Edge states and topological orders in the spin liquid phases of star lattice

  • Guang-Yao Huang
  • Shi-Dong LiangEmail author
  • Dao-Xin YaoEmail author
Regular Article


The integer quantum Hall effect (IQHE) on star lattice is studied through edge states in the context of spin liquid. We apply the bulk-edge correspondence to the star lattice and analyze the edge states and their topological orders for different spin liquid phases. The band structures and Chern number depend on the local spontaneous magnetic flux and hopping parameters due to the breaking of the time reversal and space inversion symmetries. We give the characteristics of bulk and edge energy structures and their corresponding Chern numbers in the uniform, nematic and chiral spin liquids. In particular, we obtain analytically the phase diagram of the topological orders for the chiral spin liquid states SL[φ,φ,−2φ], where φ is the magnetic flux in two triangles and a dodecagon in one unit cell. Moreover, because of the direct connection between Chern number and the conductance of IQHE, we can further distinguish the different spin liquid phases through a Hall measurement.


Mesoscopic and Nanoscale Systems 


  1. 1.
    D.J. Thouless, M. Kohmoto, M.P. Nightingale, M. den Nijs, Phys. Rev. Lett. 49, 405 (1982) ADSCrossRefGoogle Scholar
  2. 2.
    Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993) MathSciNetADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Y. Hatsugai, Phys. Rev. B 48, 11851 (1993) ADSCrossRefGoogle Scholar
  4. 4.
    N. Goldman, A. Kubasiak, A. Bermudez, P. Gaspard, M. Lewenstein, M.A. Martin-Delgado, Phys. Rev. Lett. 103, 035301 (2009) ADSCrossRefGoogle Scholar
  5. 5.
    N. Goldman, I. Satija, P. Nikolic, A. Bermudez, M.A. Martin-Delgado, M. Lewenstein, I.B. Spielman, Phys. Rev. Lett. 105, 255302 (2010) ADSCrossRefGoogle Scholar
  6. 6.
    M. Arikawa, S. Tanaya, I. Maruyama, Y. Hatsugai, Phys. Rev. B 79, 205107 (2009) ADSCrossRefGoogle Scholar
  7. 7.
    A. Bermudez, D. Patane, L. Amico, M.A. Martin-Delgado, Phys. Rev. Lett. 102, 135702 (2009) ADSCrossRefGoogle Scholar
  8. 8.
    A. Bermudez, L. Amico, M.A. Martin-Delgado, New J. Phys. 12, 055014 (2010) ADSCrossRefGoogle Scholar
  9. 9.
    Y. Hatsugai, T. Fukui, H. Aoki, Phys. Rev. B 74, 205414 (2006) ADSCrossRefGoogle Scholar
  10. 10.
    Z. Wang, P. Zhang, Phys. Rev. B 77, 125119 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    Z. Wang, P. Zhang, New J. Phys. 11, 123014 (2010) CrossRefGoogle Scholar
  12. 12.
    A. Kitaev, Ann. Phys. 321, 2 (2006) MathSciNetADSCrossRefzbMATHGoogle Scholar
  13. 13.
    H. Yao, S.A. Kivelson, Phys. Rev. Lett. 99, 247203 (2007) ADSCrossRefGoogle Scholar
  14. 14.
    S. Dusuel, K.P. Schmidt, J. Vidal, R.L. Zaffino, Phys. Rev. B 78, 125102 (2008) ADSCrossRefGoogle Scholar
  15. 15.
    G. Kells, D. Mehta, J.K. Slingerland, J. Vala, Phys. Rev. B 81, 104429 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    J. Wen, A. Rüegg, J.C.C. Wang, G.A. Fiete, Phys. Rev. B 82, 075125 (2010) ADSCrossRefGoogle Scholar
  17. 17.
    Y.Z. Zheng, M.L. Tong, W. Xue, W.X. Zhang, X.M. Chen, F. Grandjean, G.J. Long, Angew. Chem. Int. Ed. 46, 6076 (2007) CrossRefGoogle Scholar
  18. 18.
    B.J. Yang, A. Paramekanti, Y.B. Kim, Phys. Rev. B 81, 134418 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    P.G. Harper, Proc. Phys. Soc. London A 68, 874 (1955) ADSCrossRefzbMATHGoogle Scholar
  20. 20.
    H. Aoki, M. Ando, H. Matsumura, Phys. Rev. B 54, R17296 (1996) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics and Engineering, Sun Yat-sen UniversityGuangzhouP.R. China

Personalised recommendations