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
  • Featured in Physics
  • Editors' Suggestion
  • Open Access

Visualization of Defect-Induced Interband Proximity Effect at the Nanoscale

Thomas Gozlinski1,*, Qili Li1,*,†, Rolf Heid2, Oleg Kurnosikov3, Alexander Haas1, Ryohei Nemoto4, Toyo Kazu Yamada4,5, Jörg Schmalian2,6, and Wulf Wulfhekel1,2

  • *These authors contributed equally to this work.
  • †Contact author: qili.li@kit.edu

Phys. Rev. Lett. 136, 056401 – Published 4 February, 2026

DOI: https://doi.org/10.1103/4vhj-s1fq

Abstract

The majority of superconductors have more than one Fermi surface, on which the electrons pair below the critical temperature, yet their behavior can be well described by a single-band Bardeen-Cooper-Schrieffer theory. This is mostly due to interband scattering, especially in superconductors in the dirty limit, rigidly linking the pairing amplitude of the bands. This has limited experimental studies of the complex physics of multiband superconductivity. Here, we utilize the fact that elementary Pb—as a clean limit system—has two Fermi surfaces that are only weakly coupled by interband scattering, allowing the formation of two separate condensates. By studying stacking fault tetrahedra with a millikelvin scanning tunneling microscope, we show how to locally tune interband coupling ranging from weak to strong coupling and modify the superconducting order parameters from two well separated gaps to one merged gap around defects. The experiments critically test the theory of multiband superconductors and give a route to access a wide range of predicted quantum effects in these systems.

View figure in article

Physics Subject Headings (PhySH)

synopsis

When Two Superconductors Become One

Published 4 February, 2026

By exploiting defects in a superconductor, scientists have observed the switching of a material’s two superconducting states into one.

See more in Physics

Article Text

Supplemental Material

References (76)

