Advertisement

Macroscopic Quantum Phenomena in Superconductors

  • R. de Bruyn Ouboter
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 21)

Abstract

The essential feature of superfluidity (superconductivity) is according to F. London [1] a condensation of a macroscopic number of particles (bound-electron pairs, first described by Cooper [2]) in the same single quasi-particle quantum state. Such a condensation can be described, as usual, by an internal order parameter. According to the phenomenological theory of Ginzburg and Landau [3] the order parameter ΨS is a complex quantity, with properties similar to those of the wave function of the macroscopically occupied single quasi-particle quantum state. This complex order parameter ΨS has an amplitude \( {{\psi }_{O}}\left( {\vec{r},t,T} \right) \) and a phase \( \phi \left( {\vec{r},t} \right) \)
$$ {{\psi }_{S}} = {{\psi }_{O}}\left( {\vec{r},t,T} \right){{e}^{{i\phi \left( {\vec{r},t} \right)}}} $$
(1)
In the Ginzburg-Landau theory |ψS|2 is interpreted as the internal order parameter of the original two fluid model of Gorter and Casimir [4]. The charge density ρS(T) of the super fluid particles at a given temperature T is equal to the square of the amplitude ρS = |ψS|2 and hence,
$$ {{\psi }_{S}} = \sqrt {{{{\rho }_{S}}\left( {\vec{r},t,T} \right)}} \quad {{e}^{{i\phi \left( {\vec{r},t} \right)}}} $$
(2)
in which ρS → 0 if T → Tc. The absolute phase is not observable, but we will show that phase differences are directly observable quantities.

Keywords

Magnetic Flux Critical Current Weak Link Flux Quantum Double Junction 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. General ReferencesGoogle Scholar
  2. M. Tinkham, Introduction to Superconductivity, McGraw Hill, New York (1975).Google Scholar
  3. P.G. de Gennes, Superconductivity of Metals and Alloys, Benjamin, New York (1966).Google Scholar
  4. J. Bardeen, J.R. Schrieffer, Progr. in Low Temp. Phys., vol. 3 (C.J. Gorter ed.) North-Holland, Amsterdam (1961).Google Scholar
  5. P.W. Anderson, Progr. in Low Temp. Phys., vol. 5 (1967).Google Scholar
  6. R. de Bruyn Ouboter, A.Th.A.M. de Waele, Progr. in Low Temp. Phys., vol. 6 (1970).Google Scholar
  7. Superconductivity (R.D. Parks, ed.), Dekker, New York (1969), Chap. 8 by J.E. Mercereau and Chap. 9 by B.D. Josephson.Google Scholar
  8. A.H. Silver, J.E. Zimmerman, Applied Superconductivity (V.L. Newhouse, ed.) Vol. I (1975).Google Scholar
  9. O. V. Lounasmaa, Experimental principles and methods below 1 K, Academic Press, New York (1975).Google Scholar
  10. 1.
    F. London, Superfluids, Vol. I, Dover Public, New York (1960).Google Scholar
  11. 2.
    L.N. Cooper, Phys. Rev. 104, 1189 (1956);CrossRefGoogle Scholar
  12. 2a.
    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957).CrossRefGoogle Scholar
  13. 3.
    V.L. Ginzburg, L.D. Landau, Zh. Eksperim. i. Teor. Fiz. 12, 1064 (1950).Google Scholar
  14. 4.
    C.Jo Gorter, H.B.G. Casimir, Physica 1, 306 (1934),CrossRefGoogle Scholar
  15. 4a.
    C.Jo Gorter, H.B.G. Casimir, Phys. Z. 35, 963 (1934)Google Scholar
  16. 4b.
    C.Jo Gorter, H.B.G. Casimir, Z. techn. Phys. 15, 539 (1934).Google Scholar
  17. 5.
    F. London, Phys. Rev. 74, 462 (1948),Google Scholar
  18. 5a.
    F. and H. London, Proc. Roy. Soc. (London) A 149, 71 (1935).CrossRefGoogle Scholar
  19. 6.
    M. Meissner, R. Ochsenfeld, Naturwissenschaften 21, 787 (1933).CrossRefGoogle Scholar
  20. 7.
