Journal of Low Temperature Physics

, Volume 46, Issue 1–2, pp 161–189 | Cite as

Order parameters and energies of analytic and singular vortex lines in rotating3He-A

  • T. Passvogel
  • N. Schopohl
  • M. Warnke
  • L. Tewordt


We present the expressions of the generalized Ginzburg-Landau (GL) theory for the free energy and the supercurrent in terms of thed vector, the magnetic fieldH, and operators containing the spatial gradient and the rotationΩ. These expressions are then specialized to the Anderson-Brinkman-Morel (ABM) state. We consider eight single-vortex lines of cylindrical symmetry and radiusR=[2/ℏ]−1/2: the Mermin-Ho vortex, a second analytic vortex, and six singular vortices, i.e., the orbital and radial disgyrations, the orbital and radial phase vortices, and two axial phase vortices. These eight vortex states are determined by solving the Euler-Lagrange equations whose solutions minimize the GL free energy functional. For increasing field, the core radius of the\(\hat l\) texture of the Mermin-Ho vortex tends to a limiting value, while the core radius of the\(\hat d\) texture goes to zero. The gap of the singular vortices behaves likerα forr → 0, where α ranges between\(\sqrt {1/2} \) and\(\sqrt {9/2} \). The energy of the radial disgyration becomes lower than that of the Mermin-Ho vortex for fieldsH≥6.5H*=6.5×25 G (atT=0.99T c and forR=10L*=60 µm, orω=2.9 rad/sec). ForR → 2ξ T T is the GL coherence length) orωω c2 (upper critical rotation speed), the energies of the singular vortices become lower than the energies of the analytic vortices. This is in agreement with the exact result of Schopohl for a vortex lattice atΩ c 2. Finally, we calculate the correction of order (1 -T/T c ) to the GL gap for the axial phase vortex.


Vortex Free Energy Coherence Coherence Length Spatial Gradient 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Schopohl and L. Tewordt,J. Low Temp. Phys. 41, 305 (1980).Google Scholar
  2. 2.
    M. C. Cross,J. Low Temp. Phys. 21, 525 (1975).Google Scholar
  3. 3.
    L. Neumann and L. Tewordt,Z. Phys. (Lpz)189, 55 (1966).Google Scholar
  4. 4.
    N. D. Mermin and T.-L. Ho,Phys. Rev. Lett. 36, 594 (1976).Google Scholar
  5. 5.
    L. J. Buchholtz and A. L. Fetter,Phys. Rev. B 15, 5225 (1977).Google Scholar
  6. 6.
    N. Schopohl,J. Low Temp. Phys. 41, 409 (1980).Google Scholar
  7. 7.
    T. Fujita, M. Nakahara, T. Ohmi, and Tsueneto,Progr. Theor. Phys. 60, 671 (1978).Google Scholar
  8. 8.
    M. Nakahara, T. Ohmi, T. Tsuneto, and T. Fujita,Progr. Theor. Phys. 62, 874 (1979); M. Nakahara and T. Ohmi,Progr. Theor. Phys. 61, 709 (1979).Google Scholar
  9. 9.
    G. E. Volovik and P. J. Hakonen,J. Low Temp. Phys. 42, 503 (1981).Google Scholar
  10. 10.
    M. R. Williams and A. L. Fetter,Phys. Rev. B 20, 169 (1979).Google Scholar
  11. 11.
    D. Vollhardt, Diplomarbeit, Hamburg (1977).Google Scholar
  12. 12.
    J. Stoer and R. Bulirsch,Introduction to Numerical Analysis (Springer, Heidelberg, 1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • T. Passvogel
    • 1
  • N. Schopohl
    • 1
  • M. Warnke
    • 1
  • L. Tewordt
    • 1
  1. 1.Abteilung für Theoretische FestkörperphysikUniversität HamburgHamburgWest Germany

Personalised recommendations