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JETP Letters

, Volume 91, Issue 4, pp 201–205 | Cite as

Topological superfluid 3He-B in magnetic field and ising variable

  • G. E. Volovik
Condensed Matter

Abstract

The topological superfluid 3He-B provides many examples of the interplay of symmetry and topology. Here we consider the effect of magnetic field on topological properties of 3He-B. Magnetic field violates the time reversal symmetry. As a result, the topological invariant supported by this symmetry ceases to exist; and thus the gapless fermions on the surface of 3He-B are not protected any more by topology: they become fully gapped. Nevertheless, if perturbation of symmetry is small, the surface fermions remain relativistic with mass proportional to symmetry violating perturbation—magnetic field. The 3He-B symmetry gives rise to the Ising variable I = ±1, which emerges in magnetic field and which characterizes the states of the surface of 3He-B. This variable also determines the sign of the mass term of surface fermions and the topological invariant describing their effective Hamiltonian. The line on the surface, which separates the surface domains with different I, contains 1 + 1 gapless fermions, which are protected by combined action of symmetry and topology.

Keywords

Magnetic Field Surface Fermion JETP Letter Spin Orbit Spin Orbit Interaction 
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.

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References

  1. 1.
    L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. 98, 106803 (2007).CrossRefADSGoogle Scholar
  2. 2.
    J. E. Moore and L. Balents Phys. Rev. B 75, 121306 (2007).CrossRefADSGoogle Scholar
  3. 3.
    A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, AIP Conf. Proc. 1134, 10 (2009); arXiv:0905.2029.CrossRefADSGoogle Scholar
  4. 4.
    A. Kitaev, AIP Conf. Proc. 1134, 22 (2009); arXiv:0901.2686.CrossRefMathSciNetADSGoogle Scholar
  5. 5.
    G. E. Volovik, Pis’ma Zh. Eksp. Teor. Fiz. 90, 639 (2009) [JETP Lett. 90, 587 (2009)]; arXiv:0909.3084.Google Scholar
  6. 6.
    M. M. Salomaa and G. E. Volovik, Phys. Rev. B 37, 9298 (1988).CrossRefMathSciNetADSGoogle Scholar
  7. 7.
    Suk Bum Chung and Shou-Cheng Zhang, Phys. Rev. Lett. 103, 235301 (2009).CrossRefADSGoogle Scholar
  8. 8.
    G. E. Volovik, JETP Lett. 90, 398 (2009); arXiv:0907.5389.CrossRefADSGoogle Scholar
  9. 9.
    N. B. Kopnin, P. I. Soininen, and M. M. Salomaa, J. Low Temp. Phys. 85, 267 (1991).CrossRefADSGoogle Scholar
  10. 10.
    K. Nagai, Y. Nagato, M. Yamamoto, and S. Higashitani, J. Phys. Soc. Jpn. 77, 111003 (2008).CrossRefADSGoogle Scholar
  11. 11.
    Y. Nagato, S. Higashitani, and K. Nagai, J. Phys. Soc. Jpn. 78, 123603 (2009).CrossRefADSGoogle Scholar
  12. 12.
    C. A. M. Castelijns, K. F. Coates, A. M. Guénault, et al., Phys. Rev. Lett. 56, 69 (1986).CrossRefADSGoogle Scholar
  13. 13.
    J. P. Davis, J. Pollanen, H. Choi, et al., Phys. Rev. Lett. 101, 085301 (2008).CrossRefADSGoogle Scholar
  14. 14.
    S. Murakawa, Y. Tamura, Y. Wada, et al., Phys. Rev. Lett. 103, 155301 (2009).CrossRefADSGoogle Scholar
  15. 15.
    L. V. Levitin, R. G. Bennett, A. J. Casey, et al., J. Low Temp. Phys. 158, 159 (2010).CrossRefADSGoogle Scholar
  16. 16.
    D. Vollhardt and O. Wölfle, The Superfluid Phases of Helium 3 (Taylor and Francis, London, 1990).Google Scholar
  17. 17.
    M. M. Salomaa and G. E. Volovik, Rev. Mod. Phys. 59, 533 (1987).CrossRefADSGoogle Scholar
  18. 18.
    V. V. Dmitriev, V. B. Eltsov, M. Krusius, et al., Phys. Rev. B 59, 165 (1999).CrossRefADSGoogle Scholar
  19. 19.
    W. F. Brinkman and M. C. Cross, Progress in Low Temperature Physics, Ed. by D. F. Brewer (North-Holland, Amsterdam, 1978), Vol. VIIA, p. 105.Google Scholar
  20. 20.
    Yu. M. Bunkov, and G. E. Volovik, JETP 76, 794 (1993).ADSGoogle Scholar
  21. 21.
    Jiadong Zang and Naoto Nagaosa, arXiv:1001.1578.Google Scholar
  22. 22.
    K. Ishikawa and T. Matsuyama, Z. Phys. C 33, 41 (1986).CrossRefADSGoogle Scholar
  23. 23.
    K. Ishikawa and T. Matsuyama, Nucl. Phys. B 280, 523 (1987).CrossRefADSGoogle Scholar
  24. 24.
    T. Matsuyama, Progr. Theor. Phys. 77, 711 (1987).CrossRefMathSciNetADSGoogle Scholar
  25. 25.
    G. E. Volovik, JETP 67, 1804 (1988).Google Scholar
  26. 26.
    G. E. Volovik and V. M. Yakovenko, J. Phys.: Condens. Matter 1, 5263 (1989).CrossRefADSGoogle Scholar
  27. 27.
    G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).zbMATHGoogle Scholar
  28. 28.
    A. J. Leggett, J. Phys. C 6, 3187 (1973).CrossRefMathSciNetADSGoogle Scholar
  29. 29.
    In relativistic theories the 4D analog of the broken relative spinorbit symmetry is the broken relative Lorentz symmetry, see [30, 31].CrossRefADSGoogle Scholar
  30. 30.
    G. E. Volovik, Physica B 162, 222 (1990).CrossRefADSGoogle Scholar
  31. 31.
    C. Wetterich, Phys. Rev. D 70, 105004 (2004).CrossRefMathSciNetADSGoogle Scholar
  32. 32.
    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.Google Scholar
  33. 33.
    G. E. Volovik, Pis’ma Zh. Eksp. Teor. Fiz. 91, 61 (2010); arXiv:0912.0502.Google Scholar
  34. 34.
    D. Wilkinson and A. S. Goldhaber, Phys. Rev. D 16, 1221 (1977).CrossRefADSGoogle Scholar
  35. 35.
    A. A. Balinskii, G. E. Volovik, and E. I. Kats, Zh. Eksp. Teor. Fiz. 87, 1305 (1984) [Sov. Phys. JETP 60, 748 (1984)].Google Scholar
  36. 36.
    S. Ryu, A. Schnyder, A. Furusaki, and A. Ludwig, arXiv:0912.2157.Google Scholar
  37. 37.
    P. Horava, Phys. Rev. Lett. 95, 016405 (2005).CrossRefADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Low Temperature LaboratoryAalto UniversityAaltoFinland
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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