Advertisement

JETP Letters

, Volume 107, Issue 2, pp 115–118 | Cite as

Topology of a 3He-A Film on a Corrugated Graphene Substrate

Condensed Matter

Abstract

A thin film of superfluid 3He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the superfluidity even in a very thin film, where the system can be considered as quasi two-dimensional topological material. This will allow us to study the effect of disorder on different classes of the 2 + 1 topological materials: the chiral 3He-A with intrinsic quantum Hall effect and the time reversal invariant planar phase with intrinsic spin quantum Hall effect. In the limit of smooth disorder, the system can be considered as a Chern mosaic, i.e., a collection of domains with different values of Chern numbers. In this limit, the quantization of the Hall conductance is determined by the percolated domain, while the density of the fermionic states is determined by the edge modes on the boundaries of the finite domains. This system can be useful for the general consideration of disorder in the topological matter.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. I. Katsnelson and G. E. Volovik, J. Low Temp. Phys. 175, 655 (2014); arXiv:1310.3581.ADSCrossRefGoogle Scholar
  2. 2.
    G. E. Volovik, Exotic Properties of Superfluid 3He (World Scientific, Singapore, New Jersey, London, Hong Kong, 1992).CrossRefGoogle Scholar
  3. 3.
    Yu. Makhlin, M. Silaev, and G. E. Volovik, Phys. Rev. B 89, 174502 (2014).ADSCrossRefGoogle Scholar
  4. 4.
    G. E. Volovik, Sov. Phys. JETP 67, 1804 (1988).Google Scholar
  5. 5.
    H. So, Prog. Theor. Phys. 74, 585 (1985).ADSCrossRefGoogle Scholar
  6. 6.
    K. Ishikawa and T. Matsuyama, Z. Phys. C 33, 41 (1986).ADSCrossRefGoogle Scholar
  7. 7.
    K. Ishikawa and T. Matsuyama, Nucl. Phys. B 280, 523 (1987).ADSCrossRefGoogle Scholar
  8. 8.
    G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).MATHGoogle Scholar
  9. 9.
    G. E. Volovik, JETP Lett. 55, 368 (1992).ADSGoogle Scholar
  10. 10.
    A. A. Burkov, Phys. Rev. Lett. 120, 016603 (2018).ADSCrossRefGoogle Scholar
  11. 11.
    N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667 (1991).ADSCrossRefGoogle Scholar
  12. 12.
    G. E. Volovik, JETP Lett. 93, 66 (2011).ADSCrossRefGoogle Scholar
  13. 13.
    J. Röntynen and T. Ojanen, Phys. Rev. B 93, 094521 (2016).ADSCrossRefGoogle Scholar
  14. 14.
    K. Pöyhönen and T. Ojanen, Phys. Rev. B 96, 174521 (2017).ADSCrossRefGoogle Scholar
  15. 15.
    P. Hořava, Phys. Rev. Lett. 95, 016405 (2005).ADSCrossRefGoogle Scholar
  16. 16.
    E. M. Chudnovsky, Phys. Rev. B 33, 245 (1986).ADSCrossRefGoogle Scholar
  17. 17.
    R. Movassagh, Phys. Rev. Lett. 119, 220504 (2017).ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    T. Morimoto, A. Furusaki, and Ch. Mudry, Phys. Rev. B 91, 235111 (2015).ADSCrossRefGoogle Scholar
  19. 19.
    J. Song and E. Prodan, Phys. Rev. B 92, 195119 (2015).ADSCrossRefGoogle Scholar
  20. 20.
    R.-J. Slager, L. Rademaker, J. Zaanen, and L. Balents, Phys. Rev. B 92, 085126 (2015).ADSCrossRefGoogle Scholar
  21. 21.
    E. Prodan, arXiv:1602.00306.Google Scholar
  22. 22.
    B. Lian, J. Wang, X.-Q. Sun, A. Vaezi, and Sh.-Ch. Zhang, arXiv:1709.05558.Google Scholar
  23. 23.
    B. Wu, J. Song, J. Zhou, and H. Jiang, Chin. Phys. B 25, 117311 (2016); arXiv:1711.10725.ADSCrossRefGoogle Scholar
  24. 24.
    G. E. Volovik, J. Low Temp. Phys. 150, 453 (2008); arXiv:0704.2484.ADSCrossRefGoogle Scholar
  25. 25.
    V. V. Dmitriev, D. A. Krasnikhin, N. Mulders, A. A. Senin, G. E. Volovik, and A. N. Yudin, JETP Lett. 91, 599 (2010).ADSCrossRefGoogle Scholar
  26. 26.
    E. M. Chudnovsky and D. A. Garanin, arXiv:1710.10608.Google Scholar
  27. 27.
    T. H. R. Skyrme, Nucl. Phys. 31, 556 (1962).MathSciNetCrossRefGoogle Scholar
  28. 28.
    G. E. Volovik and V. P. Mineev, Sov. Phys. JETP 46, 401 (1977).ADSGoogle Scholar
  29. 29.
    V. M. H. Ruutu, Ü. Parts, J. H. Koivuniemi, M. Krusius, E. V. Thuneberg, and G. E. Volovik, JETP Lett. 60, 671 (1994).ADSGoogle Scholar
  30. 30.
    Yu. G. Makhlin and T. Sh. Misirpashaev, JETP Lett. 61, 49 (1995).ADSGoogle Scholar
  31. 31.
    S. W. Hawking, Nucl. Phys. B 144, 349 (1978).ADSCrossRefGoogle Scholar
  32. 32.
    A. J. Hanson and T. Regge, Lect. Notes Phys. 94, 354 (1979).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Low Temperature LaboratoryAalto UniversityAaltoFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  3. 3.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

Personalised recommendations