Skip to main content

Quantum effects and the onset of superconductivity in granular films

  • Chapter
  • First Online:
Book cover Festkörperprobleme 29

Part of the book series: Advances in Solid State Physics ((ASSP,volume 29))

  • 43 Accesses

Abstract

Recent experiments on granular films have shown an apparently universal maximum normal state sheet resistance of around 6.5 above which superconductivity cannot be established. A possible explanation for this phenomenon is presented which is based on the competition between quantum fluctuations in the phase of the superconducting order parameter and dissipative effects. The films are modelled by locally superconducting grains coupled through Josephson junctions. Quantum fluctuations in the phases of individual grains may lead to a state in which the Cooper pair number rather than its conjugate phase is a good quantum number and superconductivity is destroyed. Dissipative effects tend to suppress these fluctuations and lead to the appearance of a new type of superconducting state possessing only short range phase coherence. This occurs for normal state resistances smaller than the quantum unit h/4e 2=6.5 kΩ, in agreement with the experimentally observed threshold.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.I. Shalnikov, Zh. Eksper. i Teor. Fiz. 10, 630 (1940)

    Google Scholar 

  2. W. Buckel, and R. Hilsch, Z. Phys. 138, 109 (1954)

    Article  ADS  Google Scholar 

  3. See e.g. the review by W.J. Skocpol and M. Tinkham, in: Rep. Prog. Phys.38, 1049 (1975)

    Google Scholar 

  4. See e.g. the review by J.E. Mooij, in: Percolation, Localization and Superconductivity ed. by A.M. Goldman, and S.A. Wolf (Plenum Press, New York 1984), p. 325

    Google Scholar 

  5. H. Ebisawa, H. Fukuyama, and S. Maekawa, J. Phys. Soc. Jpn. 54, 2257 (1985)

    Article  ADS  Google Scholar 

  6. M. Strongin, R.S. Thompson, O.F. Kammerer, and J.E. Crow, Phys. Rev. B1, 1078 (1970)

    Article  ADS  Google Scholar 

  7. B.G. Orr, H.M. Jaeger, and A.M. Goldman, Phys. Rev. B32, 7586 (1985)

    Article  ADS  Google Scholar 

  8. B.G. Orr, H.M. Jaeger, A.M. Goldman, and C.G. Kuper, Phys. Rev. Letters 56, 378 (1986)

    Article  ADS  Google Scholar 

  9. H.M. Jaeger, D.B. Haviland, A.M. Goldman, and B.G. Orr, Phys. Rev. B34, 4920 (1986)

    Article  ADS  Google Scholar 

  10. H.M. Jaeger, D.B. Haviland, B.G. Orr, and A.M. Goldman, Preprint, University of Minnesota (1988)

    Google Scholar 

  11. Note that in a two dimensional film the resistance is independent of the sample dimensions (assuming isotropy and a square geometry for simplicity). This peculiar scale invariance allows us to relate the local tunnel resistances between the grains to the overall film resistance.

