Three “Universal” Mesoscopic Josephson Effects

  • C. W. J. Beenakker
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 109)

Abstract

A recent theory is reviewed for the sample-to-sample fluctuations in the critical current of a Josephson junction consisting of a disordered point contact or microbridge. The theory is based on a relation between the super-current and the scattering matrix in the normal state. The root-mean-square amplitude rms I c of the critical current I c at zero temperature is given by rms I c eΔ0/ℏ, up to a numerical coefficient of order unity (eΔ0 is the energy gap). This is the superconducting analogue of “Universal Conductance Fluctuations” in the normal state. The theory can also be applied to a ballistic point contact, where it yields the analogue of the quantized conductance, and to a quantum dot, where it describes supercurrent resonances. All three phenomena provide a measurement of the supercurrent unit eΔ0/ℏ, and are “universal” through the absence of a dependence on junction parameters.

Keywords

Coherence Dition Meso Asta Harman 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. W. J. Beenakker and H. van Houten, Phys. Rev. Lett. 66, 3056 (1991).CrossRefGoogle Scholar
  2. 2.
    L. I. Glazman and K. A. Matveev, Pis’ma Zh. Eksp. Teor. Fiz. 49, 570 (1989) [JETP Lett. 49, 659 (1989)].Google Scholar
  3. 3.
    C W. J. Beenakker and H. van Houten, in: Proc. 4th Int. Conf. on Superconducting and Quantum Effect Devices and their Applications (SQUID’91), ed. by H. Koch and H. Lübbig (Springer, Berlin, to be published).Google Scholar
  4. 4.
    C. W. J. Beenakker, Phys. Rev. Lett. 67, 3836 (1991); Erratum (ibidem, to be published). The assertion made in this Ref. (directly above Eq. 16) that T p ≪ 1 for lL is incorrect (see Sec. 5.3 of the present paper).CrossRefGoogle Scholar
  5. 5.
    B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, Phys. Rev. Lett. 60, 848 (1988).CrossRefGoogle Scholar
  6. 6.
    D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. C 21, L209 (1988).CrossRefGoogle Scholar
  7. 7.
    A review of quantum transport in semiconductor nanostructures is: C. W. J. Beenakker and H. van Houten, Solid State Phys. 44, 1 (1991).CrossRefGoogle Scholar
  8. 8.
    A. Furusaki, H. Takayanagi, and M. Tsukada, Phys. Rev. Lett. 67, 132 (1991); Phys. Rev. B (to be published).CrossRefGoogle Scholar
  9. 9.
    B. L. Al’tshuler, Pis’ma Zh. Eksp. Teor. Fiz. 41, 530 (1985) [JETP Lett. 41, 648 (1985)].Google Scholar
  10. 10.
    P. A. Lee and A. D. Stone, Phys. Rev. Lett. 55, 1622 (1985).CrossRefGoogle Scholar
  11. 11.
    A review of mesoscopic fluctuation phenomena is: B. L. Al’tshuler, P. A. Lee, and R. A. Webb, eds., Mesoscopic Phenomena in Solids (North-Holland, Amsterdam, 1991).Google Scholar
  12. 12.
    B. L. Al’tshuler and B. Z. Spivak, Zh. Eksp. Teor. Fiz. 92, 609 (1987) [Sov. Phys. JETP 65, 343 (1987)].Google Scholar
  13. 13.
    C. W. J. Beenakker and H. van Houten, in: Nanostructures and Mesoscopic Systems, ed. by W. P. Kirk and M. A. Reed (Academic, New York, to be published).Google Scholar
  14. 14.
    A. Furusaki and M. Tsukada, Solid State Comm. 78, 299 (1991).CrossRefGoogle Scholar
  15. 15.
    B. J. van Wees, K.-M. H. Lenssen, and C. J. P. M. Harmans, Phys. Rev. B 44, 470 (1991).CrossRefGoogle Scholar
  16. 16.
    P. G. de Gennes, Superconductivity of Metals and Alloys (Benjamin, New York, 1966).Google Scholar
  17. 17.
    K. K. Likharev, Rev. Mod. Phys. 51, 101 (1979).CrossRefGoogle Scholar
  18. 18.
    M. Yu. Kupriyanov and V. F. Lukichev, Fiz. Nizk. Temp. 8, 1045 (1982) [Sov. J. Low Temp. Phys. 8, 526 (1982)]; A. A. Zubkov and M. Yu. Kupriyanov, Fiz. Nizk. Temp. 9, 548 (1983) [Sov. J. Low Temp. Phys. 9, 279 (1983)].Google Scholar
  19. 19.
    J. Bardeen, R. Kümmel, A. E. Jacobs, and L. Tewordt, Phys. Rev. 187, 556 (1969).CrossRefGoogle Scholar
  20. 20.
    A. F. Andreev, Zh. Eksp. Teor. Fiz. 46,1823 (1964); 49, 655 (1965) [Sov. Phys. JETP 19, 1228 (1964); 22, 455 (1966)].Google Scholar
  21. 21.
    E. Akkermans, A. Auerbach, J. E. Avron, and B. Shapiro, Phys. Rev. Lett. 66, 76 (1991).CrossRefGoogle Scholar
  22. 22.
    A. D. Stone and Y. Imry, Phys. Rev. Lett. 56, 189 (1986).CrossRefGoogle Scholar
  23. 23.
    Y. Imry, in: Directions in Condensed Matter Physics, Vol. 1, ed. by G. Grinstein and G. Mazenko (World Scientific, Singapore, 1986).Google Scholar
  24. 24.
    W. Haberkorn, H. Knauer, and J. Richter, Phys. Status Solidi A 47, K161 (1978).CrossRefGoogle Scholar
  25. 25.
    A. V. Zaĭtsev, Zh. Eksp. Teor. Fiz. 86, 1742 (1984) [Sov. Phys. JETP 59, 1015 (1984)].Google Scholar
  26. 26.
    G. B. Arnold, J. Low Temp. Phys. 59, 143 (1985).CrossRefGoogle Scholar
  27. 27.
    A. Furusaki and M. Tsukada, Physica B 165M&166, 967 (1990).CrossRefGoogle Scholar
  28. 28.
    D. S. Fisher and P. A. Lee, Phys. Rev. B 23, 6851 (1981).CrossRefGoogle Scholar
  29. 29.
    I. O. Kulik and A. N. Omel’yanchuk, Fiz. Nizk. Temp. 3, 945 (1977); 4, 296. (1978) [Sov. J. Low Temp. Phys. 3, 459 (1977); 4, 142 (1978)].Google Scholar
  30. 30.
    L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1977).Google Scholar
  31. 31.
    M. Büttiker, IBM J. Res. Dev. 32, 63 (1988).CrossRefGoogle Scholar
  32. 32.
    V. Kalmeyer and R. B. Laughlin, Phys. Rev. B 35, 9805 (1987).CrossRefGoogle Scholar
  33. 33.
    W. Xue and P. A. Lee, Phys. Rev. B 38, 3913 (1988).CrossRefGoogle Scholar
  34. 34.
    A. D. Stone, P. A. Mello, K. A. Muttalib, and J.-L. Pichard, in Ref. [11].Google Scholar
  35. 35.
    I. O. Kulik and A. N. Omel’yanchuk, Pis’ma Zh. Eksp. Teor. Fiz. 21, 216 (1975) [JETP Lett. 21, 96 (1975)].Google Scholar
  36. 36.
    V. Ambegaokar and A. Baratoff, Phys. Rev. Lett. 10, 486 (1963); 11, 104(E) (1963).CrossRefGoogle Scholar
  37. 37.
    Y. Imry, Europhys. Lett. 1, 249 (1986).CrossRefGoogle Scholar
  38. 38.
    H. Takayanagi and T. Kawakami, Phys. Rev. Lett. 54, 2449 (1985).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • C. W. J. Beenakker
    • 1
  1. 1.Instituut-LorentzUniversity of LeidenLeidenThe Netherlands

Personalised recommendations