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

Regular Article

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 px ± ipy 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.

Keywords

Solid State and Materials 

References

  1. 1.
    S. Das Sarma, M. Freedman, C. Nayak, S.H. Simon, A. Stern, Rev. Mod. Phys. 80, 1083 (2008) MATHMathSciNetCrossRefADSGoogle Scholar
  2. 2.
    D.A. Ivanov, Phys. Rev. Lett. 86, 268 (2001)CrossRefADSGoogle Scholar
  3. 3.
    J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M.R.A. Fisher, Nat. Phys. 7, 412 (2011)CrossRefGoogle Scholar
  4. 4.
    S. Das Sarma, M. Freedman, C. Nayak, Phys. Rev. Lett. 94, 166802 (2005) CrossRefADSGoogle Scholar
  5. 5.
    N. Read and D. Green, Phys. Rev. B 61, 10267 (2000) CrossRefADSGoogle Scholar
  6. 6.
    L. Fu and C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008) CrossRefADSGoogle Scholar
  7. 7.
    X.L. Qi, T.L. Hughes, S.C. Zhang, Phys. Rev. B 82, 184516 (2010) CrossRefADSGoogle Scholar
  8. 8.
    J.D. Sau, R.M. Lutchyn, S. Tewari, S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010)CrossRefADSGoogle Scholar
  9. 9.
    R.M. Lutchyn, J.D. Sau, S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010)CrossRefADSGoogle Scholar
  10. 10.
    Y. Oreg, G. Refael, F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010) CrossRefADSGoogle Scholar
  11. 11.
    M. Sato, Y. Takahashi, S. Fujimoto, Phys. Rev. Lett. 103, 020401 (2009) CrossRefADSGoogle Scholar
  12. 12.
    G.E. Volovik, Zh. Eksp. Teor. Fiz. 94, 123 (1988)Google Scholar
  13. 13.
    M.R. Zirnbauer, J. Math. Phys. 37, 4986 (1996) MATHMathSciNetCrossRefADSGoogle Scholar
  14. 14.
    A. Altland, M.R. Zirnbauer, Phys. Rev. B 55, 1142 (1997) CrossRefADSGoogle Scholar
  15. 15.
    A.Y. Kitaev, AIP Conf. Proc. 22, 1134 (2009) Google Scholar
  16. 16.
    Sh. Ryu, A.P. Schnyder, A. Furusaki, A.W.W. Ludwig, New J. Phys. 12, 065010 (2010) CrossRefADSGoogle Scholar
  17. 17.
    S. Tewari, S. Das Sarma, D.-H. Lee, Phys. Rev. Lett. 99, 037001 (2007) CrossRefADSGoogle Scholar
  18. 18.
    Zhengkun Fu, Lianghui Huang, Zengming Meng, Pengjun Wang, Long Zhang, Shizhong Zhang, Hui Zhai, Peng Zhang, Jing Zhang, Nat. Phys. 10, 110 (2014) CrossRefGoogle Scholar
  19. 19.
    C. Zhang, S. Tewari, R.M. Lutchyn, S. Das Sarma, Phys. Rev. Lett. 101, 160401 (2008)CrossRefADSGoogle Scholar
  20. 20.
    X.-J. Liu, K.T. Law, T.K. Ng, Phys. Rev. Lett. 112, 086401 (2014) CrossRefADSGoogle Scholar
  21. 21.
    F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988) MathSciNetCrossRefADSGoogle Scholar
  22. 22.
    L.B. Shao, S.-L. Zhu, L. Sheng, D.Y. Xing, Z.D. Wang, Phys. Rev. Lett. 101, 246810 (2008) CrossRefADSGoogle Scholar
  23. 23.
    G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, Th. Uehlinger, D. Greif, T. Esslinger, Nature 515, 237 (2014) CrossRefADSGoogle Scholar
  24. 24.
    J. He, S.P. Kou, Y. Liang, S.P. Feng, Phys. Rev. B 83, 205116 (2011) CrossRefADSGoogle Scholar
  25. 25.
    J. He, Y.H. Zong, S.P. Kou, Y. Liang, S.P. Feng, Phys. Rev. B. 84, 035127 (2011) CrossRefADSGoogle Scholar
  26. 26.
    J. He, Y. Liang, S.P. Kou, Phys. Rev. B 85, 205107 (2012) CrossRefADSGoogle Scholar
  27. 27.
    I.B. Spielman, Ann. Phys. 10, 797 (2013)MathSciNetCrossRefGoogle Scholar
  28. 28.
    N. Goldman, J. Dalibard, A. Dauphin, F. Gerbier, M. Lewenstein, P. Zoller, I.B. Spielman, Proc. Natl. Acad. Sci. 110, 6736 (2013) CrossRefADSGoogle Scholar
  29. 29.
    N. Goldman, J. Beugnon, F. Gerbier, Phys. Rev. Lett. 108, 255303 (2012) CrossRefADSGoogle Scholar
  30. 30.
    V.L. Berezinskii, Sov. Phys. J. Exp. Theor. Phys. 34, 610 (1972)ADSGoogle Scholar
  31. 31.
    J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)CrossRefADSGoogle Scholar
  32. 32.
    M. Iskin, C.A.R. Sá de Melo, Phys. Rev. B 72, 024512 (2005) CrossRefADSGoogle Scholar
  33. 33.
    E. Taylor, A. Griffin, N. Fukushima, Y. Ohashi, Phys. Rev. A 74, 063626 (2006) CrossRefADSGoogle Scholar
  34. 34.
    E. Zhao, A. Paramekanti, Phy. Rev. Lett. 97, 230404 (2006) CrossRefADSGoogle Scholar
  35. 35.
    C. Chin et al., Rev. Mod. Phys. 82, 1225 (2010) CrossRefADSGoogle Scholar
  36. 36.
    T. Köhler, K. Góral, Rev. Mod. Phys. 78, 1311 (2006) CrossRefADSGoogle Scholar
  37. 37.
    Y.-J. Lin, R.L. Compton, K. Jiménez-García, J.V. Porto, I.B. Spielman, Nature 462, 628 (2009) CrossRefADSGoogle Scholar
  38. 38.
    A.M. Dudarev, R.B. Diener, I. Carusotto, Q. Niu, Phys. Rev. Lett. 92, 153005 (2004) CrossRefADSGoogle Scholar
  39. 39.
    D. Makogon, I.B. Spielman, C. Morais Smith, Europhys. Lett. 97, 33002 (2012)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Science, Xi’an Technological UniversityXi’anP.R. China
  2. 2.Department of PhysicsBeijing Normal UniversityBeijingP.R. China

Personalised recommendations