    Google Scholar 

  12. R.C. Dynes, J.P. Garno, and J.M. Rowell, Phys. Rev. Letters 40, 479 (1978)

    Article  ADS  Google Scholar 

  13. S. Kobayashi, Y. Tada, and W. Sasaki, J. Phys. Soc. Jpn. 49, 2075 (1980)

    Article  ADS  Google Scholar 

  14. A.F. Hebard, and M.A. Paalanen, Phys. Rev. B30, 4063 (1984)

    Article  ADS  Google Scholar 

  15. S. Kobayashi, and F. Komori, J. Phys. Soc. Jpn. 57, 1884 (1988)

    Article  ADS  Google Scholar 

  16. V. Ambegaokar, B.I. Halperin, and J.S. Langer, Phys. Rev. B4, 2612 (1971)

    Article  ADS  Google Scholar 

  17. C.G. Neugebauer, and M.B. Webb, J. Appl. Phys. 33, 74 (1962)

    Article  ADS  Google Scholar 

  18. B. Abeles, P. Sheng, M.D. Coutts, and Y. Arie, Adv. Phys. 24, 407 (1975)

    Article  ADS  Google Scholar 

  19. For a recent discussion see: R. Németh, and B. Mühlschlegel, Z. Phys. B70, 159 (1988)

    Article  ADS  Google Scholar 

  20. Y. Imry, and M. Strongin, Phys. Rev. B24, 6353 (1981)

    Article  ADS  Google Scholar 

  21. R. Brown, and E. Šimánek, Phys. Rev. B34, 2957 (1986)

    Article  ADS  Google Scholar 

  22. B. Mühlschlegel, D.J. Scalapino, and R. Denton, Phys. Rev. B6, 1767 (1972)

    Article  ADS  Google Scholar 

  23. G. Deutscher, Y. Imry, and L. Gunther, Phys. Rev. B10, 4598 (1974)

    Article  ADS  Google Scholar 

  24. L.J. Geerligs, and J.E. Mooij, Physica B152, 212 (1988)

    Article  ADS  Google Scholar 

  25. For a recent review see: P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987)

    Article  ADS  Google Scholar 

  26. J.M. Graybeal, and M.R. Beasley, Phys. Rev. B29, 4167 (1984)

    Article  ADS  Google Scholar 

  27. B. Abeles, Phys. Rev. B15, 2828 (1977)

    Article  ADS  Google Scholar 

  28. K.B. Efetov, Sov. Phys. JETP 51, 1015 (1980)

    ADS  Google Scholar 

  29. E. Šimánek, Solid State Comm. 31, 419 (1979)

    Article  Google Scholar 

  30. S. Doniach, Phys. Rev. B24, 5063 (1981)

    Article  ADS  Google Scholar 

  31. P. Fazekas, B. Mühlschlegel, and M. Schröter, Z. Phys. B57, 193 (1984)

    Article  ADS  Google Scholar 

  32. A.O. Caldeira, and A.J. Leggett, Ann. Phys. 149, 374 (1983)

    Article  ADS  Google Scholar 

  33. W. Zwerger, Europhys. Letters, in print (1989)

    Google Scholar 

  34. A. Schmid, Phys. Rev. Letters 51, 1506 (1983)

    Article  ADS  Google Scholar 

  35. M.P.A. Fisher, and W. Zwerger, Phys. Rev. B32, 6190 (1985)

    Article  ADS  Google Scholar 

  36. W. Zwerger, Phys. Rev. B35, 4737 (1987)

    Article  ADS  Google Scholar 

  37. S.T. Chui, and J.D. Weeks, Phys. Rev. B14, 4978 (1976)

    Article  ADS  Google Scholar 

  38. J.A. Hertz, Phys. Rev. B14, 1165 (1976)

    Article  ADS  Google Scholar 

  39. R.M. Bradley, and S. Doniach, Phys. Rev. B30, 1138 (1984)

    Article  ADS  Google Scholar 

  40. M.P.A. Fisher, Phys. Rev. B36, 1917 (1987)

    Article  ADS  Google Scholar 

  41. S. Chakravarty, S. Kivelson, G. Zimanyi, and B.I. Halperin, Phys. Rev. B35, 7256 (1987)

    Article  ADS  Google Scholar 

  42. A. Kampf, and G. Schön, Phys. Rev. B36, 3651 (1987)

    Article  ADS  Google Scholar 

  43. A.D. Zaikin, Physica B152, 251 (1988)

    Article  ADS  Google Scholar 

  44. R.A. Ferrell, and B. Mirhashem, Phys.Rev. B37, 648 (1988)

    Article  ADS  Google Scholar 

  45. S. Chakravarty, G.L. Ingold, S. Kivelson, and G. Zimanyi, Phys. Rev. B37, 3283 (1988)

    Article  ADS  Google Scholar 

  46. J.S. Langer, and V. Ambegaokar, Phys. Rev. 164, 498 (1967)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Ulrich Rössler

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

About this chapter

Cite this chapter

Zwerger, W. (1989). Quantum effects and the onset of superconductivity in granular films. In: Rössler, U. (eds) Festkörperprobleme 29. Advances in Solid State Physics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108005

Download citation

  • DOI: https://doi.org/10.1007/BFb0108005

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-528-08035-8

  • Online ISBN: 978-3-540-75350-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics