Advertisement

JETP Letters

, Volume 95, Issue 8, pp 411–415 | Cite as

Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

  • M. I. Katsnelson
  • G. E. Volovik
Condensed Matter

Abstract

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Hořava in relation to the quantum theory of gravity. In such vacua, the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED.

Keywords

JETP Letter Quantum Electrodynamic Dirac Point Single Layer Graphene Bilayer Graphene 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).zbMATHGoogle Scholar
  2. 2.
    A. H. Castro Neto, F. Guinea, N. M. R. Peres, et al., Rev. Mod. Phys. 81, 109 (2009).ADSCrossRefGoogle Scholar
  3. 3.
    M. A. H. Vozmediano, M. I. Katsnelson, and F. Guinea, Phys. Rep. 496, 109 (2010).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge Univ. Press, Cambridge, 2012).CrossRefGoogle Scholar
  5. 5.
    G. E. Volovik, draft for Chapter in Proceedings of the Como Summer School on Analogue Gravity, arXiv:1111.4627.Google Scholar
  6. 6.
    W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936).ADSCrossRefGoogle Scholar
  7. 7.
    J. Schwinger, Phys. Rev. 82, 664 (1951).MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    G. E. Volovik, Exotic Properties of Superfluid 3 He (World Scientific, Singapore, 1992).Google Scholar
  9. 9.
    N. Schopohl and G. E. Volovik, Ann. Phys. (N.Y.) 215, 372 (1992).ADSCrossRefGoogle Scholar
  10. 10.
    A. A. Abrikosov and S. D. Beneslavskii, Sov. Phys. JETP 32, 699 (1971).ADSGoogle Scholar
  11. 11.
    H. B. Nielsen and M. Ninomiya, Phys. Lett. B 130, 389 (1983).MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    A. A. Abrikosov, Phys. Rev. B 58, 2788 (1998).ADSCrossRefGoogle Scholar
  13. 13.
    X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83, 205101 (2011).ADSCrossRefGoogle Scholar
  14. 14.
    A. A. Burkov and L. Balents, Phys. Rev. Lett. 107, 127205 (2011).ADSCrossRefGoogle Scholar
  15. 15.
    V. Aji, arXiv:1108.4426.Google Scholar
  16. 16.
    T. D. C. Bevan, A. J. Manninen, J. B. Cook, et al., Nature 386, 689 (1997).ADSCrossRefGoogle Scholar
  17. 17.
    P. Hořava, Phys. Rev. Lett. 102, 161301 (2009).MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    P. Hořava, Phys. Rev. D 79, 084008 (2009).MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    P. Hořava, J. High Energy Phys. 0903, 020 (2009).ADSGoogle Scholar
  20. 20.
    C. Xu and P. Hořava, Phys. Rev. D 81, 104033 (2010).ADSCrossRefGoogle Scholar
  21. 21.
    S. A. Safran, Phys. Rev. B 30, 421 (1984).ADSCrossRefGoogle Scholar
  22. 22.
    M. Koshino and T. Ando, Phys. Rev. B 76, 085425 (2007).ADSCrossRefGoogle Scholar
  23. 23.
    A. S. Mayorov, D. C. Elias, M. Mucha-Kruczynski, et al., Science 333, 860 (2011).ADSCrossRefGoogle Scholar
  24. 24.
    J. O. Andersen and T. Haugset, Phys. Rev. D 51, 3073 (1995).ADSCrossRefGoogle Scholar
  25. 25.
    O. Andreev, Int. J. Mod. Phys. A 25, 2087 (2010); arXiv:0910.1613.ADSzbMATHCrossRefGoogle Scholar
  26. 26.
    D. Allor, T. D. Cohen, and D. A. McGady, Phys. Rev. D 78, 096009 (2008).ADSCrossRefGoogle Scholar
  27. 27.
    N. M. Vildanov, J. Phys.: Condens. Matter 21, 445802 (2009).ADSCrossRefGoogle Scholar
  28. 28.
    M. A. Zubkov, Pis’ma Zh. Eksp. Teor. Fiz. 95, 540 (2012).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Institute for Molecules and MaterialsRadboud University NijmegenNijmegenThe Netherlands
  2. 2.Low Temperature LaboratoryAalto University, School of Science and TechnologyAALTOFinland
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations