Topological phase diagram of a Kitaev ladder

  • Alfonso Maiellaro
  • Francesco Romeo
  • Roberta Citro
Regular Article
Part of the following topical collections:
  1. Topological States of Matter: Theory and Applications


We investigate the topological properties of a Kitaev ladder, i.e., a system made of two Kitaev chains coupled together by transversal hopping and pairing term, t1 and Δ1, respectively. Using the Chern number invariant, we present the topological phase diagram of the system. It is shown that beyond a non-topological phase, the system exhibits a topological phase either with four or two Majorana (zero energy) modes. In particular, we find that for some critical values of the transversal hopping t1, and at a given transversal paring Δ1, the topological phase survives also when the Kitaev criterion for the single chain (Δ > 0,   |μ| < 2t) is violated. Using a tight-binding analysis for a finite-size system we numerically check the bulk-edge correspondence.


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  1. 1.
    J.K. Pachos, Introduction to topological quantum computation (Cambridge University Press, Cambridge, 2012) Google Scholar
  2. 2.
    A. Kitaev, Ann. Phys. 303, 2 (2003) ADSCrossRefGoogle Scholar
  3. 3.
    C. Nayak, S.H. Simon, A. Stern, M. Freedmanand, S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008) ADSCrossRefGoogle Scholar
  4. 4.
    C. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013) ADSCrossRefGoogle Scholar
  5. 5.
    A.Y. Kitaev, Phys. Usp. 44, 131 (2001) ADSCrossRefGoogle Scholar
  6. 6.
    L. Fu, C. Kane, Phys. Rev. Lett. 100, 096407 (2008) ADSCrossRefGoogle Scholar
  7. 7.
    V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A. Brakkers, L.P. Kouwenhoven, Science 336, 1003 (2012) ADSCrossRefGoogle Scholar
  8. 8.
    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) ADSCrossRefGoogle Scholar
  9. 9.
    A.C. Potter, P.A. Lee, Phys. Rev. Lett. 105, 227003 (2010) ADSCrossRefGoogle Scholar
  10. 10.
    M. Wimmer, A.R. Akhmerov, M.V. Medvedyeva, J. Tworzydlo, C.W.J. Beenakker, Phys. Rev. Lett. 105, 046803 (2010) ADSCrossRefGoogle Scholar
  11. 11.
    B. Zhou, S.-Q. Shen, Phys. Rev. B 84, 054532 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    R. Wakatsuki, M. Ezawa, N. Nagaosa, Phys. Rev. B 89, 174514 (2014) ADSCrossRefGoogle Scholar
  13. 13.
    C. Schrade, M. Thakurathi, C. Reeg, S. Hoffman, J. Klinovaja, D. Loss, Phys. Rev. B 96, 035306 (2017) ADSCrossRefGoogle Scholar
  14. 14.
    L. Li, C. Yang, S. Chen, Eur. Phys. J. B 89, 195 (2016) ADSCrossRefGoogle Scholar
  15. 15.
    B. Huagan, C.F. Chan, J. Li, M. Gong, Phys. Rev. B 91, 134512 (2015) ADSCrossRefGoogle Scholar
  16. 16.
    B.-Z. Zhou, D.-H. Xu, B. Zhou, Phys. Lett. A 381, 2426 (2017) ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A. Pàli, J.K. Asbòth, L. Oroszlány, A short course on topological insulators: band structure and edge states, in Lecture notes on physics (Springer, Berlin, 2016), Vol. 919 Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alfonso Maiellaro
    • 1
  • Francesco Romeo
    • 1
  • Roberta Citro
    • 1
    • 2
  1. 1.Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di SalernoFisciano (SA)Italy
  2. 2.Spin-CNR, Università di SalernoFisciano (SA)Italy

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