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Physics and Applications of the Quantum Hall Effect

  • Klaus v. Klitzing
Part of the NATO ASI Series book series (NSSB, volume 170)

Abstract

The most fascinating property of the Quantum Hall Effect (QHE) is the phenomenon that from a relatively simple experiment on a semiconductor a new type of electrical resistor R0 can be deduced which is independent of microscopic properties of the semiconductor and reproducable at a level of better than 10-6. In the recent publication of “The 1986 Adjustment of the Fundamental Physical Constants”1 one finds a new general constant, the quantized Hall resistance with a recommended value R0=(25812.8056±0.00012) Ohm. This value is identical with the ratio h/e2, the ratio between the Planck constant h and the square of the electron charge e. The surprising result is, that this universal constant R0 can be measured directly on a macroscopic system. In principle all Hall effect measurements in strong magnetic fields and low temperatures on a two- dimensional electron gas show the QHE. However, for the experimental realization of this quantum phenomenon one has to specify the condition “low temperature”, “high magnetic field” and “two-dimensional system”. The inversion layer at the Si-Si02 interface of a silicon MOS fieldeffect transistor is the classical example for a two-dimensional system2 but in a more general way all structures with a vanishing conductivity in one direction may be called two-dimensional electron gas. Even a superlattice with a macroscopic thickness of some micrometers can show two-dimensional properties if the periodicity of the superlattice leads to well separated minihands3. In this respect most of the structures discussed at this school are related to the physics of two-dimensional systems and can be used for a discussion of the quantum Hall effect. The reduced dimensionality is necessary in order to obtain gaps in the electronic spectrum.

