Localization and the Integral Quantum Hall Effect

  • Adrianus M. M. Pruisken
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 61)

Abstract

In the early theoretical investigations [1–4] of the Integral Quantum Hall Effect (IQHE) [5,6], it was recognized that the observed plateaus of quantized Hall conductance should be explainable from the two-dimensional, free electron gas subject to a constant magnetic background field and to a random impurity potential. The concept of localization due to the randomness turned out to be essential in the explanation of the width of the plateaus, as well as the precision of the quantization [7].

Keywords

Manifold Eter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.B. Laughlin, Phys. Rev. B 23 5632 (1981).CrossRefGoogle Scholar
  2. 2.
    D.J. Thouless, J. Phys. C 14 3475 (1981).CrossRefGoogle Scholar
  3. 3.
    R.E. Prange, Phys. Rev. B 23 4802 (1981);CrossRefGoogle Scholar
  4. R.E. Prange and R. Joynt, Phys. Rev. B 25 2943 (1982)CrossRefGoogle Scholar
  5. 4.
    B.I. Haiperin, Phys. Rev. B 25 2185 (1982).CrossRefGoogle Scholar
  6. 5.
    K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45 494 (1980).CrossRefGoogle Scholar
  7. 6.
    D.C. Tsui and A.C. Gossard, Appl. Phys. Lett. 38 550 (1981); See also: “Fifth Int. Conf. on Electronic Properties of Two Dimensional Systems”, Univ. Oxford, UK (1983).CrossRefGoogle Scholar
  8. 7.
    B.I. Haiperin, Helv. Phys. Acta 56 75 (1983).Google Scholar
  9. 8.
    Anderson Localization, Springer Series in Solid State Sciences 39, edited by Y. Nagaoka and H. Fukuyama (1982).Google Scholar
  10. 9.
    H. Aoki and T. Ando, Solid State Communications 38 1079 (1981).CrossRefGoogle Scholar
  11. 10.
    E. Abrahams, P.W. Anderson, D.C. Lieciardello and T.V. Ramakrishnan, Phys. Rev. Lett. 42 673 (1979).CrossRefGoogle Scholar
  12. 11.
    S. Hikami, Phys. Rev. B 24 2671 (1981); See also Ref.[8].CrossRefGoogle Scholar
  13. 12.
    K.B. Efetov, Sov. Phys. JETP 55 521 (1982);Google Scholar
  14. K.B. Efetov, A.I Larkin and D.E. Khmelnitskii, Sov. Phys. JETP 52 568 (1980);Google Scholar
  15. K. Juengling and R. Oppermann, Z. Phys. B 38 93 (1980);CrossRefGoogle Scholar
  16. S. Hikami, “Anderson Localization of the Two Dimensional Electron in a Random Potential under a strong Magnetic Field”, preprint (1984);Google Scholar
  17. T. Streit, J. Physique Lett. 45 L713 (1984).CrossRefGoogle Scholar
  18. 13.
    A.M.M Pruisken, Nucl. Phys. B 235 FS[11] 277 (1984)CrossRefGoogle Scholar
  19. 14.
    H. Levine, S.B. Libby and A.M.M Pruisken, Phys. Rev. Lett. 51 1915 (1983).CrossRefGoogle Scholar
  20. 15.
    H. Levine, S.B. Libby and A.M.M. Pruisken, Nucl. Phys. B 240[FS12] 30 (1984).CrossRefGoogle Scholar
  21. 16.
    H. Levine, S.B. Libby and A.M.M. Pruisken, Nuel. Phys. B 240[FS12] 49 (1984).CrossRefGoogle Scholar
  22. 17.
    H. Levine, S.B. Libby and A.M.M. Pruisken, Nucl. Phys. B 240[FS12] 71 (1984).CrossRefGoogle Scholar
  23. 18.
    A.M.M. Pruisken, “The Dilute Istanton Gas as the Precursor to the Integral Quantum Hall Effect”, SDR and IAS preprint (July 1984).Google Scholar
  24. 19.
    F. Wegner, Z. Phys. B 51 279 (1983).CrossRefGoogle Scholar
  25. 20.
    For references, see: T. Ando, A. Fowler and F. Stern, Rev. Mod. Phys. 45 437 (1982)CrossRefGoogle Scholar
  26. 21.
    P. Streda, J. Phys. C 15 1717 (1982)Google Scholar
  27. 22.
    F. Wegner, Z. Phys. B 38 207 (1979) and this conference.Google Scholar
  28. 23.
    L. Smrcka and P. Streda, J. Phys. C 10 2153 (1977).CrossRefGoogle Scholar
  29. 24.B. Kramer, A.M.M. Pruisken and L. Schweitzer, in preparationGoogle Scholar
  30. 25.
    A.J. MacFarlane, Phys. Lett. B 82 239 (1979);CrossRefGoogle Scholar