  1. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 106, 162 (1957).
  2. R. C. Dynes, V. Narayanamurti, and J. P. Garno, Phys. Rev. Lett. 41, 1509 (1978).
  3. F. Herman and R. Hlubina, Phys. Rev. B 94, 144508 (2016).
  4. H. Suhl, B. T. Matthias, and L. R. Walker, Phys. Rev. Lett. 3, 552 (1959).
  5. C. C. Sung and V. K. Wong, J. Phys. Chem. Solids 28, 1933 (1967).
  6. W. L. McMillan, Phys. Rev. 175, 537 (1968).
  7. N. Schopohl and K. Scharnberg, Solid State Commun. 22, 371 (1977).
  8. C. Noce and L. Maritato, Phys. Rev. B 40, 734 (1989).
  9. I. M. Tang, Phys. Rev. B 2, 129 (1970).
  10. W. S. Chow, Phys. Rev. B 4, 111 (1971).
  11. P. W. Anderson, J. Phys. Chem. Solids 11, 26 (1959).
  12. M. Hoyer, M. S. Scheurer, S. V. Syzranov, and J. Schmalian, Phys. Rev. B 91, 054501 (2015).
  13. M. Iavarone, G. Karapetrov, A. E. Koshelev, W. K. Kwok, G. W. Crabtree, D. G. Hinks, W. N. Kang, E.-M. Choi, H. J. Kim, H.-J. Kim, and S. I. Lee, Phys. Rev. Lett. 89, 187002 (2002).
  14. T. Hanaguri, K. Kitagawa, K. Matsubayashi, Y. Mazaki, Y. Uwatoko, and H. Takagi, Phys. Rev. B 85, 214505 (2012).
  15. Q.-Y. Wang, Z. Li, W.-H. Zhang, Z.-C. Zhang, J.-S. Zhang, W. Li, H. Ding, Y.-B. Ou, P. Deng, K. Chang, J. Wen, C.-L. Song, K. He, J.-F. Jia, S.-H. Ji, Y.-Y. Wang, L.-L. Wang, X. Chen, X.-C. Ma, and Q.-K. Xue, Chin. Phys. Lett. 29, 037402 (2012).
  16. Y. Noat, J. A. Silva-Guillén, T. Cren, V. Cherkez, C. Brun, S. Pons, F. Debontridder, D. Roditchev, W. Sacks, L. Cario, P. Ordejón, A. García, and E. Canadell, Phys. Rev. B 92, 134510 (2015).
  17. M. Ruby, B. W. Heinrich, J. I. Pascual, and K. J. Franke, Phys. Rev. Lett. 114, 157001 (2015).
  18. P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Rep. Prog. Phys. 74, 124508 (2011).
  19. I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Phys. Rev. Lett. 101, 057003 (2008).
  20. A. D. Christianson, E. A. Goremychkin, R. Osborn, S. Rosenkranz, M. D. Lumsden, C. D. Malliakas, I. S. Todorov, H. Claus, D. Y. Chung, M. G. Kanatzidis, R. I. Bewley, and T. Guidi, Nature (London) 456, 930 (2008).
  21. A. V. Chubukov, D. V. Efremov, and I. Eremin, Phys. Rev. B 78, 134512 (2008).
  22. J. Lee, S. Lee, A. Kreisel, J. Paaske, B. M. Andersen, K. M. Bastiaans, D. Chatzopoulos, G. Gu, D. Cho, and M. P. Allan, Nano Lett. 25, 4227 (2025).
  23. I. I. Mazin, O. K. Andersen, O. Jepsen, O. V. Dolgov, J. Kortus, A. A. Golubov, A. B. Kuz’menko, and D. van der Marel, Phys. Rev. Lett. 89, 107002 (2002).
  24. A. Floris, A. Sanna, S. Massidda, and E. K. U. Gross, Phys. Rev. B 75, 054508 (2007).
  25. T. G. Saunderson, J. F. Annett, B. Újfalussy, G. Csire, and M. Gradhand, Phys. Rev. B 101, 064510 (2020).
  26. T. Gozlinski, Q. Li, R. Heid, R. Nemoto, R. Willa, T. K. Yamada, J. Schmalian, and W. Wulfhekel, Sci. Adv. 9, eadh9163 (2023).
  27. T.-S. Choy, J. Naset, J. Chen, S. Hershfield, and C. Stanton, Bull. Am. Phys. Soc. 45, L36 (2000), http://www.phys.ufl.edu/fermisurface/.
  28. T. Balashov, M. Meyer, and W. Wulfhekel, Rev. Sci. Instrum. 89, 113707 (2018).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/4vhj-s1fq for Notes I-X.
  30. M. Müller, N. Néel, S. Crampin, and J. Kröger, Phys. Rev. Lett. 117, 136803 (2016).
  31. S. Y. Song and J. Seo, Sci. Rep. 7, 12177 (2017).
  32. J. F. Wolf and H. Ibach, Appl. Phys. A 52, 218 (1991).
  33. J. Engbæk, J. Schiøtz, B. Dahl-Madsen, and S. Horch, Phys. Rev. B 74, 195434 (2006).
  34. A. Y. Aladyshkin, A. S. Aladyshkina, and S. I. Bozhko, J. Phys. Chem. C 125, 26814 (2021).
  35. M. Ohmori, H. Hirayama, and K. Takayanagi, Phys. Rev. B 59, 5612 (1999).
  36. K. Schouteden and C. Van Haesendonck, Phys. Rev. Lett. 108, 076806 (2012).
  37. K. Schouteden, B. Amin-Ahmadi, Z. Li, D. Muzychenko, D. Schryvers, and C. Van Haesendonck, Nat. Commun. 7, 14001 (2016).
  38. J. Silcox and P. B. Hirsch, Philos. Mag. 4, 72 (1959).
  39. R. M. J. Cotterill, Philos. Mag. 6, 1351 (1961).
  40. M. J. Yokota and J. Washburn, Philos. Mag. 16, 459 (1967).
  41. F. Bonsignori, V. Bortolani, and G. Velo, Nuovo Cimento B 57, 194 (1968).
  42. Q. F. Guan, L. Pan, H. Zou, A. M. Wu, S. Z. Hao, Q. Y. Zhang, C. Dong, and G. T. Zou, J. Mater. Sci. 39, 6349 (2004).
  43. R. Schäublin, Z. Yao, N. Baluc, and M. Victoria, Philos. Mag. 85, 769 (2005).
  44. G. J. Hardy and M. L. Jenkins, Philos. Mag. 52, L19 (2006).
  45. Y. N. Osetsky, D. Rodney, and D. J. Bacon, Philos. Mag. 86, 2295 (2006).
  46. B. P. Uberuaga, R. G. Hoagland, A. F. Voter, and S. M. Valone, Phys. Rev. Lett. 99, 135501 (2007).
  47. Y. Matsukawa, Y. N. Osetsky, R. E. Stoller, and S. J. Zinkle, Philos. Mag. 88, 581 (2008).
  48. J. Wei Wang, S. Narayanan, J. Yu Huang, Z. Zhang, T. Zhu, and S. X. Mao, Nat. Commun. 4, 2340 (2013).
  49. K. Y. Yu, D. Bufford, C. Sun, Y. Liu, H. Wang, M. A. Kirk, M. Li, and X. Zhang, Nat. Commun. 4, 1377 (2013).
  50. Y. Guo, Y.-F. Zhang, X.-Y. Bao, T.-Z. Han, Z. Tang, L.-X. Zhang, W.-G. Zhu, E. G. Wang, Q. Niu, Z. Q. Qiu, J.-F. Jia, Z.-X. Zhao, and Q.-K. Xue, Science 306, 1915 (2004).
  51. M. Schackert, T. Märkl, J. Jandke, M. Hölzer, S. Ostanin, Eberhard K. U. Gross, A. Ernst, and W. Wulfhekel, Phys. Rev. Lett. 114, 047002 (2015).
  52. O. Kurnosikov, O. A. O. Adam, H. J. M. Swagten, W. J. M. de Jonge, and B. Koopmans, Phys. Rev. B 77, 125429 (2008).
  53. O. Kurnosikov, J. H. Nietsch, M. Sicot, H. J. M. Swagten, and B. Koopmans, Phys. Rev. Lett. 102, 066101 (2009).
  54. O. Kurnosikov, H. J. M. Swagten, and B. Koopmans, Phys. Rev. Lett. 106, 196803 (2011).
  55. A. Weismann, M. Wenderoth, S. Lounis, P. Zahn, N. Quaas, R. G. Ulbrich, P. H. Dederichs, and S. Blügel, Science 323, 1190 (2009).
  56. M. Uhl, P. Kot, R. Drost, H. Huang, J. Ankerhold, J. C. Cuevas, and C. R. Ast, Phys. Rev. Res. 6, 043233 (2024).
  57. H. Schmidt, J. F. Zasadzinski, K. E. Gray, and D. G. Hinks, Phys. Rev. Lett. 88, 127002 (2002).
  58. T. Ekino, T. Takasaki, T. Muranaka, J. Akimitsu, and H. Fujii, Phys. Rev. B 67, 094504 (2003).
  59. H. Schmidt, J. F. Zasadzinski, K. E. Gray, and D. G. Hinks, Physica (Amsterdam) 385C, 221 (2003).
  60. J. A. Silva-Guillén, Y. Noat, T. Cren, W. Sacks, E. Canadell, and P. Ordejón, Phys. Rev. B 92, 064514 (2015).
  61. Y. Noat, T. Cren, F. Debontridder, D. Roditchev, W. Sacks, P. Toulemonde, and A. San Miguel, Phys. Rev. B 82, 014531 (2010).
  62. J. Senkpiel, C. Rubio-Verdú, M. Etzkorn, R. Drost, L. M. Schoop, S. Dambach, C. Padurariu, B. Kubala, J. Ankerhold, C. R. Ast, and K. Kern, Phys. Rev. B 100, 014502 (2019).
  63. Y. Noat, T. Cren, P. Toulemonde, A. San Miguel, F. Debontridder, V. Dubost, and D. Roditchev, Phys. Rev. B 81, 104522 (2010).
  64. S. Datta, A. Vasdev, S. Halder, J. Singh, Y. Singh, and G. Sheet, J. Phys. Condens. Matter 32, 315701 (2020).
  65. L. Kleinman, Phys. Rev. B 21, 2630 (1980).
  66. D. Vanderbilt, Phys. Rev. B 32, 8412 (1985).
  67. C. Elsasser, N. Takeuchi, K. M. Ho, C. T. Chan, P. Braun, and M. Fahnle, J. Phys. Condens. Matter 2, 4371 (1990).
  68. J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).
  69. B. Meyer and M. Fähnle, Phys. Rev. B 56, 13595 (1997).
  70. R. Heid, K. P. Bohnen, I. Y. Sklyadneva, and E. V. Chulkov, Phys. Rev. B 81, 174527 (2010).
  71. D. F. Agterberg, J. C. S. Davis, S. D. Edkins, E. Fradkin, D. J. Van Harlingen, S. A. Kivelson, P. A. Lee, L. Radzihovsky, J. M. Tranquada, and Y. Wang, Annu. Rev. Condens. Matter Phys. 11, 231 (2020).
  72. Y. Tanaka, Phys. Rev. Lett. 88, 017002 (2001).
  73. S. V. Kuplevakhsky, A. N. Omelyanchouk, and Y. S. Yerin, Low Temp. Phys. 37, 667 (2011).
  74. E. Babaev, Phys. Rev. Lett. 89, 067001 (2002).
  75. Y. M. Cho and P. Zhang, Phys. Rev. B 73, 180506(R) (2006).
  76. A. J. Leggett, Prog. Theor. Phys. 36, 901 (1966).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation