Skip to main content
SpringerLink
Log in

Berry phases and zero-modes in toroidal topological insulator

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

Abstract

An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential, which ultimately yields the zero-modes whose wave-functions harmonically oscillate around the toroidal surface. In addition, two distinct Berry phases are predicted to take place by the virtue of the toroidal topology.

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. X.L. Qi, S.C. Zhang, Phys. Today 63, 33 (2010)

    Article  ADS  Google Scholar 

  2. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

    Article  ADS  Google Scholar 

  3. X.L. Qi, S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  4. Y. Ando, J. Phys. Soc. Jpn 82, 102001 (2013)

    Article  ADS  Google Scholar 

  5. S.Q. Shen, Topological Insulators: Dirac Equation in Condensed Matters (Springer, Berlin, 2012)

  6. G. Napoli, L. Vergori, Phys. Rev. Lett. 108, 207803 (2012)

    Article  ADS  Google Scholar 

  7. G. Napoli, L. Vergori, Int. J. Non-Linear Mech. 49, 66 (2013)

    Article  ADS  Google Scholar 

  8. J.M. Fonseca, W.A. Moura-Melo, A.R. Pereira, Phys. Lett. A 374, 4359 (2010)

    Article  ADS  Google Scholar 

  9. A. Cortijo, M.A.H. Vozmediano, Nucl. Phys. B 763, 293 (2007)

    Article  ADS  Google Scholar 

  10. V.L. Carvalho-Santos, R.G. Elias, J.M. Fonseca, D. Altbir, J. Appl. Phys. 117, 17E518 (2015)

    Article  Google Scholar 

  11. A. Vansteenkiste, M. Weigand, M. Curcic, H. Stoll, G. Schtz, B. Van Waeyenberge, New J. Phys. 11, 063006 (2009)

    Article  ADS  Google Scholar 

  12. P.S.C. Vilas-Boas, R.G. Elias, D. Altbir, J.M. Fonseca, V.L. Carvalho-Santos, Phys. Lett. A 379, 47 (2015)

    Article  ADS  Google Scholar 

  13. V.L. Carvalho-Santos, R.G. Elias, D. Altbir, J.M. Fonseca, J. Magn. Magn. Mater. 391, 179 (2015)

    Article  ADS  Google Scholar 

  14. V.L. Carvalho-Santos, F.A. Apolonio, N.M. Oliveira-Neto, Phys. Lett. A 377, 1308 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  15. F. Zhang, C.L. Kane, E.J. Mele, Phys. Rev. B 86, 081303 (2012)

