Nucleation of Superconductivity in Low-Dimensional Systems Under Magnetic Fields

  • Vladimir Mineev
Part of the Lecture Notes in Physics book series (LNP, volume 595)


This chapter presents a survey of the current state of art of the theory of the upper critical field in low-dimensional superconducting materials. Starting from the Ginzburg-Landau equation in the vicinity of the critical temperature we derive a new analytical expression for the angular and temperature dependence of the critical field in layered superconducting materials. This formula is shown to reproduce as limiting cases the well known results of Tinkham for an isolated film of finite thickness and of Lawrence-Doniach for the stacked array of films of zero thickness with its particular anisotropic Ginzburg-Landau limit. The well known theoretical statements of A.Lebed’ about a low temperature divergence of the upper critical field parallel to the conducting layers in the layered superconductors and the reentrance of the superconductivity in ultra-high magnetic fields are reinvestigated taking into account the scattering of quasiparticles by impurities. The upper limit of the superconductor purity yielding to a finite value of the upper critical field is established. The problem of the low temperature divergence of the upper critical field in bulk materials in the quantized magnetic field is discussed. The high field behavior of the critical temperature as a function of the magnetic field for a finite but high enough crystal purity is derived.


Critical Temperature Landau Level Critical Field Landau Equation Layered Superconductor 
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  1. 1.
    L.P. Gorkov, T.K. Melik-Barkhudarov: Zh. Eksp. Teor. Fiz. 45, 1493 (1963) [Sov.Phys.-JETP 18, 1031 (1964)]Google Scholar
  2. 2.
    M. Tinkham: ‘Introduction to superconductivity’, Second Edition, McGraw-Hill, Inc., 1996Google Scholar
  3. 3.
    V.P. Mineev: Phys.Rev. B 65, 012508 (2002)CrossRefADSGoogle Scholar
  4. 4.
    A.G. Lebed’: Pis’ma Zh. Eksp. Teor. Fiz. 44, 89 (1986) [JETP Lett. 44, 114 (1986)]ADSGoogle Scholar
  5. 5.
    A.G. Lebed’, K. Yamaji: Phys. Rev. Lett. 80, 2697 (1998)CrossRefADSGoogle Scholar
  6. 6.
    I.J. Lee, P.M. Chaikin, M.J. Naughton: Phys. Rev. B 62 R14669 (2000)CrossRefADSGoogle Scholar
  7. 7.
    Y. Maeno, T.M. Rice, M. Sigrist: Phys. Today 54, 42 (2001)CrossRefADSGoogle Scholar
  8. 8.
    T. Akima, S. Nishizaki, Y. Maeno: J. Phys. Soc. Jpn. 68, 694 (1999)CrossRefADSGoogle Scholar
  9. 9.
    E. Ohmichi, Y. Maeno, S. Nagai, Z.Q. Mao, M.A. Tanatar, T. Ishiguro: Phys. Rev. B 61, 7101 (2000)CrossRefADSGoogle Scholar
  10. 10.
    V.P. Mineev: J. Phys. Soc. Jpn. 69, 3371 (2000)CrossRefADSGoogle Scholar
  11. 11.
    L.W. Gruenberg, L. Gunther: Phys. Rev. 176, 606 (1968)CrossRefADSGoogle Scholar
  12. 12.
