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Localization and the Integral Quantum Hall Effect

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Localization, Interaction, and Transport Phenomena

Part of the book series: Springer Series in Solid-State Sciences ((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].

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References

  1. R.B. Laughlin, Phys. Rev. B 23 5632 (1981).

    Article  Google Scholar 

  2. D.J. Thouless, J. Phys. C 14 3475 (1981).

    Article  CAS  Google Scholar 

  3. R.E. Prange, Phys. Rev. B 23 4802 (1981);

    Article  CAS  Google Scholar 

  4. R.E. Prange and R. Joynt, Phys. Rev. B 25 2943 (1982)

    Article  Google Scholar 

  5. B.I. Haiperin, Phys. Rev. B 25 2185 (1982).

    Article  Google Scholar 

  6. K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45 494 (1980).

    Article  Google Scholar 

  7. 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).

    Article  CAS  Google Scholar 

  8. B.I. Haiperin, Helv. Phys. Acta 56 75 (1983).

    Google Scholar 

  9. Anderson Localization, Springer Series in Solid State Sciences 39, edited by Y. Nagaoka and H. Fukuyama (1982).

    Google Scholar 

  10. H. Aoki and T. Ando, Solid State Communications 38 1079 (1981).

    Article  CAS  Google Scholar 

  11. E. Abrahams, P.W. Anderson, D.C. Lieciardello and T.V. Ramakrishnan, Phys. Rev. Lett. 42 673 (1979).

    Article  Google Scholar 

  12. S. Hikami, Phys. Rev. B 24 2671 (1981); See also Ref.[8].

    Article  CAS  Google Scholar 

  13. 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);

    Article  CAS  Google 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).

    Article  Google Scholar 

  18. A.M.M Pruisken, Nucl. Phys. B 235 FS[11] 277 (1984)

    Article  Google Scholar 

  19. H. Levine, S.B. Libby and A.M.M Pruisken, Phys. Rev. Lett. 51 1915 (1983).

    Article  Google Scholar 

  20. H. Levine, S.B. Libby and A.M.M. Pruisken, Nucl. Phys. B 240[FS12] 30 (1984).

    Article  Google Scholar 

  21. H. Levine, S.B. Libby and A.M.M. Pruisken, Nuel. Phys. B 240[FS12] 49 (1984).

    Article  Google Scholar 

  22. H. Levine, S.B. Libby and A.M.M. Pruisken, Nucl. Phys. B 240[FS12] 71 (1984).

    Article  Google Scholar 

  23. 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. F. Wegner, Z. Phys. B 51 279 (1983).

    Article  Google Scholar 

  25. For references, see: T. Ando, A. Fowler and F. Stern, Rev. Mod. Phys. 45 437 (1982)

    Article  Google Scholar 

  26. P. Streda, J. Phys. C 15 1717 (1982)

    Google Scholar 

  27. F. Wegner, Z. Phys. B 38 207 (1979) and this conference.

    Google Scholar 

  28. L. Smrcka and P. Streda, J. Phys. C 10 2153 (1977).

    Article  CAS  Google Scholar 

  29. 24.B. Kramer, A.M.M. Pruisken and L. Schweitzer, in preparation

    Google Scholar 

  30. A.J. MacFarlane, Phys. Lett. B 82 239 (1979);

    Article  Google Scholar 

  31. H. Eichenherr and M. Forger, Nucl. Phys. B 155 381 (1979);

    Article  Google Scholar 

  32. R. Pisarski, Phys. Rev. D 15 3385 (1979).

    Google Scholar 

  33. A.M.M. Pruisken and L. Schaefer, Nucl. Phys. B 200 20 (1982);

    Article  Google Scholar 

  34. A.M.M. Pruisken and L. Schaefer Phys. Rev. Lett. 46 490(1981).

    Google Scholar 

  35. L. Schaefer and F. Wegner, Z. Phys. B 38 113 (1980).

    Article  CAS  Google Scholar 

  36. A.J. McKane and M. Stone, Ann. of Phys. 131 36 (1981).

    Article  Google Scholar 

  37. R. Oppermann and F. Wegner, Z. Phys. B 34 327 (1979).

    Article  Google Scholar 

  38. S. Hikami, Phys. Rev. B 29 (1984).

    Google Scholar 

  39. 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. E. Brezin, S. Hikami and J. Zinn-Justin, Nucl. Phys. B 165 528 (1980).

    Article  Google Scholar 

  42. S. Hikami, Phys. Lett. B 98 208 (1981).

    Google Scholar 

  43. F. Wegner, Z. Phys. B 36 209 (1979).

    Google Scholar 

  44. A.M.M. Pruisken, Phys. Rev. B, to be published (Januari 1985).

    Google Scholar 

  45. A.A. Belavin and A.M. Polyakov, JETP Lett. 22 245 (1975).

    Google Scholar 

  46. A.M. Polyakov, Phys. Lett. B 59 82 (1975);

    Article  Google Scholar 

  47. A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Y.S. Tyupkin, Phys. Lett. B 59 85 (1975);

    Article  Google 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).

    Article  Google Scholar 

  49. 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);

    Article  Google 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);

    Article  Google Scholar 

  53. B. Berg and M. Luescher, Comm. Math. Phys. 69 57 (1979).

    Article  Google Scholar 

  54. E. Witten, Nueb Phys. B 149 285 (1979).

    Article  Google Scholar 

  55. S. Coleman, Ann. Phys. 101 239 (1983).

    Google Scholar 

  56. I. Affleck, privat communication.

    Google Scholar 

  57. N. Seiberg, Phys. Rev. Lett. 53 637 (1984).

    Article  CAS  Google Scholar 

  58. J.T. Edwards and D.J. Thouless, J. Phys. c 5 807 (1972)

    Article  Google Scholar 

  59. C. Callan, R. Dashen and D. Gross, Phys. Rev. D 20 3279 (1979);

    Article  CAS  Google Scholar 

  60. R. Jackiw, C. Rebbi, Phys. Rev. Lett. 37 172 (1976).

    Article  Google Scholar 

  61. D.J. Gross, Nucl. Phys B 132 439 (1978).

    Article  Google Scholar 

  62. 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. 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. 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. 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 

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Author information

Authors and Affiliations

  1. The Institute for Advanced Study, School of Natural Sciences, 08540, Princeton, NJ, USA

    Adrianus M. M. Pruisken

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  1. Adrianus M. M. Pruisken
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Editor information

Editors and Affiliations

  1. Physikalisch-Technische Bundesanstalt Braunschweig, Postfach 3345, D-3300, Braunschweig, Fed. Rep. of Germany

    Bernhard Kramer

  2. Kernforschungsanlage Jülich, Institut für Festkörperforschung, Postfach 1913, D-5170, Jülich, Fed. Rep. of Germany

    Gerd Bergmann

  3. Laboratorium voor Vaste Stof-Fysika en Magnetisme, Celestijnenlaan 200 D, B-3030, Leuven, Belgium

    Yvan Bruynseraede

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Pruisken, A.M.M. (1985). Localization and the Integral Quantum Hall Effect. In: Kramer, B., Bergmann, G., Bruynseraede, Y. (eds) Localization, Interaction, and Transport Phenomena. Springer Series in Solid-State Sciences, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82516-3_19

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  • DOI: https://doi.org/10.1007/978-3-642-82516-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82518-7

  • Online ISBN: 978-3-642-82516-3

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