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Journal of Superconductivity

, Volume 5, Issue 3, pp 219–237 | Cite as

Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order

  • S. Fujita
  • S. Watanabe
Articles

Abstract

A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V11,V22,V12) among and between “electron” (1) and “hole” (2) Cooper pairs are differentiated, and identifying “electrons” (“holes”) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of “electron” and “hole” ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between “electron” and “hole” Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengthsξ observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveT c are shown to move like free bosons with the energy-momentum relationɛ=1/2vFq. They undergo a Bose-Einstein condensation atT c = 0.977ħvFk b −1 n1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT c (∼100 K) arises from the fact that the densityn is high:n1/2∼ξ−1 ∼107 cm−1. The phase transition is of the third order, and the heat capacity has a reversed lambda (λ)-like peak atT c .

Key words

Theory of superconductivity new formula forTc high-Tc superconductor Bose-Einstein condensation 

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References

  1. 1.
    J. G. Bednorz and K. A. Müller,Z. Phys. B, Cond. Matter 64, 189 (1986).Google Scholar
  2. 2.
    J. W. Halley, ed.,Theory of High-Temperature Superconductivity (Addison-Wesley, Redwood City, California, 1988).Google Scholar
  3. 3.
    S. Lundquistet al. eds.,Towards the Theoretical Understanding of High-T c Superconductors (Progress in High-Temperature Superconductivity, Vol. 14) (World Scientific, Singapore, 1988).Google Scholar
  4. 4.
    D. M. Ginsberg, ed.,Physical Properties of High-Temperature Superconductors. I (World Scientific, Singapore, 1989).Google Scholar
  5. 5.
    S. A. Wolf and V. Z. Kresin,Novel Superconductivity (Plenum, New York, 1987); K. Kitazawa and T. Ishiguro, eds.,Advances in Superconductivity (Springer, Tokyo, 1989).Google Scholar
  6. 6.
    M. K. Wuet al. Phys. Rev. Lett. 58, 908 (1987).Google Scholar
  7. 7.
    See, e.g., D. M. Ginsberg's overview, Ref. 4, pp. 1–38.Google Scholar
  8. 8.
    J. Bardeen, L. N. Cooper, and J. R. Schrieffer,Phys. Rev. 108, 1175 (1957).Google Scholar
  9. 9.
    S. Fujita,J. Supercond. 4, 297 (1991).Google Scholar
  10. 10.
    S. Fujita,J. Supercond. 5, 83 (1992).Google Scholar
  11. 11.
    F. Bloch,Z. Phys. 52, 555 (1928).Google Scholar
  12. 12.
    N. W. Ashcroft and N. D, Mermin,Solid State Physics (Saunders, Philadelphia, 1976), pp. 132–141.Google Scholar
  13. 13.
    S. Godoy and S. Fujita,J. Eng. Sci. 29, 1201 (1991).Google Scholar
  14. 14.
    J. R. Schrieffer,Theory of Superconductivity (Benjamin, New York, 1964), p. 33, Eq. (2–15).Google Scholar
  15. 15.
    A. Einstein,Sitz. Ber. Berl. Akad. 261 (1924); 3 (1925).Google Scholar
  16. 16.
    S. Fujita, T. Kimura, and Y. Zheng,Found. Phys. 21, 1117 (1991).Google Scholar
  17. 17.
    D. E. Farrellet al. Phys. Rev. B 42, 6758 (1990).Google Scholar
  18. 18.
    J. H. Kang, R. T. Kampwirth, and K. E. Gray,Appl. Phys. Lett. 52, 2080 (1988); M. J. Naughtonet al. Phys. Rev. B 38, 9280 (1988).Google Scholar
  19. 19.
    S. Watanabe and S. Fujita,J. Phys. Chem. Solids 52, 985 (1991).Google Scholar
  20. 20.
    L. Onsager,Philos. Mag. 43, 1006 (1952); see Ref. 12, pp. 264–270.Google Scholar
  21. 21.
    J. Wosnitzaet al. Phys. Rev. Lett. 67, 263 (1991).Google Scholar
  22. 22.
    L. N. Cooper,Phys. Rev. 104, 1189 (1956).Google Scholar
  23. 23.
    H. Fröhlich,Phys. Rev. 79, 845 (1950);Proc. R. Soc. London A 215, 291 (1952); J. Bardeen and D. Pines,Phys. Rev. 99, 1140 (1955).Google Scholar
  24. 24.
    C. Kittel,Introduction to Solid State Physics, 5th edn. (McGraw-Hill, New York, 1976), pp. 112–116.Google Scholar
  25. 25.
    H. Yukawa,Proc. Phys. Math. Soc, Jpn. 17, 48 (1935).Google Scholar
  26. 26.
    L. D. Landau,Sov. Phys. JETP 3, 920 (1957);5, 101 (1957);8, 70 (1959).Google Scholar
  27. 27.
    See, e.g., Ref. 12, pp. 132–328; Ref. 24, pp. 183–204.Google Scholar
  28. 28.