  31. H. Eichenherr and M. Forger, Nucl. Phys. B 155 381 (1979);CrossRefGoogle Scholar
  32. R. Pisarski, Phys. Rev. D 15 3385 (1979).Google Scholar
  33. 26.
    A.M.M. Pruisken and L. Schaefer, Nucl. Phys. B 200 20 (1982);CrossRefGoogle Scholar
  34. A.M.M. Pruisken and L. Schaefer Phys. Rev. Lett. 46 490(1981).Google Scholar
  35. 27.
    L. Schaefer and F. Wegner, Z. Phys. B 38 113 (1980).CrossRefGoogle Scholar
  36. 28.
    A.J. McKane and M. Stone, Ann. of Phys. 131 36 (1981).CrossRefGoogle Scholar
  37. 29.
    R. Oppermann and F. Wegner, Z. Phys. B 34 327 (1979).CrossRefGoogle Scholar
  38. 30.
    S. Hikami, Phys. Rev. B 29 (1984).Google Scholar
  39. 31.
    A.M. Polyakov, Phys. Lett. B 59 79 (1975);Google Scholar
  40. E. Brezin, J. Zinn-Justin and S.C. LeGuillou, Phys. Rev. B 14 2614 (1976).Google Scholar
  41. 32.
    E. Brezin, S. Hikami and J. Zinn-Justin, Nucl. Phys. B 165 528 (1980).CrossRefGoogle Scholar
  42. 33.
    S. Hikami, Phys. Lett. B 98 208 (1981).Google Scholar
  43. 34.
    F. Wegner, Z. Phys. B 36 209 (1979).Google Scholar
  44. 35.
    A.M.M. Pruisken, Phys. Rev. B, to be published (Januari 1985).Google Scholar
  45. 36.
    A.A. Belavin and A.M. Polyakov, JETP Lett. 22 245 (1975).Google Scholar
  46. 37.
    A.M. Polyakov, Phys. Lett. B 59 82 (1975);CrossRefGoogle Scholar
  47. A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Y.S. Tyupkin, Phys. Lett. B 59 85 (1975);CrossRefGoogle Scholar
  48. G. ‘T Hooft, Phys. Rev. Lett. 37 8 (1976); for a review on the subject, the reader is referred to R. Rajaraman, Solitons and Instantons, North Holland (1982).CrossRefGoogle Scholar
  49. 38.
    V.A. Fateev, I.V.Frolov and A.S. Schwarz, Nucl. Phys. B 154;Google Scholar
  50. B. Berg and M. Luescher, Nucl. Phys. B 190 [FS3] 412 (1981);CrossRefGoogle Scholar
  51. B. Berg and M. Luescher, G. ‘t Hooft et al (Cargese 1979), (Plenum Press, New York, 1980);Google Scholar
  52. M. Luescher, Nucl. Phys B 200 [FS4] 61 (1982);CrossRefGoogle Scholar
  53. B. Berg and M. Luescher, Comm. Math. Phys. 69 57 (1979).CrossRefGoogle Scholar
  54. 39.
    E. Witten, Nueb Phys. B 149 285 (1979).CrossRefGoogle Scholar
  55. 40.
    S. Coleman, Ann. Phys. 101 239 (1983).Google Scholar
  56. 41.
    I. Affleck, privat communication.Google Scholar
  57. 42.
    N. Seiberg, Phys. Rev. Lett. 53 637 (1984).CrossRefGoogle Scholar
  58. 43.
    J.T. Edwards and D.J. Thouless, J. Phys. c 5 807 (1972)CrossRefGoogle Scholar
  59. 44.
    C. Callan, R. Dashen and D. Gross, Phys. Rev. D 20 3279 (1979);CrossRefGoogle Scholar
  60. R. Jackiw, C. Rebbi, Phys. Rev. Lett. 37 172 (1976).CrossRefGoogle Scholar
  61. 45.
    D.J. Gross, Nucl. Phys B 132 439 (1978).CrossRefGoogle Scholar
  62. 46.
    The same diagram as fig.2 has been conjectured in: D.E. Khmernitzkii, JETP Lett. 38 552 (1983) as a pedagogical guide to the theory of refs [13–17].Google Scholar
  63. 47.
    The renormalization group equations where also proposed in: V. G. Khizhnik and A. Yu. Morozov, JETP Lett. 39 240 (1984); the author is endebted to Dr D.E. Khmernitzkii for bringing this reference to his attention.Google Scholar
  64. 48.
    H.P. Wei, A.M. Chang, D.C. Tsui, A.M.M. Pruisken and M. Razeghi, “Localization in the Quantized Hall Regime”, preprint.Google Scholar
  65. 49.
    R.B. Laughlin, M.L. Cohen, M.J. Kosterlitz, H. Levine, S.B. Libby and A.M.M. Pruisken, “Scaling of Conductivities in the Fractional Quantum Hall Effect”-, preprint.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Adrianus M. M. Pruisken
    • 1
  1. 1.The Institute for Advanced StudySchool of Natural SciencesPrincetonUSA

Personalised recommendations