    B.S. Deaver, W.M. Fairbank, Phys. Rev. Lett. 7, 43 (1961).CrossRefGoogle Scholar
  21. 8.
    M. Doll, M. Näbauer, Phys. Rev. Lett. 7, 51 (1961),CrossRefGoogle Scholar
  22. 8a.
    M. Doll, M. Näbauer, Zeitschrift für Physik 169, 526 (1962).CrossRefGoogle Scholar
  23. 9.
    N. Byers, C.N. Yang, Phys. Rev. Lett. 7, 49 (1961).CrossRefGoogle Scholar
  24. 10.
    C.N. Yang, Rev. Mod. Phys. 34, 694 (1962).CrossRefGoogle Scholar
  25. 11.
    Y. Aharonov, D. Bohn, Phys. Rev. 115, 485 (1959).CrossRefGoogle Scholar
  26. 12.
    F. Bloch, Phys. Rev. 137, A 787 (1955),Google Scholar
  27. 12a..
    F. Bloch, Phys. Rev. Lett. 21, 1241 (1968).CrossRefGoogle Scholar
  28. 13.
    B.B. Schwartz, L.N. Cooper, Phys. Rev. 137, A 829 (1965).Google Scholar
  29. 14.
    W.A. Little, R.D. Parks, Phys. Rev. Lett. 9, 9 (1963),CrossRefGoogle Scholar
  30. 14a.
    W.A. Little, R.D. Parks, Phys. Rev. 133, A97 (1964),CrossRefGoogle Scholar
  31. 14b.
    R.P. Groff, R.D. Parks, Phys. Rev. 176, 557(1968).CrossRefGoogle Scholar
  32. 15.
    B.D. Josephson, Phys. Lett. 1, 251 (1962),CrossRefGoogle Scholar
  33. 15a.
    B.D. Josephson, Rev. Mod. Phys. 36, 216 (1964)CrossRefGoogle Scholar
  34. 15b.
    B.D. Josephson, Advances Physics 14, 419 (1965).CrossRefGoogle Scholar
  35. 16.
    P.W. Anderson, J.M. Rowell, Phys. Rev. Lett. 10, 230 (1963).CrossRefGoogle Scholar
  36. 17.
    J.M. Rowell, Phys. Rev. Lett. 11, 200 (1963).CrossRefGoogle Scholar
  37. 18.
    R.C. Jaklevic, J. Lambe, J.E. Mercereau, A.H. Silver, Phys. Rev. 140, A 1628 (1965),CrossRefGoogle Scholar
  38. 18a.
    R.C. Jaklevic, J. Lambe, J.E. Mercereau, A.H. Silver, Phys. Rev. Lett. 12, 159 (1965),CrossRefGoogle Scholar
  39. 18b.
    R.C. Jaklevic, J. Lambe, J.E. Mercereau, A.H. Silver, Phys. Rev. Lett. 12, 274 (1975),CrossRefGoogle Scholar
  40. 18c.
    R.C. Jaklevic, J. Lambe, J.E. Mercereau, A.H. Silver, Phys. Rev. Lett. 14, 887 (1965).CrossRefGoogle Scholar
  41. 19.
    R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. 3, chap. 21, Addison Wesley, New York (1965).Google Scholar
  42. 20.
    P.G. de Gennes, Phys. Lett. 5, 22 (1963).CrossRefGoogle Scholar
  43. 21.
    A. Baratoff, J.A. Blackburn, B.B. Schwartz, Phys. Rev. Lett. 25, 1096 (1970),CrossRefGoogle Scholar
  44. 21a.
    A. Baratoff, J.A. Blackburn, B.B. Schwartz, J. Low Temp. Phys. 20, 523 (1975).CrossRefGoogle Scholar
  45. 22.
    N.F. Pedersen, T.F. Finnegan, D.N. Langenberg, Phys. Rev. B6, 4151 (1972).Google Scholar
  46. 23.
    C.M. Falco, W.H. Parker, S.E. Trullinger, Phys. Rev. Lett. 31, 933 (1973).CrossRefGoogle Scholar
  47. 24.
    D.A. Vincent, B.S. Deaver Jr., Phys. Rev. Lett. 32, 212 (1974).CrossRefGoogle Scholar
  48. 25.
