Textures of 3He-A in a Sphere: Topological Theory of Boundary Effects and a New Defect

  • P. W. Anderson
  • R. G. Palmer


Brinkman1 in 1974 was the first to comment on the possibility of point defects in the 3He anisotropic superfluids, and he gave what is surely the correct answer: There are point defects in the B liquid when dipolar energy is considered, but not in the interior of A because of the well-known topological difficulty of “signposting the sphere”: mapping the orientation of rigid triads continuously onto a sphere, so that if, for example, the pair angular momentum vector \(\hat \ell\) points radially outward from a supposed defect, no nonsingular assignment of phases is possible. By phase we mean the orientation of the two gap parameters vectors \(\overrightarrow {{\vartriangle _i}}\) and \(i\overrightarrow {{\vartriangle _2}}\) about \(\hat \ell\). This follows from the complete topological theory of order parameter singularities given by Toulouse and Kleman, who show that the only topologically stable defect of the orbital portion of the order parameter in the interior of 3He-A is one type of line, which can be deformed continuously from 2π vortex to dis gyration to -2π vortex.


Point Defect Surface Defect Vortex Line Vortex Point Phase Slippage 


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  1. (1).
    W. F. Brinkman, in lectures at the Scottish Universities Summer School, St. Andrews, 1974;Google Scholar
  2. (1a).
    published in P. W. Anderson and W. F. Brinkman, in The Helium Liquids (Farquhar, ed.), 1975, p. 315.Google Scholar
  3. (2).
    G. Toulouse and M. Kleman, J. de Physique Letters 37, 2149 (1976).Google Scholar
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    S. Blaha, Phys. Rev. Letters, 36, 874 (1976).ADSCrossRefGoogle Scholar
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    K. Maki, various preprints (1976).Google Scholar
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    D. Mermin, Proceedings of “Simon” Symposium, Sussex, Aug. 1976.Google Scholar
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    P. W. Anderson and G. Toulouse, submitted to Phys. Rev. Letters.Google Scholar
  8. (7).
    D. Mermin suggests “flower.”Google Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • P. W. Anderson
    • 1
  • R. G. Palmer
    • 1
  1. 1.Joseph Henry Laboratories of PhysicsPrinceton UniversityPrincetonUSA

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