Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Topological phases of a Kitaev tie

  • 4 Accesses

Abstract

We investigate the topological properties of a Kitaev chain in the shape of a legged-ring, which is here referred to as Kitaev tie. We demonstrate that the Kitaev tie is a frustrated system in which topological properties are determined by the position of the movable bond (the tie knot). We determine the phase diagram of the system as a function of the knot position and chemical potential, also discussing the effects of topological frustration. The stability of the topological Kitaev tie is addressed by a careful analysis of the system free energy.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    A.Y. Kitaev, Physics-Uspekhi 44, 131 (2001)

  2. 2.

    L. Fu, C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008)

  3. 3.

    V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, Science 336, 1003 (2012)

  4. 4.

    S. Nadj-Perge, I.K. Drozdov, B.A. Bernevig, A. Yazdani, Phys. Rev. B 88, 020407(R) (2013)

  5. 5.

    S. Nadj-Perge, I.K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A.H. MacDonald, B.A. Bernevig, A. Yazdani, Science 346, 602 (2014)

  6. 6.

    C.W.J. Beenakker, Ann. Rev. Condens. Matter Phys. 4, 113 (2013)

  7. 7.

    R. Aguado, La Rivista Del Nuovo Cimento 40, 523 (2017)

  8. 8.

    M. Mazziotti, N. Scopigno, M. Grilli, S. Caprara, Condens. Matter 3, 37 (2018)

  9. 9.

    A. Maiellaro, F. Romeo, R. Citro, Eur. Phys. J. Special Topics 227, 1397 (2018)

  10. 10.

    A. Maiellaro, F. Romeo, C.A. Perroni, V. Cataudella, R. Citro, Nanomaterials 9, 894 (2019)

  11. 11.

    J. Liu, A.C. Potter, K.T. Law, P.A. Lee, Phys. Rev. Lett. 109, 267002 (2012)

  12. 12.

    C.-X. Liu, J.D. Sau, S. Das Sarma, Phys. Rev. B 97, 214502 (2018)

  13. 13.

    C. Fleckenstein, F. Domínguez, N. Traverso Ziani, B. Trauzettel, Phys. Rev. B 97, 155425 (2018)

  14. 14.

    T.S. Jespersen, J. Nygard, Nano Lett. 5, 1838 (2005)

  15. 15.

    G. Refael, J. Heo, M. Bockrath, Phys. Rev. Lett. 98, 246803 (2007)

  16. 16.

    J. Li, Y.He, Y. Han, K. Liu, J. Wang, Q. Li, S. Fan, K. Jiang, Nano Lett. 12, 4095 (2012)

  17. 17.

    A. Kasumov, R. Deblock, M. Kociak, B. Reulet, H. Bouchiat, I. Khodos, Y. Gorbatov, V. Volkov, C. Journet, O. Stephan, M. Burghard, C. R. Acad. Sci. Mech. Phys. Astron. 327, 933 (1999)

  18. 18.

    J.A. Robinson, E.S. Snow, Ş.C. Bǎdescu, T.L. Reinecke, F.K. Perkins, Nano Lett. 6, 1747 (2006)

  19. 19.

    D. Sticlet, C. Bena, P. Simon, Phys. Rev. Lett. 108, 096802 (2012)

  20. 20.

    D. Chevallier, D. Sticlet, P. Simon, C. Bena, Phys. Rev. B 85, 235307 (2012)

  21. 21.

    E. Perfetto, Phys. Rev. Lett. 110, 087001 (2013)

  22. 22.

    P.-G. de Gennes, Superconductivity of Metals and Alloys, Advanced Book Program (Perseus Books, Reading, MA, 1999)

  23. 23.

    W. Liang, M. Bockrath, D. Bozovic, J.H. Hafner, M. Tinkham, H. Park, Nature 411, 665 (2001)

  24. 24.

    R. Bustos-Marún, G. Refael, F. von Oppen, Phys. Rev. Lett. 111, 060802 (2013)

  25. 25.

    W. DeGottardi, D. Sen, S. Vishveshwara, New J. Phys. 13, 065028 (2011)

  26. 26.

    S.S. Hegde, S. Vishveshwara, Phys. Rev. B 94, 115166 (2016)

  27. 27.

    N. Lambert, Y.-N. Chen, Y.-C. Cheng, C.-M. Li, G.-Y. Chen, F. Nori, Nat. Phys. 9, 10 (2013)

Download references

Author information

Correspondence to Alfonso Maiellaro.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Maiellaro, A., Romeo, F. & Citro, R. Topological phases of a Kitaev tie. Eur. Phys. J. Spec. Top. 229, 637–646 (2020). https://doi.org/10.1140/epjst/e2019-900180-x

Download citation