    Article  ADS  Google Scholar 

  16. P.G. Silvestrov, P.W. Brouwer, E.G. Mishchenko, Phys. Rev. B 86, 075302 (2012)

    Article  ADS  Google Scholar 

  17. K.I. Imura, Y. Yoshimura, Y. Takane, T. Fukui, Phys. Rev. B 86, 235119 (2012)

    Article  ADS  Google Scholar 

  18. V. Parente, P. Lucignano, P. Vitale, A. Tagliacozzo, F. Guinea, Phys. Rev. B 83, 075424 (2011)

    Article  ADS  Google Scholar 

  19. D.-H. Lee, Phys. Rev. Lett. 103, 196804 (2009)

    Article  ADS  Google Scholar 

  20. Y. Takane, K.I. Imura, J. Phys. Soc. Jpn 82, 074712 (2013)

    Article  ADS  Google Scholar 

  21. J.M. Fonseca, W.A. Moura-Melo, A.R. Pereira, J. Appl. Phys. 111, 064913 (2012)

    Article  ADS  Google Scholar 

  22. R. Egger, A. Zazunov, A.L. Yeyati, Phys. Rev. Lett. 105, 136403 (2010)

    Article  ADS  Google Scholar 

  23. L.-T. Huang, D.-H. Lee, Phys. Rev. B 84, 193106 (2011)

    Article  ADS  Google Scholar 

  24. J.P. Dahlhaus, C.-Y. Hou, A.R. Akhmerov, C.W.J. Beenakker, Phys. Rev. B 82, 085312 (2010)

    Article  ADS  Google Scholar 

  25. F. Zhang, C.L. Kane, E.J. Mele, Phys. Rev. B 86, 081303(R) (2012)

    Article  ADS  Google Scholar 

  26. F.M.H. Crompvoets, H.L. Bethlem, R.T. Jongma, G. Meijer, Nature 411, 174 (2001)

    Article  ADS  Google Scholar 

  27. S. Gupta, K.W. Murch, K.L. Moore, T.P. Purdy, D.M. Stamper-Kurn, Phys. Rev. Lett. 95, 143201 (2005)

    Article  ADS  Google Scholar 

  28. B.I. Dunlap, Phys. Rev. B 46, 1933 (1992)

    Article  ADS  Google Scholar 

  29. J. Liu, H. Dai, J.H. Hafner, D.T. Colbert, R.E. Smalley, S.T. Tans, C. Dekker, Nature 385, 780 (1997)

    Article  ADS  Google Scholar 

  30. S. Zhao, S. Zhang, M. Xia, E. Zhang, X. Zuo, Phys. Lett. A 331, 238 (2004)

    Article  ADS  Google Scholar 

  31. H. Watanabe, C. Manabe, T. Shigematsu, M. Shimizu, Appl. Phys. Lett. 78, 2928 (2001)

    Article  ADS  Google Scholar 

  32. V.L. Carvalho-Santos, A.R. Moura, W.A. Moura-Melo, A.R. Pereira, Phys. Rev. B 77, 134450 (2008)

    Article  ADS  Google Scholar 

  33. V.L. Carvalho-Santos, W.A. Moura-Melo, A.R. Pereira, J. Appl. Phys. 108, 094310 (2010)

    Article  ADS  Google Scholar 

  34. H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang, Nat. Phys. 5, 438 (2009)

    Article  Google Scholar 

  35. C.-X. Liu, X.-L. Qi, H. Zhang, X. Dai, Z. Fang, S.-C. Zhang, Phys. Rev. B 82, 045122 (2010)

    Article  ADS  Google Scholar 

  36. M. Nakahara, Geometry, Topology and Physics (Taylor & Francis, 1990)

  37. M.A.H. Vozmediano, M.I. Katsnelson, F. Guinea, Phys. Rep. 496, 109 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  38. Y. Zhang, A. Vishwanath, Phys. Rev. Lett. 105, 206601 (2010)

    Article  ADS  Google Scholar 

  39. M. Ansourian, Phys. Lett. B 70, 301 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  40. J.K. Pachvos, M. Stone, Int. J. Mod. Phys. B 21, 5113 (2007)

    Article  ADS  Google Scholar 

  41. R. Jackiw, Phys. Scr. T146, 014005 (2012)

    Article  ADS  Google Scholar 

  42. R. Jackiw, Phys. Rev. D 29, 2375 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  43. J.M. Fonseca, W.A. Moura-Melo, A.R. Pereira, Eur. Phys. J. B 86, 481 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, Brazil

    Jakson M. Fonseca, Winder A. Moura-Melo & Afranio R. Pereira

  2. Instituto Federal de Educação, Ciência e Tecnologia Baiano, 48970-000, Senhor do Bonfim, Brazil

    Vagson L. Carvalho-Santos

  3. Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Santiago, Chile

    Vagson L. Carvalho-Santos

Authors
  1. Jakson M. Fonseca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vagson L. Carvalho-Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Winder A. Moura-Melo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Afranio R. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jakson M. Fonseca.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fonseca, J., Carvalho-Santos, V., Moura-Melo, W. et al. Berry phases and zero-modes in toroidal topological insulator. Eur. Phys. J. B 89, 153 (2016). https://doi.org/10.1140/epjb/e2016-70076-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2016-70076-8

Keywords

Search

Navigation