Skip to main content
SpringerLink
Log in

Chiral topological superfluids in the attractive Haldane-Hubbard model with opposite Zeeman energy at two sublattice sites

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Ultracold atoms in an optical lattice provide a platform for the realization of the topological superfluid. Motivated by the recent cold atom realization of the topological Haldane model [G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, Th. Uehlinger, D. Greif, T. Esslinger, Nature 515, 237 (2014)], in this paper we propose an alternative way to realize chiral topological superfluids with Chern number 𝒞 = 1 and 2 by considering attractive Haldane-Hubbard model with the site-dependent Zeeman field. The topological superfluids support the robust chiral edge modes, and the one-half of flux quantum-π flux in 𝒞 = 1 topological superfluid traps a pair of Majorana zero modes different from the case in the spinless p x ± i p y topological superfluid due to the extra freedom of A-B sublattices. In addition, we discuss the superfluid stability and calculate Kosterlitz-Thouless transition temperature by random-phase-approximation approach.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Das Sarma, M. Freedman, C. Nayak, S.H. Simon, A. Stern, Rev. Mod. Phys. 80, 1083 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. D.A. Ivanov, Phys. Rev. Lett. 86, 268 (2001)

    Article  ADS  Google Scholar 

  3. J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M.R.A. Fisher, Nat. Phys. 7, 412 (2011)

    Article  Google Scholar 

  4. S. Das Sarma, M. Freedman, C. Nayak, Phys. Rev. Lett. 94, 166802 (2005)

    Article  ADS  Google Scholar 

  5. N. Read and D. Green, Phys. Rev. B 61, 10267 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. X.L. Qi, T.L. Hughes, S.C. Zhang, Phys. Rev. B 82, 184516 (2010)

    Article  ADS  Google Scholar 

  8. J.D. Sau, R.M. Lutchyn, S. Tewari, S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010)

    Article  ADS  Google Scholar 

  9. R.M. Lutchyn, J.D. Sau, S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010)

    Article  ADS  Google Scholar 

  10. Y. Oreg, G. Refael, F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010)

    Article  ADS  Google Scholar 

  11. M. Sato, Y. Takahashi, S. Fujimoto, Phys. Rev. Lett. 103, 020401 (2009)

    Article  ADS  Google Scholar 

  12. G.E. Volovik, Zh. Eksp. Teor. Fiz. 94, 123 (1988)

    Google Scholar 

  13. M.R. Zirnbauer, J. Math. Phys. 37, 4986 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. A. Altland, M.R. Zirnbauer, Phys. Rev. B 55, 1142 (1997)

    Article  ADS  Google Scholar 

  15. A.Y. Kitaev, AIP Conf. Proc. 22, 1134 (2009)

    Google Scholar 

  16. Sh. Ryu, A.P. Schnyder, A. Furusaki, A.W.W. Ludwig, New J. Phys. 12, 065010 (2010)

    Article  ADS  Google Scholar 

  17. S. Tewari, S. Das Sarma, D.-H. Lee, Phys. Rev. Lett. 99, 037001 (2007)

    Article  ADS  Google Scholar 

  18. Zhengkun Fu, Lianghui Huang, Zengming Meng, Pengjun Wang, Long Zhang, Shizhong Zhang, Hui Zhai, Peng Zhang, Jing Zhang, Nat. Phys. 10, 110 (2014)

    Article  Google Scholar 

  19. C. Zhang, S. Tewari, R.M. Lutchyn, S. Das Sarma, Phys. Rev. Lett. 101, 160401 (2008)

    Article  ADS  Google Scholar 

  20. X.-J. Liu, K.T. Law, T.K. Ng, Phys. Rev. Lett. 112, 086401 (2014)

    Article  ADS  Google Scholar 

  21. F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  22. L.B. Shao, S.-L. Zhu, L. Sheng, D.Y. Xing, Z.D. Wang, Phys. Rev. Lett. 101, 246810 (2008)

    Article  ADS  Google Scholar 

  23. G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, Th. Uehlinger, D. Greif, T. Esslinger, Nature 515, 237 (2014)

    Article  ADS  Google Scholar 

  24. J. He, S.P. Kou, Y. Liang, S.P. Feng, Phys. Rev. B 83, 205116 (2011)

    Article  ADS  Google Scholar 

  25. J. He, Y.H. Zong, S.P. Kou, Y. Liang, S.P. Feng, Phys. Rev. B. 84, 035127 (2011)

    Article  ADS  Google Scholar 

  26. J. He, Y. Liang, S.P. Kou, Phys. Rev. B 85, 205107 (2012)

    Article  ADS  Google Scholar 

  27. I.B. Spielman, Ann. Phys. 10, 797 (2013)

    Article  MathSciNet  Google Scholar 

  28. N. Goldman, J. Dalibard, A. Dauphin, F. Gerbier, M. Lewenstein, P. Zoller, I.B. Spielman, Proc. Natl. Acad. Sci. 110, 6736 (2013)

    Article  ADS  Google Scholar 

  29. N. Goldman, J. Beugnon, F. Gerbier, Phys. Rev. Lett. 108, 255303 (2012)

    Article  ADS  Google Scholar 

  30. V.L. Berezinskii, Sov. Phys. J. Exp. Theor. Phys. 34, 610 (1972)

    ADS  Google Scholar 

  31. J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)

    Article  ADS  Google Scholar 

  32. M. Iskin, C.A.R. Sá de Melo, Phys. Rev. B 72, 024512 (2005)

    Article  ADS  Google Scholar 

  33. E. Taylor, A. Griffin, N. Fukushima, Y. Ohashi, Phys. Rev. A 74, 063626 (2006)

    Article  ADS  Google Scholar 

  34. E. Zhao, A. Paramekanti, Phy. Rev. Lett. 97, 230404 (2006)

    Article  ADS  Google Scholar 

  35. C. Chin et al., Rev. Mod. Phys. 82, 1225 (2010)

    Article  ADS  Google Scholar 

  36. T. Köhler, K. Góral, Rev. Mod. Phys. 78, 1311 (2006)

    Article  ADS  Google Scholar 

  37. Y.-J. Lin, R.L. Compton, K. Jiménez-García, J.V. Porto, I.B. Spielman, Nature 462, 628 (2009)

    Article  ADS  Google Scholar 

  38. A.M. Dudarev, R.B. Diener, I. Carusotto, Q. Niu, Phys. Rev. Lett. 92, 153005 (2004)

    Article  ADS  Google Scholar 

  39. D. Makogon, I.B. Spielman, C. Morais Smith, Europhys. Lett. 97, 33002 (2012)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Xi’an Technological University, Xi’an, 710032, P.R. China

    Ya-Jie Wu & Ning Li

  2. Department of Physics, Beijing Normal University, Beijing, 100875, P.R. China

    Su-Peng Kou

Authors
  1. Ya-Jie Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ning Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Su-Peng Kou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya-Jie Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, YJ., Li, N. & Kou, SP. Chiral topological superfluids in the attractive Haldane-Hubbard model with opposite Zeeman energy at two sublattice sites. Eur. Phys. J. B 88, 255 (2015). https://doi.org/10.1140/epjb/e2015-60412-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2015-60412-y

Keywords

Search

Navigation