Advertisement

Journal of Low Temperature Physics

, Volume 72, Issue 5–6, pp 371–380 | Cite as

Topology of gap nodes in superfluid3He: π4 Homotopy group for3He-B disclination

  • P. G. Grinevich
  • G. E. Volovik
Article

Abstract

The topologically stable zeros in the energy spectrum of Fermi excitations in superfluid3He both in uniform phases and in textures are classified. This generalizes the classification of the defects of the order parameter in real coordinate space to the classification of zeros in the gap, which are the more general defects in coherent superfluid or superconducting states both in real space and momentumk space. The zeros are described by classes of mappings of the spherical surfacesS n , embracing the (6-n-1)-dimensional manifold of zeros in six-dimensional (k, r) space, into the space of the Bogolyubov-Nambu matrices, which describe the Fermi excitations. The examples of topologically nontrivial manifolds of zeros are discussed, including the closed line of zeros in five-dimensional space, which is described by the π4 homotopy groups and exists in the core of the3He-B disclination. This object demonstrates the coupling between the real space topology of disclination and the extended space topology of zeros in the disclination core.

Keywords

Manifold Energy Spectrum Magnetic Material Space Topology Real Space 
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.
    P. A. Lee, T. M. Rice, J. W. Serene, L. J. Sham, and J. W. Wilkins,Comments Cond. Matter Phys. 12, 99 (1986).Google Scholar
  2. 2.
    M. Sigrist and T. M. Rice,Z. Phys. B Condensed Matter 68, 9 (1987).Google Scholar
  3. 3.
    G. E. Volovik and L. P. Gor'kov,Zh. Eksp. Teor. Fiz. 88, 599 (1985) [Sov. Phys. JETP 61, 843 (1985)].Google Scholar
  4. 4.
    M. M. Salomaa and G. E. Volovik,Rev. Mod. Phys. 59, 533 (1987).Google Scholar
  5. 5.
    G. E. Volovik and V. P. Mineev,Zh. Eksp. Teor. Fiz. 83, 1025 (1982) [Sov. Phys. JETP 56, 579 (1982)].Google Scholar
  6. 6.
    L. P. Gor'kov and P. A. Kalugin,Pis'ma Zh. Eksp. Teor. Fiz. 41, 208 (1985) [Sov. Phys. JETP Lett. 41, 253 (1985)].Google Scholar
  7. 7.
    G. E. Volovik,J. Low Temp. Phys. 67, 301 (1987);Zh. Eksp. Teor. Fiz. 92, 2116 (1987).Google Scholar
  8. 8.
    G. E. Volovik and V. A. Konyshev,Pis'ma Zh. Eksp. Teor. Fiz. 47, 207 (1988).Google Scholar
  9. 9.
    J. Von Neumann and E. P. Wigner,Phys. Z. 30, 467 (1929).Google Scholar
  10. 10.
    M. V. Berry,Proc. R. Soc. A 392, 45 (1984).Google Scholar
  11. 11.
    G. E. Volovik,Pis'ma Zh. Eksp. Teor. Fiz. 46, 81 (1987).Google Scholar
  12. 12.
    S. P. Novikov,Doklady Akad. Neuk SSSR 257, 538 (1981).Google Scholar
  13. 13.
    J. E. Avron, R. Seiler, and B. Simon,Phys. Rev. Lett. 51, 51 (1983).Google Scholar
  14. 14.
    B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov,Modern Geometry—Methods and Applications (Springer-Verlag).Google Scholar
  15. 15.
    N. D. Mermin,Rev. Mod. Phys. 51, 591 (1979); L. Michel,Rev. Mod. Phys. 52, 617 (1980); V. P. Mineev, inSoviet Scientific Reviews, Section A: Physics Reviews, I. M. Khalatnikov, ed. (Harwood Academic, Chur, Switzerland, 1980), Vol. 2, p. 173.Google Scholar
  16. 16.
    M. M. Salomaa and G. E. Volovik,Phys. Rev. B. 37, 929 (1988).Google Scholar
  17. 17.
    E. V. Thuneberg,Phys. Rev. Lett. 56, 359 (1986).Google Scholar
  18. 18.
    A. P. Balachandran,Nucl. Phys. B 271, 227 (1986).Google Scholar
  19. 19.
    A. Garg, V. P. Nair and M. Stone,Ann. Phys. (N.Y.)173, 149 (1987).Google Scholar
  20. 20.
    R. Combescot and T. Dombre,Phys. Rev. B 33, 79 (1986).Google Scholar
  21. 21.
    A. V. Balatsky and V. A. Konyshev,Zh. Eksp. Teor. Fiz. 92, 841 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • P. G. Grinevich
    • 1
    • 2
  • G. E. Volovik
    • 1
    • 2
  1. 1.L. D. Landau Institute for Theoretical PhysicsMoscowUSSR
  2. 2.NORDITACopenhagenDenmark

Personalised recommendations