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


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.


Manifold Energy Spectrum Magnetic Material Space Topology Real Space 
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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

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