    V.P. Mineev: Phil. Mag. 80, 307 (2000)CrossRefGoogle Scholar
  13. 13.
    S.T. Rugigiero, T.W. Barbee, Jr., M.R. Beasley: Phys. Rev. Lett. 45, 1299 (1980)CrossRefADSGoogle Scholar
  14. 14.
    B.Y. Jin, J.B. Ketterson, E.J. McNiff, Jr., S. Foner, I. Schuller: J. Low Temp. Phys. 69, 39 (1987)CrossRefADSGoogle Scholar
  15. 15.
    M.J. Naughton, R.C. Yu, P.K. Davies, J.E. Fisher, R.V. Chamberlin, Z.Z. Wang, T.W. Jing, N.P. Ong, P.M. Chaikin: Phys. Rev. B 38, 9280 (1988)CrossRefADSGoogle Scholar
  16. 16.
    R. Marcon, E. Silva, R. Fastampa, M. Giura: Phys. Rev. B 46, 3612 (1992)CrossRefADSGoogle Scholar
  17. 17.
    M. Tinkham: Phys. Rev. 129, 2413 (1963)CrossRefADSGoogle Scholar
  18. 18.
    F.E. Harper, M. Tinkham: Phys. Rev. 172, 441 (1968)CrossRefADSGoogle Scholar
  19. 19.
    G. Deutscher, O. Entin-Wohlman: Phys. Rev. B 17, 1249 (1978)CrossRefADSGoogle Scholar
  20. 20.
    L.I. Glazman: Zh. Eksp. Teor. Fiz. 193, 1373 (1987) [Sov. Phys. JETP 66, 780 (1987)]ADSGoogle Scholar
  21. 21.
    K. Tanaka: J. Phys. Soc. Jpn. 56, 4245 (1987)CrossRefADSGoogle Scholar
  22. 22.
    B.Y. Jin, J.B. Ketterson: Adv. Phys. 38, 189 (1989)CrossRefADSGoogle Scholar
  23. 23.
    V. Gvozdikov: Fiz. Nizk. Temp. 16, 5 (1990) [Sov. J. Low Temp. Phys 16, 1 (1990)]Google Scholar
  24. 24.
    T. Schneider, A. Schmidt: Phys. Rev. B 47, 5915 (1993)CrossRefADSGoogle Scholar
  25. 25.
    N. Takezawa, T. Koyama, M. Tachiki: Physica C 207, 231 (1993)CrossRefADSGoogle Scholar
  26. 26.
    W.E. Lawrence, S. Doniach, E. Kanda eds.: Proc. 12th Int. Conf. Low. Temp. Phys. (Kyoto, 1970; Keigaku, Tokyo 1971), p.361Google Scholar
  27. 27.
    E.I. Kats: Zh. Eksp. Teor. Fiz. 56, 1675 (1969) [Sov.Phys.-JETP 29, 897 (1969)]Google Scholar
  28. 28.
    Yu.A. Bychkov: Zh. Eksp. Teor. Fiz. 39, 1401 (1960) [Sov. Phys. JETP 12, 977 (1961)]Google Scholar
  29. 29.
    L.P. Gor’kov: Zh. Eksp. Teor. Fiz. 193, 1373 (1987) [Sov. Phys. JETP 66, 780 (1987)]Google Scholar
  30. 30.
    M.G. Vavilov, V.P. Mineev: Zh. Éksp. Teor. Fiz. 112, 1873 (1997) [Sov. Phys. JETP 85, 1024 (1997)]Google Scholar
  31. 31.
    T.J.B.M. Janssen, C. Haworth, S.M. Hayden, P. Meeson, M. Springford: Phys. Rev. B 57, 11698 (1998)CrossRefADSGoogle Scholar
  32. 32.
    H. Ohkuni, T. Ishida, Y. Inada, Y. Haga, E. Yamamoto, Y. Onuki, S. Takahashi: J. Phys. Soc. Jpn. 66, 945 (1997)CrossRefADSGoogle Scholar
  33. 33.
    T. Terashima, C. Haworth, H. Takeya, S. Uji, H. Aoki: Phys. Rev. 56, 5120 (1997)ADSCrossRefGoogle Scholar
  34. 34.
    C. Bergemann, S.R. Julian, G.J. McMullan, B.K. Howard, G.G. Lonzarich, P. Lejay, J.P. Brison, J. Flouquet: Physica B 230–232, 438 (1997)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Vladimir Mineev
    • 1
  1. 1.Commissariat à l’Energie Atomique, Département de Recherche Fondamentale sur la Matière CondenséeSPSMSGrenobleFrance

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