Skip to main content
SpringerLink
Log in

Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface

  • Condensed Matter
  • Published:
JETP Letters Aims and scope Submit manuscript

Abstract

We consider the dimensional crossover in the topological matter, which involves the transformation of different types of topologically protected zeroes in the fermionic spectrum. In the considered case, the multiple Dirac (Fermi) point in quasi 2-dimensional system evolves into the flat band on the surface of the 3-dimensional system when the number of atomic layers increases. This is accompanied by formation of the spiral nodal lines in the bulk. We also discuss the topological quantum phase transition at which the surface flat band shrinks and changes its chirality, while the nodal spiral changes its helicity.

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. G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).

    MATH  Google Scholar 

  2. P. Hořava, Phys. Rev. Lett. 95, 016405 (2005).

    Article  ADS  Google Scholar 

  3. V. A. Khodel and V. R. Shaginyan, JETP Lett. 51, 553 (1990).

    ADS  Google Scholar 

  4. G. E. Volovik, JETP Lett. 53, 222 (1991).

    ADS  Google Scholar 

  5. G. E. Volovik, in Quantum Analogues: From Phase Transitions to Black Holes and Cosmology, Ed. by W. G. Unruh and R. Schützhold, Springer Lecture Notes in Physics 718, 31 (2007); cond-mat/0601372.

  6. V. R. Shaginyan, M. Ya. Amusia, A. Z. Msezane, and K. G. Popov, Phys. Rep. 492, 31 (2010).

    Article  ADS  Google Scholar 

  7. N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667 (1991).

    Article  ADS  Google Scholar 

  8. G. E. Volovik, JETP Lett. 59, 830 (1994).

    ADS  Google Scholar 

  9. T. Sh. Misirpashaev and G. E. Volovik, Physica B 210, 338 (1995).

    Article  ADS  Google Scholar 

  10. Sung-Sik Lee, Phys. Rev. D 79, 086006 (2009).

    Article  ADS  Google Scholar 

  11. F. Guinea, A. H. Castro Neto, and N. M. R. Peres, Phys. Rev. B 73, 245426 (2006).

    Article  ADS  Google Scholar 

  12. A. P. Schnyder and Shinsei Ryu, arXiv:1011.1438.

  13. G. E. Volovik and V. A. Konyshev, JETP Lett. 47, 250 (1988).

    ADS  Google Scholar 

  14. J. L. Manes, F. Guinea, and M. A. H. Vozmediano, Phys. Rev. B 75, 155424 (2007).

    Article  ADS  Google Scholar 

  15. P. Dietl, F. Piechon, and G. Montambaux, Phys. Rev. Lett. 100, 236405 (2008); G. Montambaux, F. Piechon, J.-N. Fuchs, and M. O. Goerbig, Eur. Phys. J. B 72, 509 (2009); arXiv:0907.0500.

    Article  ADS  Google Scholar 

  16. Y. D. Chong, X. G. Wen, and M. Soljacic, Phys. Rev. B 77, 235125 (2008).

    Article  ADS  Google Scholar 

  17. S. Banerjee, R. R. Singh, V. Pardo, and W. E. Pickett, Phys. Rev. Lett. 103, 016402 (2009).

    Article  ADS  Google Scholar 

  18. K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson, Phys. Rev. Lett. 103, 046811 (2009).

    Article  ADS  Google Scholar 

  19. L. Fu, arXiv:1010.1802.

  20. T. T. Heikkil’ma Zh. Eksp. Teor. Fiz. 92, 751 (2010) [JETP Lett. 92, 681 (2010)]; arXiv:1010.0393.

    Google Scholar 

  21. G. E. Volovik, JETP Lett. 73, 162 (2001); hep-ph/0101286.

    Article  ADS  Google Scholar 

  22. F. R. Klinkhamer and G. E. Volovik, Int. J. Mod. Phys. A 20, 2795 (2005); hep-th/0403037.

    Article  MATH  ADS  Google Scholar 

  23. V. Gurarie, arXiv:1011.2273.

  24. T. D. Stanescu, V. Galitski, and S. Das Sarma, Phys. Rev. A 82, 013608 (2010).

    Article  ADS  Google Scholar 

  25. J. W. McClure, Carbon 7, 425 (1969).

    Article  Google Scholar 

  26. P. G. Grinevich and G. E. Volovik, J. Low Temp. Phys. 72, 371 (1988).

    Article  ADS  Google Scholar 

  27. J. C. Y. Teo and C. L. Kane, Phys. Rev. B 82, 115120 (2010).

    Article  ADS  Google Scholar 

  28. M. A. Silaev and G. E. Volovik, J. Low Temp. Phys. 161, 460 (2010); arXiv:1005.4672.

    Article  ADS  Google Scholar 

  29. G. E. Volovik, Pis’ma Zh. Eksp. Teor. Fiz. 93, 69 (2011) [JETP Lett. 93, 66 (2011)]; arXiv:1011.4665.

    Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Xiao-Liang Qi and Shou-Cheng Zhang, arXiv:1008.2026.

  32. T. T. Heikkilpnin, and G. E. Volovik, arXiv:1012.0905.

Download references

Author information

Authors and Affiliations

  1. Low Temperature Laboratory, Aalto University, School of Science and Technology, FI-00076, AALTO, Finland

    T. T. Heikkilä

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 119334, Russia

    G. E. Volovik

Authors
  1. T. T. Heikkilä
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. E. Volovik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. T. Heikkilä.

Additional information

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Heikkilä, T.T., Volovik, G.E. Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface. Jetp Lett. 93, 59–65 (2011). https://doi.org/10.1134/S002136401102007X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S002136401102007X

Keywords

Search

Navigation