    J.E. Zimmerman, A.H. Silver, Solid State Commun. 4, 133 (1966),CrossRefGoogle Scholar
  49. 25a.
    J.E. Zimmerman, A.H. Silver, J. Appl. Phys. 39, 2679 (1968),CrossRefGoogle Scholar
  50. 25b.
    J.E. Zimmerman, A.H. Silver, Phys. Rev. Lett. 15, 888 (1965),CrossRefGoogle Scholar
  51. 25c.
    J.E. Zimmerman, A.H. Silver, Phys. Rev. 157, 317 (1967),CrossRefGoogle Scholar
  52. 25d.
    J.E. Zimmerman, A.H. Silver, J. Appl. Phys. 42, 30 (1971).CrossRefGoogle Scholar
  53. 26.
    R.P. Giffard, R.A. Webb, J.C. Wheatley, Journ. Low Temp. Phys. 6, 533 (1972).CrossRefGoogle Scholar
  54. 27.
    A.Th.A.M. de Waele, R. de Bruyn Ouboter, Physica 41, 225 (1969);CrossRefGoogle Scholar
  55. 27a.
    A.Th.A.M. de Waele, R. de Bruyn Ouboter, Physica 42, 626 (1969).CrossRefGoogle Scholar
  56. 28.
    L.D. Jackel, R.A. Buhrman, W.W. Webb, Phys. Rev. 10B, 2782 (1974).Google Scholar
  57. 29.
    C.S. Owen, D.J. Scalapino, Phys. Rev. 164, 538 (1967).CrossRefGoogle Scholar
  58. 30.
    T.A. Fulton, R.C. Dynes, Phys. Rev. Lett. 25, 794 (1970);CrossRefGoogle Scholar
  59. 30a.
    T.A. Fulton, R.C. Dynes, Phys. Rev. 3, 3015 (1971),CrossRefGoogle Scholar
  60. 30b.
    T.A. Fulton, R.C. Dynes, Solid State Commun. 8, 1353 (1970);CrossRefGoogle Scholar
  61. 30c.
    T.A. Fulton, R.C. Dynes, T.A. Fulton, L.N. Dunkelberger, R.C. Dynes, Phys. Rev. 6B, 855 (1972).Google Scholar
  62. 31.
    J.R. Waldram, J.M. Lumley, Revue de Physique Appliquée, 10, 7 (1975).CrossRefGoogle Scholar
  63. 32.
    H.H. Zappe, Appl. Phys. Lett. 25, 424 (1974);CrossRefGoogle Scholar
  64. 32a.
    H.H. Zappe, Appl. Phys. Lett. 27, 432 (1975).CrossRefGoogle Scholar
  65. 33.
    P. Guéret, Appl. Phys. Lett. 25, 426 (1974).CrossRefGoogle Scholar
  66. 34.
    I.M. Khalanikov, Introduction to the theory of superfluidity, Benjamin (1965), Chap. 9.Google Scholar
  67. 35.
    S. Putterman, R. de Bruyn üuboter, Phys. Rev. Lett. 24, 50 (1970).CrossRefGoogle Scholar
  68. 36.
    S.J. Putterman, Superfluid Hydrodynamics, North Holland (1974).Google Scholar
  69. 37.
    V. Ginzburg, Zh. Eksperim. i. Teor. Fiz. 14, 177 (1944).Google Scholar
  70. 38.
    N.V. Zavaritskii, J.E.T.P. Lett. 19, 126 (1974).Google Scholar
  71. 39.
    CM. Pegrum, A.M. Guénault, G.R. Pickett, Low Temp. Phys. LT14, North-Holland (1975), Vol. 2, p. 513;Google Scholar
  72. 39a.
    C.M. Falco, Solid State Commun. 19, 623 (1976).CrossRefGoogle Scholar
  73. 40.
    H.B.G. Casimir, A. Rademakers, Physica 13, 33 (1947).CrossRefGoogle Scholar
  74. 41.
    J.G. Daunt, K. Mendelssohn, Proc. Roy. Soc. (London) A185, 225 (1946).Google Scholar
  75. 42.
    M.L. Yu, J.E. Mercereau, Phys. Rev. Lett. 28, 1117 (1972).CrossRefGoogle Scholar
  76. 43.
