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Part of the book series: Physics of Solids and Liquids ((PSLI))

Abstract

The range of phenomena observed in electronic systems in magnetic fields is large and spectacular. Perhaps most spectacular of all are the quantum Hall effect, and fractional quantum Hall effect. This chapter will be concerned with the theoretical description of these phenomena. Many of the aspects presented are treated in greater detail in Girvin and Prange.(1)

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References

  1. S. M. Girvin and R. E. Prange, eds, The Quantum Hall Effect, Springer-Verlag (1987).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  3. D. C. Tsui, H. L. Störmer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. K. von Klitzing, Surface Science 113, 113 (1982).

    Google Scholar 

  6. H. L. Störmer. and D. C. Tsui, Science 220, 1241 (1983).

    Article  ADS  Google Scholar 

  7. T. Ando, Y. Matsumoto and Y. Uemura, J. Phys. Soc. Japan 39, 279 (1975).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. R. Joynt and R. E. Prange, Phys. Rev. B 29, 3303 (1984).

    Article  ADS  Google Scholar 

  10. W. Brenig, Z. Phys. B 50, 305 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  11. N. Levinson and K. Dan Vrdensk Selsk. Mat. Fys. Medd. 25, No. 9 (1949).

    Google Scholar 

  12. D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).

    Article  ADS  Google Scholar 

  13. B. I. Halperin, Phys. Rev. B 25, 2185 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  14. A. M. Chang, P. Berglund, D. C. Tsui, H. L. Störmer, and J. C. M. Hwang, Phys. Rev. Lett. 53, 997 (1984).

    Article  ADS  Google Scholar 

  15. R. G. Clark, in: 18th International Conference on Physics of Semiconductors (Olof Engstrom, ed., World Scientific Vol. 1, p. 393, (1986).

    Google Scholar 

  16. R. G. Clark, R. J. Nicholas, A. Usher, C. T. Foxon, and J. J. Harris, Surface Science 170, 141 (1986).

    Article  ADS  Google Scholar 

  17. R. G. Clark, S. R. Haynes, A. M. Suckling, J. R. Mallett, P A. Wright, J. J. Harris, and C. T. Foxon, Phys. Rev. Lett. 62, 1536 (1989).

    Article  ADS  Google Scholar 

  18. J. P. Eisenstein, H. L. Stormer, L. Pfeiffer and K. W. West, Phys. Rev. Lett. 62, 1540 (1989).

    Article  ADS  Google Scholar 

  19. R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).

    Article  ADS  Google Scholar 

  20. Q. Niu, D. J. Thouless, and Y. S. Wu, Phys. Rev. B 31, 3372 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  21. R. Tao and F. D. M. Haldane, Phys. Rev. B 33, 3844 (1986)

    Article  ADS  Google Scholar 

  22. J. R. Schrieffer, “Strange Quantum Numbers in Condensed Matter and Field Theory,” NSF-ITP-85-124 Preprint (1985).

    Google Scholar 

  23. B. I. Halperin, Helv. Phys. Acta 56, 75 (1983).

    Google Scholar 

  24. J. M. Caillol, D. Levesque, J. J. Weis, and J. P. Hansen, J. Stat. Phys. 28, 325 (1982).

    Article  ADS  Google Scholar 

  25. R. Morf and B. I. Halperin, Phys. Rev. B 33, 2221 (1986).

    Article  ADS  Google Scholar 

  26. S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Phys. Rev. B 33, 2481 (1986).

    Article  ADS  Google Scholar 

  27. F. D. M. Haldane and E. H. Rezayi, Phys. Rev. Lett. 54, 237 (1985).

    Article  ADS  Google Scholar 

  28. B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984).

    Article  ADS  Google Scholar 

  29. G. Fano, F. Ortolani, and E. Colombo, Phys. Rev. B 34, 2670 (1986).

    Article  ADS  Google Scholar 

  30. F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  31. D. Arovas, J. R. Schrieffer and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984)

    Article  ADS  Google Scholar 

  32. P. BĂ©ran and R. Morf, Phys. Rev. B 43, 12654 (1991).

    Article  ADS  Google Scholar 

  33. R. Morf, N. D’Ambrumenil, and B. I. Halperin, Phys. Rev. B 34, 3037 (1986).

    Article  ADS  Google Scholar 

  34. R. Willett, J. P. Eisenstein, H. L. Stormer, D. C. Tsui, A. C. Gossard, and J. H. English, Phys. Rev. Lett. 59, 1776 (1987).

    Article  ADS  Google Scholar 

  35. J. P. Eisenstein, R. Willett, H. L. Stormer, D. C. Tsui, A. C. Gossard, and J. H. English, Phys. Rev. Lett. 61, 997 (1988).

    Article  ADS  Google Scholar 

  36. F. D. M. Haldane, in: The Quantum Hall Effect (S. M. Girvin and R. E. Prange, eds.), Springer-Verlag (1987).

    Google Scholar 

  37. N. D’Ambrumenil and A. M. Reynolds, J. Phys. C 21, 119 (1988).

    Article  ADS  Google Scholar 

  38. A. H. MacDonald and S. M. Girvin, Phys. Rev. B 33, 4009 (1986).

    Article  ADS  Google Scholar 

  39. S. Kivelson, C. Callin, D. P. Arovas, and J. R. Schrieffer, Phys. Rev. Lett. 56, 873 (1986).

    Article  ADS  Google Scholar 

  40. G. Baskaran, Phys. Rev. Lett. 56, 2716 (1986).

    Article  ADS  Google Scholar 

  41. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Sections 8.95 and 8.97), Academic Press (1980).

    Google Scholar 

  42. E. Brown, Phys. Rev. 133, 1038 (1968).

    Article  ADS  Google Scholar 

  43. B. I. Halperin, Scientific American, April 1986 p. 40.

    Google Scholar 

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© 1993 Springer Science+Business Media New York

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d’Ambrumenil, N. (1993). Theory of the Quantum Hall Effect. In: Butcher, P., March, N.H., Tosi, M.P. (eds) Physics of Low-Dimensional Semiconductor Structures. Physics of Solids and Liquids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2415-5_6

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  • DOI: https://doi.org/10.1007/978-1-4899-2415-5_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-2417-9

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