Keywords

Magnetic Field High Magnetic Field Landau Level Quantum Hall Effect Hall Conductivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    E.R. Cohen and B.N. Taylor, Codata Bulletin 63, 1 (1986)Google Scholar
  2. 2.
    for a review see: T. Ando, A.B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 437 (1982)ADSCrossRefGoogle Scholar
  3. 3.
    H.L. Stornier, J.P. Eisenstein, A.C. Gossard, K.W. Baldwin, and J.H. English, Proc. 18th Int. Conf. on the Physics of Semiconductors, Stockholm 1986, ed. Olof Engström, World Scientific Publishing Co. Pte Ltd., SingaporeGoogle Scholar
  4. 4.
    J. Avron and R. Sciler, Phys. Rev. Lett. 54, 259 (1985)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    K. v. Klitzing, Rev. Mod. Phys. 58, 519 (1986)Google Scholar
  6. 6.
    The Quantum Hall Effect (Graduate Texts in Contemporary Physics, Springer Verlag New York, 1987 ), by R.E. Prange and S.M. GirvinGoogle Scholar
  7. 7.
    H. Aoki, Reports on Progress in Physics (1987)Google Scholar
  8. 8.
    E.I. Rashba and V.B. Timofeev, Sov. Phys. Semicond. 20, 617 (1986)Google Scholar
  9. 9.
    R.F. Wick, J. Appl. Phys. 25, 741 (1954)ADSMATHCrossRefGoogle Scholar
  10. 10.
    K. v. Klitzing, Festkörperprobleme 21, 1 (1981)Google Scholar
  11. 11.
    R.W. Rendell and S.M. Girvin, Phys. Rev. B23, 6610 (1981)ADSCrossRefGoogle Scholar
  12. 12.
    B. Neudecker and K.H. Hoffmann, Solid State Commun. 62, 135 (1987)ADSCrossRefGoogle Scholar
  13. 13.
    R.B. Laughlin, Phys. Rev. B23, 5632 (1981)ADSCrossRefGoogle Scholar
  14. 14.
    R. Kubo, S.J. Miyake, and N. Hashitsume, Solid State Physics 17, 269 (1965), ( Academic Press, New York), ed. by F. Scitz and D. TurnballGoogle Scholar
  15. 15.
    G.A. Baraff and D.C. Tsui, Phys. Rev. B24, 2274 (1981)ADSCrossRefGoogle Scholar
  16. 16.
    R.E. Prange, Phys. Rev. B23, 4802 (1981)ADSCrossRefGoogle Scholar
  17. 17.
    H. Aoki and T. Ando, Solid State Commun. 38, 1079 (1981)ADSCrossRefGoogle Scholar
  18. 18.
    W. Brenig, Z. Phys. B50 305 (1983)MathSciNetCrossRefGoogle Scholar
  19. 19.
    J.T. Chalker, J. Phys. C16, 4297 (1983)ADSGoogle Scholar
  20. 20.
    T. Ando and Y. Uemura, J. Phys. Soc. Japan 36, 959 (1974)ADSCrossRefGoogle Scholar
  21. 21.
    T. Ando, J. Phys. Soc. Japan 36, 1521; 37, 622; 37, 1233 (1974)CrossRefGoogle Scholar
  22. 22.
    S. Kawaji and J. Wakabayashi, Surf. Sci. 58, 238 (1976)ADSCrossRefGoogle Scholar
  23. 23.
    H. Aoki, J. Phys. C10, 2583 (1977)ADSGoogle Scholar
  24. 24.
    H. Aoki and H. Kamimura, Solid State Commun. 21, 45 (1977)ADSCrossRefGoogle Scholar
  25. 25.
    K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)Google Scholar
  26. 26.
    S.V. Iordansky, Solid State Commun. 43, 1 (1982)ADSCrossRefGoogle Scholar
  27. 27.
    R.F. Kazarinov and S. Luryi, Phys. Rev. B25, 7626 (1982)ADSCrossRefGoogle Scholar
  28. 28.
    S.A. Trugman, Phys. Rev. B27, 7539 (1983)ADSCrossRefGoogle Scholar
  29. 29.
    R.J. Haug, R.R. Gerhardts, K. v. Klitzing, and K. Ploog, to be publishedGoogle Scholar
  30. 30.
    M. Dobers, private communication. See also: G. Lommer, F. Malcher, and U. Rössler, Phys. Rev. B32, 6965 (1985)Google Scholar
  31. 31.
    R.J. Haug, K. v. Klitzing, R.J. Nicholas, J.C. Maan, and G. Weimann, to be published in Surf. Sci. (1988), Proc. Int. Conf. Electronic Properties of Two-Dimensional SystemsGoogle Scholar
  32. 32.
    K. v. Klitzing, G. Ebert, N. Kleinmichel, H. Obloh, G. Dorda, and G. Weimann, Proc. 17th Int. Conf. Physics of Semiconductors, p. 271 (Springer-Verlag Berlin, Heidelberg, New York, Tokyo) ed. By D.J. Chadi and W.A. HarrisonGoogle Scholar
  33. 33.
    M.E. Cage, B.F. Field, R.F. Dziuba, S.M. Girvin, A.C. Gossard, and D.C. Tsui, Phys. Rev. B3i0, 2286 (1984)Google Scholar
  34. 34.
    A.H. MacDonald, T.M. Rice, and W.F. Brinkman, Phys. Rev. B28, 3648 (1983)ADSGoogle Scholar
  35. 35.
    J. Riess, J. Phys. C17, L849 (1984)MathSciNetADSGoogle Scholar
  36. 36.
    O. Heinonen and P.L. Taylor, Phys. Rev. B32, 633 (1985)ADSGoogle Scholar
  37. 37.
    G. Ebert, K. v. Klitzing, and G. Weimann, J. Phys. C18, L257 (1985)Google Scholar
  38. 38.
    V. Gudmundsson and R.R. Gerhardts, Phys. Rev. B35, May 1987Google Scholar
  39. 39.
    K. v. Klitzing and G. Ebert, Metrologia 21, 11 (1985)ADSCrossRefGoogle Scholar
  40. 40.
    For a summary see: Conference on Precision Electromagnetic Measurements, IEEE Trans. Meas. IM-34, 301–327 (1985)Google Scholar
  41. 41.
    E. Braun, private communicationGoogle Scholar
  42. 42.
    High precision wire resistors in units of 1, 4, and 1/4 Klitzing are available from: Burster Präzisionsmeßtechnik, D-7562 GernsbachGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Klaus v. Klitzing
    • 1
  1. 1.Max-Planck-Institut für FestkörperforschungStuttgart 80Germany

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