    J. Clarke, Phys. Rev. Lett. 28, 1363 (1972).CrossRefGoogle Scholar
  77. 44.
    M. Tinkham, J. Clarke, Phys. Rev. Lett. 28, 1366 (1972).CrossRefGoogle Scholar
  78. 45.
    M. Tinkham, Phys. Rev. B6, 1747 (1972).Google Scholar
  79. 46.
    J.R. Waldram, Proc. Roy. Soc. (London) A345, 231 (1976).Google Scholar
  80. 47.
    S.R. de Groot, P. Mazur, Non-equilibrium thermodynamics, North-Holland (1969), Chap. 13, §4–§6.Google Scholar
  81. 48.
    T.J. Rieger D.J. Scalapino, J.E. Mercereau, Phys. Rev. Lett. 27, 1787 (1971);CrossRefGoogle Scholar
  82. 48a.
    T.J. Rieger D.J. Scalapino, J.E. Mercereau, Phys. Rev. 6B, 1734 (1972).Google Scholar
  83. 49.
    L.P. Gorkov, C.M. Eliashberg, Sov. Phys. J.E.T.P. 27, 328 (1968),Google Scholar
  84. 49a.
    L.P. Gorkov, C.M. Eliashberg, Sov. Phys. J.E.T.P. 29, 1298 (1969).Google Scholar
  85. 50.
    M. Cyrot, Repts. Progr. Phys. 36, 103 (1973);CrossRefGoogle Scholar
  86. 50a.
    M. Cyrot, J. Low Temp. Phys. 2, 161 (1970).CrossRefGoogle Scholar
  87. 51.
    W.J. Skocpol, M.R. Beasley, M. Tinkham, Journ. of Low. Temp. Phys. 16, 145 (1974).CrossRefGoogle Scholar
  88. 52.
    S. Shapiro, Phys. Rev. Lett. 11, 80 (1963).CrossRefGoogle Scholar
  89. 53.
    M.D. Fiske, Rev. Mod. Phys. 36, 221 (1964).CrossRefGoogle Scholar
  90. 54.
    I.K. Yanson, V.M. Svistuno, I.M. Dmitrenko, Sov. Phys. J.E.T.P. 48, 976 (1965).Google Scholar
  91. 55.
    R.E. Eck, D.J. Scalapino, B.N. Taylor, Phys. Rev. Lett. 13, 15 (1964).CrossRefGoogle Scholar
  92. 56.
    D.N. Langenberg, W.H. Parker, B.N. Taylor, Phys. Rev. 150, 186 (1966);CrossRefGoogle Scholar
  93. 56a.
    D.N. Langenberg, W.H. Parker, B.N. Taylor, Phys. Rev. Lett. 18, 287 (1967).CrossRefGoogle Scholar
  94. 57.
    W.H. Parker, B.N. Taylor, D.N. Langenberg, Phys. Rev. Lett. 18, 287 (1967);CrossRefGoogle Scholar
  95. 57a.
    W.H. Parker, B.N. Taylor, D.N. Langenberg, Metrologia 3, 89 (1967).CrossRefGoogle Scholar
  96. 58.
    T.F. Finnegan, A. Denenstein, D.N. Langenberg, Phys. Rev. B4, 1487 (1971);Google Scholar
  97. 58a.
    T.F. Finnegan, A. Denenstein, Rev. Mod. Phys. 41, 375 (1969).CrossRefGoogle Scholar
  98. 59.
    J. Clarke, Phys. Rev. Lett. 21, 1556 (1968).CrossRefGoogle Scholar
  99. 60.
    A.H. Dayem, C.C. Grimes, Appl. Phys. Lett. 9, 47 (1966).CrossRefGoogle Scholar
  100. 61.
    C.C. Grimes, P.L. Richards, S. Shapiro, J. Appl. Phys. 39, 3905 (1968);CrossRefGoogle Scholar
  101. 61a.
    C.C. Grimes, P.L. Richards, S. Shapiro, Phys. Rev. Lett. 17, 431 (1968);CrossRefGoogle Scholar
  102. 61b.
    C.C. Grimes, P.L. Richards, S. Shapiro, Journ. of Physics 36, 690 (1968).Google Scholar
  103. 62.