    See Ref. 14, p. 39, Eq. (2–15). The name “pairon” did not stick in the literature. So we shall use this only when very convenient. We shall often use the more familiar Cooper pair in its place.Google Scholar
  29. 29.
    P. Debye and E. Hückel,Phys. Z. 24, 185, 305 (1923).Google Scholar
  30. 30.
    L. H. Thomas,Proc. Cambridge Philos. Soc. 23, 542 (1927); E. Fermi, Z.Phys. 48, 73 (1928);49, 550 (1928).Google Scholar
  31. 31.
    See Ref. 12, pp. 225–233.Google Scholar
  32. 32.
    L. P. Eisenhart,Introduction to Differential Geometry (Princeton University Press, Princeton, 1940).Google Scholar
  33. 33.
    See Ref. 12, pp. 285–288.Google Scholar
  34. 34.
    M. S. Khaikin and R. T. Mina,Sov. Phys. JETP 15, 24 (1962);18, 896 (1964); Y. Onuki, H. Suenmatsu, and S. Tanuma,J. Phys. Chem. Solids 38, 419, 431 (1977).Google Scholar
  35. 35.
    P. A. M. Dirac,Principles of Quantum Mechanics, 4th edn. (Oxford University Press, London, 1958), pp. 251–252.Google Scholar
  36. 36.
    S. Fujita, T. Kimura, Y. Zheng, and S. Godoy,Rev. Mex. Fis. (accepted for publication).Google Scholar
  37. 37.
    P. C. Hohenberg,Phys. Rev. 158, 383 (1967).Google Scholar
  38. 38.
    P. Nozieres and D. Pines,Quantum Liquids (Benjamin, New York, 1966), Vol. 1, p. 90.Google Scholar
  39. 39.
    N. N. Bogoliubov,Sov. Phys. JETP 7, 41 (1958); L. P. Gorkov,Sov. Phys. JETP 7, 505 (1958); G. M. Eliashberg,Sov. Phys. JETP 11, 696 (1960); P. W. Anderson,Phys. Rev. 110, 827 (1958);112, 1900 (1958); S. M. Bose, T. Tanaka, and J. Halow,Phys. Kondens. Mater. 16, 319 (1973).Google Scholar
  40. 40.
    M. R. Schafroth, inSolid State Physics, Vol. 10, F. Seitz and D. Turnbull, eds. (Academic Press, New York, 1960), pp. 293–498.Google Scholar
  41. 41.
    R. D. Parks, ed.,Superconductivity (Marcel Dekker, New York, 1969); M. Tinkham,Introduction to Superconductivity (McGraw-Hill, New York, 1975); A. A. Abrikosov,Theory of Metals (North-Holland/Elsevier, Amsterdam, 1988); G. Rickayzen,Theory of Superconductivity (Interscience, New York, 1965); P. de Gennes,Superconductivity of Metals and Alloys (Benjamin, Menlo Park, California, 1966); B. T. Mathias, T. H. Geballe, and V. B. Compton,Rev. Mod. Phys. 35, 1 (1963).Google Scholar
  42. 42.
    R. E. Glover, III and M. Tinkham,Phys. Rev. 108, 243 (1957); M. A. Biondi and M. Garfunkel,Phys. Rev. 116, 853 (1959).Google Scholar
  43. 43.
    I. Giaever,Phys. Rev. Lett. 5, 147, 464 (1960).Google Scholar
  44. 44.
    B. S. Deaver and W. M. Fairbank,Phys. Rev. Lett. 7, 43 (1961); R. Doll and M. Näbauer,Phys. Rev. Lett. 7, 51 (1961).Google Scholar
  45. 45.
    B. D. Josephson,Phys. Lett. 1, 251 (1962); P. W. Anderson and J. M. Rowell,Phys. Rev. Lett. 10, 486 (1963).Google Scholar
  46. 46.
    S. Fujita and Y. Zheng, (to be published).Google Scholar
  47. 47.
    F. London,J. Phys. Chem. 43, 49 (1939);Superfluids, Vols. I and II (Wiley, New York, 1954).Google Scholar
  48. 48.
    J. File and R. G. Mills,Phys. Rev. Lett. 10, 93 (1963).Google Scholar
  49. 49.
    J. R. Anderson and D. C. Hines,Phys. Rev. B 2, 4752 (1970).Google Scholar
  50. 50.
    A. A. Abrikosov,Dokl. Akad. Nauk SSSR 86, 489 (1952); see also the book by the same author in Ref. 41, p. 366.Google Scholar
  51. 51.
    See, e.g., the book by P. de Gennes in Ref. 41, p. 24.Google Scholar
  52. 52.
    W. A. Little,Phys. Rev. A 134, 1416 (1964).Google Scholar
  53. 53.
    G. Saito and S. Kagoshima, eds.,Physics and Chemistry of Organic Superconductors (Springer, Heidelberg, 1990).Google Scholar
  54. 54.
    S. Coleman,Commun. Math. Phys. 31, 259 (1973).Google Scholar
  55. 55.
    Ref. 12, p. 217.Google Scholar
  56. 56.
    H. Katayama-Yoshidael al., Int. J. Mod. Phys. B 1, 1273 (1988).Google Scholar
  57. 57.
    R. A. Fisher, J. E. Gordon, and N. E. Phillips,J. Supercond. 1, 231 (1988).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • S. Fujita
    • 1
  • S. Watanabe
    • 2
  1. 1.Department of Physics and AstronomyState University of New York at BuffaloBuffalo
  2. 2.Metals Research InstituteHokkaido UniversitySapporoJapan

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