Skip to main content
SpringerLink
Log in

Fermions with cubic and quartic spectrum

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

Abstract

We study exotic fermions with spectrum E 2 ∝ p 2N. Such spectrum emerges in the vicinity of the Fermi point with multiple topological charge N, if special symmetry is obeyed. When this symmetry is violated, the multiple Fermi point typically splits into N elementary Fermi points, i.e., Dirac points with N = 1 and spectrum E 2 ∝ p 2.

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. H. B. Nielsen and M. Ninomiya, Nucl. Phys. B 185, 20 (1981); Nucl. Phys. B 193, 173 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  2. G. E. Volovik and V. P. Mineev, Sov. Phys. JETP 56, 579 (1982); G. E. Volovik and A. V. Balatskii, J. Low Temp. Phys. 58, 1 (1985); G. E. Volovik, J. Low Temp. Phys. 67, 301 (1987); JETP Lett. 46, 98 (1987).

    Google Scholar 

  3. J. E. Avron, R. Seiler, and B. Simon, Phys. Rev. Lett. 51, 51 (1983).

    Article  ADS  Google Scholar 

  4. G. W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  5. Qian Niu, D. J. Thouless, and Yong-Shi Wu, Phys. Rev. B 31, 3372 (1985).

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  7. G. E. Volovik, Sov. Phys. JETP 67, 1804 (1988).

    Google Scholar 

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

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. A. Kitaev, arXiv:0901.2686.

  11. Xiao-Liang Qi, T. L. Hughes, S. Raghu, and Shou-Cheng Zhang, Phys. Rev. Lett. 102, 187001 (2009).

    Article  ADS  Google Scholar 

  12. A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Phys. Rev. B 78, 195125 (2008).

    Article  ADS  Google Scholar 

  13. M. Stone, Ching-Kai Chiu, and A. Roy, arXiv:1005.3213.

  14. C. N. Varney, Kai Sun, M. Rigol, and V. Galitski, Phys. Rev. B 82, 115125 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

  18. P. Hořava, Phys. Rev. Lett. 102, 161301 (2009).

    Article  MathSciNet  ADS  Google Scholar 

  19. P. Hořava, Phys. Rev. D 79, 084008 (2009).

    Article  MathSciNet  ADS  Google Scholar 

  20. P. Hořava, J. High Energy Phys. 0903, 020 (2009); arXiv:0812.4287.

    ADS  Google Scholar 

  21. Cenke Xu and P. Hořava, Phys. Rev. D 81, 104033 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. 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, vol. 718 (Springer, New York, 2007), p. 31; cond-mat/0601372.

    Chapter  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  29. L. Fu, arXiv:1010.1802.

  30. B. Beri, Phys. Rev. Lett. 103, 016402 (2009); Phys. Rev. B 81, 134515 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Kin Fai Mak, Jie Shan, and T. F. Heinz, Phys. Rev. Lett. 104, 176404 (2010).

    Article  ADS  Google Scholar 

  33. A. H. Castro Neto, F. Guinea, N. M. R. Peres, et al., Rev. Mod. Phys. 81, 109 (2009).

    Article  ADS  Google Scholar 

  34. G. E. Volovik, JETP Lett. 91, 55 (2010); arXiv:0912.0502.

    Article  ADS  Google Scholar 

  35. B. L. Hu, J. Phys. Conf. Ser. 174, 012015 (2009).

    Article  ADS  Google Scholar 

  36. L. Fidkowski and A. Kitaev, arXiv:1008.4138.

  37. L. Fidkowski and A. Kitaev, Phys. Rev. B 81, 134509 (2010).

    Article  ADS  Google Scholar 

  38. F. Pollmann, E. Berg, A. M. Turner, and M. Oshikawa, Phys. Rev. B 81, 064439 (2010).

    Article  ADS  Google Scholar 

  39. F. R. Klinkhamer, Phys. Rev. D 73, 057301 (2006).

    Article  ADS  Google Scholar 

  40. G. Altarelli and F. Feruglio, Rev. Mod. Phys. 82, 2701 (2010).

    Article  ADS  Google Scholar 

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 & G. E. Volovik

  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. Fermions with cubic and quartic spectrum. Jetp Lett. 92, 681–686 (2010). https://doi.org/10.1134/S0021364010220091

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364010220091

Keywords

Search

Navigation