    D.B. Sullivan, J.E. Zimmerman, Am. J. of Physics 39, 1504 (1971).CrossRefGoogle Scholar
  104. 63.
    J.E. Zimmerman, A.H. Silver, Phys. Lett. 10, 47(1964);CrossRefGoogle Scholar
  105. 63a.
    J.E. Zimmerman, A.H. Silver, Phys. Rev. Lett. 13, 125 (1964);CrossRefGoogle Scholar
  106. 63b.
    J.E. Zimmerman, A.H. Silver, Phys. Rev. Lett. 15, 888 (1965);CrossRefGoogle Scholar
  107. 63c.
    J.E. Zimmerman, A.H. Silver, Phys. Rev. 141, 367 (1966).CrossRefGoogle Scholar
  108. 64.
    J. Clarke, Phil. Mag. 13, 115 (1966);CrossRefGoogle Scholar
  109. 64a.
    J. Clarke, Phys. Rev. Lett. 21, 1566 (1968).CrossRefGoogle Scholar
  110. 65.
    R. de Bruyn Ouboter, M.H. Omar, A.J.P.T. Arnold, T. Guinau, K.W. Taconis, Physica 32, 1449 and 2044 (1966);Google Scholar
  111. 65a.
    R. de Bruyn Ouboter, M.H. Omar, A.J.P.T. Arnold, T. Guinau, K.W. Taconis, Physica 34, 525 (1967).CrossRefGoogle Scholar
  112. 66.
    P.W. Anderson, A.H. Dayem, Phys. Rev. Lett, 13, 195 (1964).CrossRefGoogle Scholar
  113. 67.
    H.A. Notarys, J.E. Mercereau, Physica 55, 424 (1971).CrossRefGoogle Scholar
  114. 68.
    M. Nisenoff, Revue de Physiqe Appliquée 5, 21 (1970).CrossRefGoogle Scholar
  115. 69.
    J.E. Mercereau, Revue de Physique Apliquée 5, 13 (1970).CrossRefGoogle Scholar
  116. 70.
    R.A. Buhrman, J.E. Lukens, S.F. Strait, W.W. Webb, J. Appl. Phys. 41, 45 (1971).CrossRefGoogle Scholar
  117. 71.
    A.Th.A.M. de Waele, C.P.M. Vergouwen, A.A.J. Matsinger, R. de Bruyn Ouboter, Physica 59, 155 (1972).CrossRefGoogle Scholar
  118. 72.
    W.C. Stewart, Appl. Phys. Lett. 12, 277 (1968).CrossRefGoogle Scholar
  119. 73.
    D.E. McCumber, J. Appl. Phys. 39, 297 and 2503 and 3113 (1968).Google Scholar
  120. 74.
    J.E. Zimmerman, J.A. Cowen, A.H. Silver, Appl. Phys. Lett. 9, 353 (1966).CrossRefGoogle Scholar
  121. 75.
    J. Warman, J.A. Blackburn, Appl. Phys. Lett. 19, 60 (1971).CrossRefGoogle Scholar
  122. 76.
    L.G. Aslamazov, A.I. Larkin, So v. Phys. J.E.T.P. 9, 87 (1969).Google Scholar
  123. 77.
    L.D. Jackel, J.M. Warlaumont, T. D. Clark, J.C. Brown, R.A. Buhrman, and M.T. Levinsen, Appl. Phys. Lett. 28, 353 (1976).CrossRefGoogle Scholar
  124. 78.
    L.D. Jackel, W.H. Henkels, J.M. Warlaumont, and R.A. Buhrman, Appl. Phys. Lett. 29, 214 (1976).CrossRefGoogle Scholar
  125. 79.
    J.E. Zimmerman, A.H. Silver, Phys. Rev. 141, 367(1966).CrossRefGoogle Scholar
  126. 80.
    R.L. Forgacs, A. Warnick, Rev. Sci, Instr. 38, 214 (1967).CrossRefGoogle Scholar
  127. 81.
    R. de Bruyn Ouboter, W.H. Kraan, A.Th.A.M. de Waele, M.H. Omar, Physica 35, 335 (1967).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • R. de Bruyn Ouboter
    • 1
  1. 1.Kamerlingh Onnes LaboratoryLeidenThe Netherlands

Personalised recommendations