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Persistent Currents in Mesoscopic Rings

  • Eberhard K. Riedel
Chapter
Part of the NATO ASI Series book series (NSSB, volume 254)

Abstract

The status of the field is excellent, much is in flux. For the first time we have experimental evidence [1] for persistent currents in small normal metal rings threaded by a magnetic flux. And there are new theoretical developments that indicate that in addition to the single-electron (or quasi-particle) contribution [2, 3] to the persistent current there are also collective ones [4].

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References

  1. [1]
    L.P. Lévy, G. Dolan, J. Dunsmuir, and H. Bouchiat, Phys. Rev. Lett. 64, 2074 (1990)ADSCrossRefGoogle Scholar
  2. [2]
    H.F. Cheung, E.K. Riedel, and Y. Gefen, Phys. Rev. Lett. 62, 587 (1989);ADSCrossRefGoogle Scholar
  3. [2a]
    E.K. Riedel, H.F. Cheung, and Y. Gefen, Physica Scripta T25, 357 (1989)CrossRefGoogle Scholar
  4. [3]
    H.F. Cheung and E.K. Riedel, unpublishedGoogle Scholar
  5. [4]
    V. Ambegaokar and U. Eckern, Phys. Rev. Lett. 65, 381 (1990)ADSCrossRefGoogle Scholar
  6. [5]
    H. Bouchiat and G. Montambaux, J. Phys. (France) 50, 2695 (1989)Google Scholar
  7. [6]
    M. Büttiker, Y. Imry, and R. Landauer, Phys. Lett. A 96, 365 (1983)CrossRefGoogle Scholar
  8. [7]
    M. Büttiker, Phys. Rev. B 32, 1846 (1985);CrossRefGoogle Scholar
  9. [7a]
    R. Landauer and M. Büttiker, Phys. Rev. Lett. 54, 2049 (1985)ADSCrossRefGoogle Scholar
  10. [8]
    H.F. Cheung, Y. Gefen, E.K. Riedel, and W.H. Shih, Phys. Rev. B 37, 6050 (1988)ADSCrossRefGoogle Scholar
  11. [9]
    N. Trivedi and D.A. Browne, Phys. Rev. B 38, 9581 (1988)ADSCrossRefGoogle Scholar
  12. [10]
    S. Washburn and R.A. Webb, Adv. Phys. 35, 375 (1986)ADSCrossRefGoogle Scholar
  13. [11]
    Y. Imry, in: Directions in Condensed Matter Physics, G. Grinstein and G. Mazenko, eds., p. 101, World Scientific, Singapore, (1986)CrossRefGoogle Scholar
  14. [12]
    H.F. Cheung, Y. Gefen, and E.K. Riedel, IBM J. Res. Develop. 32, 359 (1988)CrossRefGoogle Scholar
  15. [13]
    B.L. Altshuler and B.Z. Spivak, Zh. Eksp. Teor. Fiz. 92, 609 (1987) [Sov. Phys. JETP 65, 343 (1987)]Google Scholar
  16. [14]
    B.L. Altshuler, D.E. Khmel’nitskii, and B.Z. Spivak, Sol. St. Commun. 48, 841 (1983)ADSCrossRefGoogle Scholar
  17. [15]
    N. Byers and C.N. Yang, Phys. Rev. Lett. 7, 46 (1961)ADSCrossRefGoogle Scholar
  18. [16]
    F. Bloch, Phys. Rev. B 2, 109 (1970)ADSCrossRefGoogle Scholar
  19. [17]
    Such rings would also allow the investigation of persistent currents carried by edge states [X.C.] Xie and E.K. Riedel, Bull. Am. Phys. Soc. 34, 547 (1989)]Google Scholar
  20. [18]
    R.A. Webb, private communicationGoogle Scholar
  21. [19]
    A. Benoit, this volumeGoogle Scholar
  22. [20]
    Y. Imry, Europhys. Lett. 1, 249 (1986)ADSCrossRefGoogle Scholar
  23. [21]
    G. Kirczenow, Phys. Rev. B 32, 7952 (1985)ADSCrossRefGoogle Scholar
  24. [22]
    H.F. Cheung and E.K. Riedel, Phys. Rev. B 40, 9498 (1989)ADSCrossRefGoogle Scholar
  25. [23]
    I retract a remark about ensembles of rings [in [2], p. 590] that said otherwiseGoogle Scholar
  26. [24]
    See, e.g., Y. Meir, Y. Gefen, and O. Entin-Wohlman, Phys. Rev. Lett. 63, 798 (1989)ADSCrossRefGoogle Scholar
  27. [25]
    I learned about this interaction effect in rings first from B.Z. Spivak [private communication (February 1990)], who referred me to [14]Google Scholar
  28. [26]
    F. von Oppen and E.K. Riedel, unpublishedGoogle Scholar
  29. [27]
    O. Entin-Wohlman and Y. Gefen, Europhys. Lett. 8, 477 (1989)ADSCrossRefGoogle Scholar
  30. [28]
    There is some confusion on this point, e.g. [5]Google Scholar
  31. [29]
    G. Montambaux, H. Bouchiat, D. Signetti, and R. Friesner, preprint (April 1990); and this volumeGoogle Scholar
  32. [30]
    P.A. Lee and T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985), and references therein.ADSCrossRefGoogle Scholar
  33. [31]
    The effect of spin-orbit scattering on 〈I p=2n,d in eq. (13) is not known, though a factor (– 1/2) has been mentioned in [1]. There is no sign change in the collective contribution (14) due to spin-orbit scattering [26]. However, a diamagnetic collective current contribution occurs when the effective electron-electron interaction is attractiveGoogle Scholar
  34. [32]
    In deriving eqs. (4) and (14) one can replace the Green’s functions by their standard bulk forms (except for discrete momentum variables) and consequently I use d = 3 in the diffusion constant D. The overall d-dependence is 1/d 1/2 in eq. (4) and 1/d in eq. (14). The coefficients are model dependent, while the powers of l el /L, L/l t, etc. are expected to be universalGoogle Scholar
  35. [33]
    I assume that all 107 rings contribute uniformly to the total measured signalGoogle Scholar
  36. [34]
    Disorder is characterized by U R = W(L/12M)1/2/4&#x03C0, where W is the disorder parameter in the Anderson model with random site disorder. The hopping matrix element is set equal to 1Google Scholar
  37. [35]
    I thank B.L. Altshuler for a discussion of this pointGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Eberhard K. Riedel
    • 1
  1. 1.Department of PhysicsUniversity of WashingtonSeattleUSA

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