 (2004).
  64. R. A. Snyder, C. J. Trimble, C. C. Rong, P. A. Folkes, P. J. Taylor, and J. R. Williams, Weak-link Josephson junctions made from topological crystalline insulators, Phys. Rev. Lett. 121, 097701 (2018).
  65. B. Raes, N. Tubsrinuan, R. Sreedhar, D. S. Guala, R. Panghotra, H. Dausy, C. C. de Souza Silva, and J. Van de Vondel, Fractional Shapiro steps in resistively shunted Josephson junctions as a fingerprint of a skewed current-phase relationship, Phys. Rev. B 102, 054507 (2020).
  66. J. Kölzer, A. R. Jalil, D. Rosenbach, L. Arndt, G. Mussler, P. Schüffelgen, D. Grützmacher, H. Lüth, and T. Schäpers, Supercurrent in Bi4Te3 topological material-based three-terminal junctions, Nanomaterials 13, 293 (2023).
  67. A. Iorio, A. Crippa, B. Turini, S. Salimian, M. Carrega, L. Chirolli, V. Zannier, L. Sorba, E. Strambini, F. Giazotto, and S. Heun, Half-integer Shapiro steps in highly transmissive InSb nanoflag Josephson junctions, Phys. Rev. Res. 5, 033015 (2023).
  68. T. Schäpers, Superconductor/Semiconductor Junctions, Springer Tracts in Modern Physics, Vol. 174 (Springer-Verlag, Berlin, 2001).
  69. A. Murani, Superconducting proximity effect in monocrystalline bismuth nanowires, Ph.D. thesis, Université Paris Saclay, 2017, https://theses.hal.science/tel-02057273v1.
  70. A. P. Surendran, D. Montemurro, G. Kunakova, X. Palermo, K. Niherysh, E. Trabaldo, D. S. Golubev, J. Andzane, D. Erts, F. Lombardi, and T. Bauch, Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes, Supercond. Sci. Technol. 36, 064003 (2023).
  71. A. Assouline, C. Feuillet-Palma, N. Bergeal, T. Zhang, A. Mottaghizadeh, A. Zimmers, E. Lhuillier, M. Eddrie, P. Atkinson, M. Aprili, and H. Aubin, Spin-orbit induced phase-shift in Bi2Se3 Josephson junctions, Nat. Commun. 10, 126 (2019).
  72. H. F. Legg, K. Laubscher, D. Loss, and J. Klinovaja, Parity-protected superconducting diode effect in topological Josephson junctions, Phys. Rev. B 108, 214520 (2023).
  73. J. Cayao, N. Nagaosa, and Y. Tanaka, Enhancing the Josephson diode effect with Majorana bound states, Phys. Rev. B 109, L081405 (2024).
  74. H. Courtois, M. Meschke, J. T. Peltonen, and J. P. Pekola, Origin of hysteresis in a proximity Josephson junction, Phys. Rev. Lett. 101, 067002 (2008).
  75. T. A. Fulton and L. N. Dunkleberger, Lifetime of the zero-voltage state in Josephson tunnel junctions, Phys. Rev. B 9, 4760 (1974).
  76. D. Massarotti, L. Longobardi, L. Galletti, D. Stornaiuolo, D. Montemurro, G. Pepe, G. Rotoli, A. Barone, and F. Tafuri, Escape dynamics in moderately damped Josephson junctions (review article), Low Temp. Phys. 38, 263 (2012).
  77. J. A. Blackburn, M. Cirillo, and N. Grønbech-Jensen, Investigation of low temperature quantum crossover in Josephson junctions, J. Appl. Phys. 122, 133904 (2017).
  78. T. F. Q. Larson, L. Zhao, E. G. Arnault, M.-T. Wei, A. Seredinski, H. Li, K. Watanabe, T. Taniguchi, F. Amet, and G. Finkelstein, Zero crossing steps and anomalous Shapiro maps in graphene Josephson junctions, Nano Lett. 20, 6998 (2020).
  79. D. Margineda, A. Crippa, E. Strambini, Y. Fukaya, M. T. Mercaldo, M. Cuoco, and F. Giazotto, Sign reversal diode effect in superconducting Dayem nanobridges, Commun. Phys. 6, 343 (2023).

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