Advertisement

Vortices and Charges in Tunnel Junction Networks

  • Herre S. J. van der Zant
  • Lambert J. Geerligs
  • Johan E. Mooij
Part of the NATO ASI Series book series (NSSB, volume 254)

Abstract

Films of granular materials have long been modeled as two- (2 D) or three- (3 D) dimensional networks of grains, coupled by tunnel junctions [1]. The electrical resistance of such films is supposed to be concentrated in the junctions, whereas the grains themselves are relatively pure. It has only recently become possible to fabricate such tunnel junction networks artificially, using the lithographic techniques developed for microelectronics. So far only 2D networks have been made. Now parameters can, to a certain extent, be varied independently and theoretical models can be verified quantitatively against experimental results. The networks in ‘natural’ films are irregular, which in the percola-tive limit is an essential aspect. However, many of the important properties are well represented in regular arrays of metallic islands, coupled by identical tunnel junctions. We only consider such arrays here. The interest in tunnel junction arrays is certainly not only prompted by the analogy with the films. The regularity of fabricated tunnel junction arrays also introduces special effects, with their own special physics. In these lectures, we will concentrate on two main topics: the resistive behavior of superconducting arrays and the charging effects associated with the transfer of a single electron or a single Cooper pair. Resistance in 2 D superconductors is usually associated with flow of vortices and, as the title implies, this will play a prominent role here as well. However, in junction arrays we also find a different dissipative regime, better described by coherent phase slip. When vortices are present, they may not move in the familiar viscous way.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    The field is reviewed in the Proceedings of the NATO Advanced Research Workshop on Coherence in Superconducting Networks, J.E. Mooij and G. Schön, eds., Physica B 152, 1–302 (1988)Google Scholar
  2. [2]
    J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973)ADSGoogle Scholar
  3. [3]
    V.L. Berezinskii, Zh. Eksp.Teor. Fiz. 59, 907 (1970) [Sov. Phys. JETP 32, 493 (1971)]Google Scholar
  4. [4]
    J.E. Mooij, in: Percolation, Localization and Superconductivity, A.M. Goldman and S.A. Wolf, eds., p. 325, Plenum, New York (1983)Google Scholar
  5. [5]
    C.J. Lobb, D.W. Abraham and M. Tinkham, Phys. Rev. B 27, 150 (1983)ADSCrossRefGoogle Scholar
  6. [6]
    H.S.J. van der Zant, H.A. Rijken and J.E. Mooij, J. Low Temp. Phys. 79, 289 (1990)ADSCrossRefGoogle Scholar
  7. [7]
    U. Eckern and A. Schmid, Phys. Rev. B 39, 6441 (1989)ADSCrossRefGoogle Scholar
  8. [8]
    H.S.J. van der Zant, C.J. Müller, L.J. Geerligs, C.J.P.M. Harmans and J.E. Mooij, Phys. Rev. B 38, 5154 (1988)CrossRefGoogle Scholar
  9. [9]
    D.V. Averin and K.K. Likharev, Single Electronics, in: Quantum Effects in Small Disordered Systems, B. Al’tshuler, P. Lee and R. Webb, eds., Elsevier, Amsterdam, to be publishedGoogle Scholar
  10. [10]
    L.J. Geerligs, V.F. Anderegg, P.A.M Holweg, J.E. Mooij, H. Pothier, D. Esteve, C. Urbina and M.H. Devoret, Phys. Rev. Lett. 64, 2691 (1990)ADSCrossRefGoogle Scholar
  11. [11]
    T.A. Fulton, P.L. Gammel, D.J. Bishop, L.N. Dunkleberger and G.J. Dolan, Phys. Rev. Lett. 63, 1307 (1989)ADSCrossRefGoogle Scholar
  12. [12]
    D.V. Averin and V.Ya. Aleshkin, JETP Lett. 50, 367 (1989)ADSGoogle Scholar
  13. [13]
    G. Schön and A.D. Zaikin, Quantum coherent effects phase transitions and the dissipative dynamics of ultra small tunnel junctions, submitted to Phys. ReportsGoogle Scholar
  14. [14]
    see e.g. B.G. Orr, H.M. Jaeger and A.M. Goldman, Phys. Rev. B 32, 7586 (1985)ADSCrossRefGoogle Scholar
  15. [15]
    L.J. Geerligs, M. Peters, L.E.M. de Groot, A. Verbruggen and J.E. Mooij, Phys. Rev. Lett. 63, 326 (1989)ADSCrossRefGoogle Scholar
  16. [16]
    S. Chakravarty, S. Kivelson, G. Zimanyi and B.I. Halperin, Phys. Rev. B 35, 7256 (1987)ADSCrossRefGoogle Scholar
  17. [17]
    R. Fazio and G. Schön, this volume and submitted to LT 19Google Scholar
  18. [18]
    J.E. Mooij, B.J. van Wees, L.J. Geerligs, M. Peters, R. Fazio and G. Schön, Phys. Rev. Lett. 65, 645 (1990)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Herre S. J. van der Zant
    • 1
  • Lambert J. Geerligs
    • 1
  • Johan E. Mooij
    • 1
  1. 1.Department of Applied PhysicsDelft University of TechnologyDelftThe Netherlands

Personalised recommendations