Journal of Low Temperature Physics

, Volume 26, Issue 5–6, pp 709–733 | Cite as

Elastic energy of the vortex state in type II superconductors. I. High inductions

  • E. H. Brandt


The elastic properties of the flux line lattice (FLL) in type II superconductors are calculated from the linearized Ginzburg-Landau (GL) theory for large inductionsB≈H c2 . They appear to be strongly nonlocal, i.e., the elastic modulic11 andc44 for homogeneous deformations do not apply if the strain field varies over distances λ/(1−B/H c2 )1/2d (λ is the penetration depth,d is the FL distance). For smaller strain wavelength,c11 andc44 are smaller by factors (1−B/H c2 )2/2κ 2 and (1−B/H c2 )/ 2κ 2 , respectively. The order parameter and local field of a deformed FLL exhibit the expected spatial “frequency modulation,” but also a pronounced “amplitude modulation” whose degree of modulation increases with the strain wavelength. The results of further calculations avoiding the linearization of the GL theory are given.


Vortex Frequency Modulation Magnetic Material Penetration Depth Elastic Property 
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  1. 1.
    R. Labusch,Crystal Lattice Defects 1, 1 (1969).Google Scholar
  2. 2.
    E. J. Kramer,J. Appl. Phys. 44, 1360 (1973).Google Scholar
  3. 3.
    A. I. Larkin and Yu. N. Ovchinnikov,Sov. Phys.—JETP 38, 854 (1974).Google Scholar
  4. 4.
    R. Schmucker and H. Kronmüller,Phys. Stat. Sol. (b)61, 181 (1974).Google Scholar
  5. 5.
    A. M. Campbell and J. Evetts,Critical Currents in Superconductors (Taylor and Francis, London, 1972).Google Scholar
  6. 6.
    P. Haasen and H. C. Freyhardt, eds.,Proc. Int. Discussion Meeting on Flux-Pinning in Superconductors, Sonnenberg, Germany, 1974 (Akademie der Wissenschaften, Göttingen).Google Scholar
  7. 7.
    R. Labusch,Phys. Stat. Sol. 19, 715 (1967).Google Scholar
  8. 8.
    R. Labusch,Phys. Stat. Sol. 32, 439 (1969).Google Scholar
  9. 9.
    E. H. Brandt,Phys. Stat. Sol. 36, 381 (1969).Google Scholar
  10. 10.
    E. H. Brandt,Phys. Stat. Sol. (b)77, 551 (1976).Google Scholar
  11. 11.
    E. H. Brandt,Phys. Stat. Sol. (b)51, 345 (1972).Google Scholar
  12. 12.
    A. Seeger and H. Kronmüller,Phys. Stat. Sol. 27, 371 (1968).Google Scholar
  13. 13.
    R. Labusch,Phys. Rev. 170, 470 (1968).Google Scholar
  14. 14.
    A. I. Larkin,Sov. Phys.—JETP 31, 784 (1970).Google Scholar
  15. 15.
    E. H. Brandt,Phys. Stat. Sol. (b)71, 277 (1975).Google Scholar
  16. 16.
    G. Eilenberger,Phys. Rev. 164, 628 (1967).Google Scholar
  17. 17.
    A. A. Abrikosov,Sov. Phys.—JETP 5, 1174 (1957).Google Scholar
  18. 18.
    G. Leibfried, inHandbuch der Physik, S. Flügge, ed. (Springer, Berlin, 1958), Vol. 7–1.Google Scholar
  19. 19.
    E. H. Brandt, to be published.Google Scholar
  20. 20.
    P. G. de Gennes,Superconductivity of Metals and Alloys (Benjamin, New York, 1966).Google Scholar
  21. 21.
    R. Schmucker and E. H. Brandt, to be published inPhys. Stat. Sol. (b) (February 1977).Google Scholar
  22. 22.
    V. G. Kogan,J. Low Temp. Phys. 20, 103 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • E. H. Brandt
    • 1
  1. 1.Max-Planck-Institut für Metallforschung, Institut für PhysikStuttgartGermany

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