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Persistent Currents in Mesoscopic Rings: Ensemble Average and Half-Flux-Quantum Periodicity

  • Hèléne Bouchiat
  • Gilles Montambaux
  • L. P. Levyt
  • G. Dolan
  • J. Dunsmuir
Chapter
Part of the NATO ASI Series book series (NSSB, volume 254)

Abstract

The transport properties of micron size metallic samples at low temperature have been shown to exhibit features characteristic of the quantum coherence of the electronic wave function along the whole sample. One of the most striking has been the detection of Aharonov-Bohm oscillations in the resistance of a loop pierced by a magnetic field perpendicular to its plane [1] . In such resistivity measurements, the electric probes induce a coupling of the sample with reservoirs of electrons in which dissipation occurs. Isolated metallic rings are predicted to present an even more spectacular behavior: Büttiker, Imry and Landauer [2] suggested the existence of persistent currents in the presence of a magnetic field. These currents are a consequence of the sensitivity of the eigenstates to the boundary conditions along the ring. In the presence of a magnetic field, the periodic boundary conditions are indeed modified into
$$\psi \left( {x + L} \right) = \psi \left( x \right){e^{i\varphi }}$$
(1)
where φ = 2πΦ/Φ 0 . Φ is the magnetic field through the loop. Φ 0 is the flux quantum h/e. The persistent current is related to the flux derivative of the eigenenergies by
$$I\left( \phi \right) = \sum\limits_n {\partial {E_n}/\partial \phi } $$
(2)
where n labels the N filled energy levels. The current has thus the period Φ 0. There has been recently a growing experimental interest in the detection of this persistent current. On the theoretical side, it is of course of essential interest to estimate the amplitude of this current in a model as close as possible to the experimental situation.

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References

  1. [1]
    S. Washburn and R.A. Webb, Adv. in Phys. 35, 395 (1986)ADSCrossRefGoogle Scholar
  2. [2]
    M. Büttiker, Y. Imry, and R. Landauer, Phys. Rev. A 96 , 365 (1983)Google Scholar
  3. [3]
    R. Landauer and M. Büttiker, Phys. Rev. Lett. 54, 2049 (1985);ADSCrossRefGoogle Scholar
  4. [3a]
    M. Büttiker, Phys. Rev. B 32, 1846 (1985)CrossRefGoogle Scholar
  5. [4]
    H.F. Cheung, Y. Gefen, E.K. Riedel, and W.H. Shih, Phys. Rev. B 37, 6050 (1988)ADSCrossRefGoogle Scholar
  6. [5]
    N. Trivedi and D.A. Browne, Phys. Rev. B 38, 9581 (1988)ADSCrossRefGoogle Scholar
  7. [6]
    H.F. Cheung, Y. Gefen, and E K. Riedel, IBM J. Res. Develop. 32, 359 (1988)CrossRefGoogle Scholar
  8. [7]
    E.K. Riedel, H.F. Cheung, and Y. Gefen, Physica Scripta 25, 357 (1989);CrossRefGoogle Scholar
  9. [7a]
    H.F. Cheung, E.K. Riedel, and Y. Gefen, Phys. Rev. Lett. 62, 587 (1989)ADSCrossRefGoogle Scholar
  10. [8]
    D. DiVincenzo and M.P.A. Fisher, preprintGoogle Scholar
  11. [9]
    O. Entin-Wohlmann and Y. Gefen, Europhys. Lett. 5, 447 (1989)Google Scholar
  12. [10]
    H. Bouchiat and G. Montambaux, J. Physique 50, 2695 (1989)CrossRefGoogle Scholar
  13. [11]
    G. Montambaux, H. Bouchiat, D. Sigeti and R. Friesner (preprint)Google Scholar
  14. [12]
    J.-L. Pichard and G.J. Sarma, J. Phys. C 14, L127, L617 (1981)ADSGoogle Scholar
  15. [13]
    L. Levy, G. Dolan, J. Dunsmuir and H. Bouchiat, Phys. Rev. Lett. 64, 2074 (1990)ADSCrossRefGoogle Scholar
  16. [14]
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  17. [15]
    M. Friedrichs and R. Friesner, Phys. Rev. B 57, 303 (1988)Google Scholar
  18. [16]
    J.T. Edwards and D.J. Thouless, J. Phys. C 5, 807 (1972)ADSCrossRefGoogle Scholar
  19. [17]
    D.J. Thouless, Phys. Rep. 132, 93 (1974);ADSCrossRefGoogle Scholar
  20. [17a]
    D.J. Thouless, Phys. Rev. Lett. 18, 1167 (1977)ADSCrossRefGoogle Scholar
  21. [18]
    M. Kappus and M.J. Wegner, Z. Phys. B 45, 15 (1981);CrossRefGoogle Scholar
  22. [18a]
    P.D. Kirkman and J.B. Pendry, J. Phys. C 17, 4327 (1984)ADSGoogle Scholar
  23. [19]
    Y. Imry, these volumeGoogle Scholar
  24. [20]
    V. Ambegaokar and U. Eckern, Phys. Rev. Lett. 65, 381 (1990)ADSCrossRefGoogle Scholar
  25. [21]
    B.L. Alt’shuler, D.E. Khmel’nitzkii and B.Z. Spivak, Sol. St. Commun. 48, 841 (1983)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Hèléne Bouchiat
    • 1
  • Gilles Montambaux
    • 1
  • L. P. Levyt
    • 2
  • G. Dolan
    • 2
  • J. Dunsmuir
    • 2
  1. 1.Laboratoire de Physique des Solides Associé au CNRS, Bât. 510Université Paris SudOrsayFrance
  2. 2.AT&T Bell LaboratoriesMurray HillUSA

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