Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Half-integer level shift of vortex bound states in an iron-based superconductor

Nature Physics volume 15, pages 1181–1187 (2019)Cite this article

Subjects

An Author Correction to this article was published on 13 March 2020

An Author Correction to this article was published on 13 March 2020

This article has been updated

Abstract

Vortices in topological superconductors may host Majorana zero modes (MZMs), which have been proposed as the building blocks of fault-tolerant topological quantum computers. Recently, a new single-material platform with the potential for realizing MZMs has been discovered in iron-based superconductors, without involving hybrid semiconductor–superconductor structures. Here, we report a detailed scanning tunnelling spectroscopy study of a FeTe0.55Se0.45 single crystal and show that this material hosts two distinct classes of vortex. These differ by a half-integer level shift in the energy spectra of the vortex bound states. This level shift is directly tied to the presence or absence of a zero-bias conductance peak and also alters the ratios of higher energy levels from integer to half-odd-integer. Our model calculations fully reproduce the spectra of these two types of vortex bound state, suggesting the presence of regions with and without topological surface states, which coexist within the same crystal. Our findings provide strong evidence for the presence of MZMs in FeTe0.55Se0.45 and establish it as an excellent platform for further studies.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: CBSs in a vortex with MZM.
Fig. 2: Integer quantized CBSs in a topological vortex.
Fig. 3: Half-odd-integer quantized CBSs in an ordinary vortex.
Fig. 4: Spatial pattern of integer quantized CBSs.
Fig. 5: Half-integer level shift around a MZM.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request.

Change history

  • 13 March 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

References

  1. Nayak, C. et al. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    ADS  MathSciNet  MATH  Google Scholar 

  2. Read, N. et al. Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Phys. Rev. B 61, 10267–10297 (2000).

    ADS  Google Scholar 

  3. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys. Uspekhi 44, 131–136 (2001).

    ADS  Google Scholar 

  4. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    ADS  Google Scholar 

  5. Lutchyn, R. M., Sau, J. D. & Sarma, S. D. Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).

    ADS  Google Scholar 

  6. Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).

    ADS  Google Scholar 

  7. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    ADS  Google Scholar 

  8. Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).

    ADS  Google Scholar 

  9. Sun, H. H. et al. Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor. Phys. Rev. Lett. 116, 257003 (2016).

    ADS  Google Scholar 

  10. Deng, M. T. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016).

    ADS  Google Scholar 

  11. Jeon, S. et al. Distinguishing a Majorana zero mode using spin-resolved measurements. Science 358, 772–776 (2017).

    ADS  Google Scholar 

  12. Zhang, H. et al. Quantized Majorana conductance. Nature 556, 74–79 (2018).

    ADS  Google Scholar 

  13. Wang, Z.-J. et al. Topological nature of the FeSe0.5Te0.5 superconductor. Phys. Rev. B 92, 115119 (2015).

    ADS  Google Scholar 

  14. Wu, X.-X. et al. Topological characters in Fe(Te1 − xSex) thin films. Phys. Rev. B 93, 115129 (2016).

    ADS  Google Scholar 

  15. Xu, G. et al. Topological superconductivity on the surface of Fe-based superconductors. Phys. Rev. Lett. 117, 047001 (2016).

    ADS  Google Scholar 

  16. Zhang, P. et al. Observation of topological superconductivity on the surface of iron-based superconductor. Science 360, 182–186 (2018).

    ADS  Google Scholar 

  17. Wang, D. et al. Evidence for Majorana bound states in an iron-based superconductor. Science 362, 333–335 (2018).

    ADS  Google Scholar 

  18. Liu, Q. et al. Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe. Phys. Rev. X 8, 041056 (2018).

    Google Scholar 

  19. Xu, J.-P. et al. Experimental detection of a Majorana mode in the core of a magnetic vortex inside a topological insulator–superconductor Bi2Te3/NbSe2 heterostructure. Phys. Rev. Lett. 114, 017001 (2015).

    ADS  Google Scholar 

  20. Rinott, S. et al. Tuning across the BCS–BEC crossover in the multiband superconductor Fe1 + ySexTe1 − x: an angle-resolved photoemission study. Sci. Adv. 3, e1602372 (2017).

    ADS  Google Scholar 

  21. Hayashi, N. et al. Low-lying quasiparticle excitations around a vortex core in quantum limit. Phys. Rev. Lett. 80, 2921–2924 (1998).

    ADS  Google Scholar 

  22. Caroli, C., de Gennes, P. G. & Matricon, J. Bound Fermion states on a vortex line in a type II superconductor. Phys. Lett. 9, 307–309 (1964).

    ADS  MATH  Google Scholar 

  23. Gygi, F. & Schluter, M. Self-consistent electronic structure of a vortex line in a type-II superconductor. Phys. Rev. B 43, 7609–7621 (1990).

    ADS  Google Scholar 

  24. Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Rep. Prog. Phys. 75, 076501 (2012).

    ADS  Google Scholar 

  25. He, X.-B. et al. Nanoscale chemical phase separation in FeTe0.55Se0.45 as seen via scanning tunneling spectroscopy. Phys. Rev. B 83, 220502 (2011).

    ADS  Google Scholar 

  26. Lin, W.-Z. et al. Direct probe of interplay between local structure and superconductivity in FeTe0.55Se0.45. ACS Nano 7, 2634–2641 (2013).

    Google Scholar 

  27. Singh, U. R. et al. Spatial inhomogeneity of the superconducting gap and order parameter in FeSe0.4Te0.6. Phys. Rev. B 88, 155124 (2013).

    ADS  Google Scholar 

  28. Massee, F. et al. Imaging atomic-scale effects of high-energy ion irradiation on superconductivity and vortex pinning in Fe(Se,Te). Sci. Adv. 1, e1500033 (2015).

    ADS  Google Scholar 

  29. Suderow, H. et al. Imaging superconducting vortex cores and lattices with a scanning tunneling microscope. Supercond. Sci. Technol. 27, 063001 (2014).

    ADS  Google Scholar 

  30. Chen, M. et al. Discrete energy levels of Caroli–de Gennes–Martricon states in quantum limit in FeTe0.55Se0.45. Nat. Commun. 9, 970 (2018).

    ADS  Google Scholar 

  31. Yin, Z. P., Haule, K. & Kotliar, G. Spin dynamics and orbital–antiphase pairing symmetry in iron-based superconductors. Nat. Phys. 10, 845–850 (2014).

    Google Scholar 

  32. Khaymovich, I. M. et al. Vortex core states in superconducting graphene. Phys. Rev. B 79, 224506 (2009).

    ADS  Google Scholar 

  33. Jackiw, R. & Rossi, P. Zero modes of the vortex–fermion system. Nucl. Phys. B 190, 681–691 (1981).

    ADS  Google Scholar 

  34. Ghaemi, P. & Wilczek, F. Near-zero modes in superconducting graphene. Phys. Scr. 146, 014019 (2012).

    Google Scholar 

  35. Colbert, J. & Lee, P. A. Proposal to measure the quasiparticle poisoning time of Majorana bound states. Phys. Rev. B 89, 140505 (2014).

    ADS  Google Scholar 

  36. Liu, C.-X., Liu, D. E., Zhang, F.-C. & Chiu, C.-K. Protocol for reading out Majorana qubit and testing non-Abelian statistics. Preprint at https://arxiv.org/abs/1901.06083 (2019).

  37. Shan, L. et al. Observation of ordered vortices with Andreev bound states in Ba0.6K0.4Fe2As2. Nat. Phys. 7, 325–331 (2011).

    Google Scholar 

  38. Hanaguri, T. et al. Scanning tunneling microscopy/spectroscopy of vortices in LiFeAs. Phys. Rev. B 85, 214505 (2012).

    ADS  Google Scholar 

  39. Hess, H. F., Robinson, R. B. & Waszczak, J. V. Vortex-core structure observed with a scanning tunneling microscopy. Phys. Rev. Lett. 64, 2711–2714 (1990).

    ADS  Google Scholar 

  40. Kaneko, S.-I. et al. Quantum limiting behaviors of a vortex core in an anisotropic gap superconductor. J. Phys. Soc. Jpn 81, 063701 (2012).

    ADS  Google Scholar 

  41. Coldea, A. I. & Watson, M. D. The key ingredients of the electronic structure of FeSe. Annu. Rev. Condens. Matter Phys. 9, 125–146 (2018).

    ADS  Google Scholar 

  42. Hu, L.-H. et al. Theory of spin-selective Andreev reflection in the vortex core of a topological superconductor. Phys. Rev. B 94, 224501 (2016).

    ADS  Google Scholar 

  43. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    ADS  Google Scholar 

  44. Schubert, G. et al. Fate of topological-insulator surface states under strong disorder. Phys. Rev. B 85, 201105 (2012).

    ADS  Google Scholar 

  45. Sacksteder, V., Ohtsuki, T. & Kobayashi, K. Modification and control of topological insulator surface states using surface disorder. Phys. Rev. Appl. 3, 064006 (2015).

    ADS  Google Scholar 

  46. Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007).

    ADS  Google Scholar 

  47. Noguchi, R. et al. A weak topological insulator state in quasi-one-dimensional bismuth iodide. Nature 566, 518–522 (2019).

    ADS  Google Scholar 

  48. Qin, S.-S. et al. Topological vortex phase transitions in iron-based superconductors. Preprint at https://arxiv.org/abs/1901.03120 (2019).

  49. Shi, X. et al. FeTe1 - xSex monolayer films: towards the realization of high-temperature connate topological superconductivity. Sci. Bull. 62, 503–507 (2017).

    Google Scholar 

  50. Peng, X.-L. et al. Observation of topological transition in high-T c superconductor FeTe1 - xSex/SrTiO3(001) monolayers. Preprint at https://arxiv.org/abs/1903.05968 (2019).

Download references

Acknowledgements

We thank N.F. Yuan, C.-K. Chiu, C. Schrade, S.-S. Qin and R.-X. Zhang for helpful discussions and F.-Z. Yang, G.-J. Qian for technical assistance. The work at IOP is supported by grants from the Ministry of Science and Technology of China (2015CB921000, 2015CB921300 and 2016YFA0202300), the National Natural Science Foundation of China (11234014, 11574371 and 61390501), and the Chinese Academy of Sciences (XDB28000000 and XDB07000000). The work at MIT is supported by DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award no. DE-SC0019275. G.D.G. is supported by US DOE DE-SC0012704. J.S. and R.D.Z. are supported by the Center for Emergent Superconductivity, an EFRC funded by the US DOE.

Author information

Author notes

  1. These authors contributed equally: Lingyuan Kong, Shiyu Zhu, Michał Papaj, Hui Chen.

Authors and Affiliations

  1. Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, China

    Lingyuan Kong, Shiyu Zhu, Hui Chen, Lu Cao, Yuqing Xing, Wenyao Liu, Dongfei Wang, Peng Fan, Yujie Sun, Shixuan Du, Hong-Jun Gao & Hong Ding

  2. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Lingyuan Kong, Shiyu Zhu, Lu Cao, Yuqing Xing, Wenyao Liu, Dongfei Wang, Peng Fan & Hong-Jun Gao

  3. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Michał Papaj, Hiroki Isobe & Liang Fu

  4. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China

    Yujie Sun, Shixuan Du, Hong-Jun Gao & Hong Ding

  5. Songshan Lake Materials Laboratory, Dongguan, Guangdong, China

    Yujie Sun & Hong Ding

  6. Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY, USA

    John Schneeloch, Ruidan Zhong & Genda Gu

Authors
  1. Lingyuan Kong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiyu Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michał Papaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hui Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lu Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hiroki Isobe
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yuqing Xing
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Wenyao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Dongfei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Peng Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Yujie Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Shixuan Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. John Schneeloch
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Ruidan Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. Genda Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Liang Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. Hong-Jun Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  18. Hong Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

H.D. and H.-J.G. designed the experiments. S.Z., L.C., H.C. and Y.X. performed the STM experiments with assistance from L.K., W.L., D.W., P.F. and S.D. M.P., H.I. and L.F. provided theoretical models and simulations. J.S., R.Z. and G.D.G. provided samples. L.K., S.Z. and H.D. analysed experiment data with input from all other authors. L.K., M.P. and S.Z. plotted figures with input from all other authors. All authors participated in writing the manuscript. H.D., H.-J.G. and L.F. supervised the project.

Corresponding authors

Correspondence to Liang Fu, Hong-Jun Gao or Hong Ding.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information: Nature Physics thanks Peter Wahl and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Additional theoretical and experimental details, Supplementary Figs. 1–11 and refs. 1–41.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kong, L., Zhu, S., Papaj, M. et al. Half-integer level shift of vortex bound states in an iron-based superconductor. Nat. Phys. 15, 1181–1187 (2019). https://doi.org/10.1038/s41567-019-0630-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-019-0630-5

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing