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Localization in Landau Levels of 2D Systems and the Quantum Hall Effect

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High Magnetic Fields in Semiconductor Physics

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 71))

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Abstract

A recent development in understanding the problem of electron localization in two-dimensional systems in strong magnetic fields is reviewed mainly from a theoretical point of view with emphasis on the relation to the quantum Hall effect. It is shown that all the states are localized exponentially except those just at the center of the Landau level in sufficiently strong magnetic fields. The energy of extended states is shifted to the higher energy side with decreasing magnetic field. There is a scaling relation between the diagonal and off-diagonal components of the conductivity tensor.

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References

  1. T. Ando, A.B. Fowler and F. Stern: Rev. Mod. Phys. 54, 437 (1982).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. S. Kawaji and J. Wakabayashi: In Physics in High Magnetic Fields, ed. S. Chikazumi and N. Miura (Springer, Berlin, 1981), p.284.

    Google Scholar 

  4. T. Ando, Y. Matsumoto and Y. Uemura: J. Phys. Soc. Jpn. 32, 859 (1972).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Q. Niu, D.J. Thouless and Y.-S. Wu: Phys. Rev. B 28, 3372 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  7. D.C. Licciardello and D.J. Thouless: J. Phys. C 8, 4157 (1975)

    Article  ADS  Google Scholar 

  8. D.C. Licciardello and D.J. Thouless: J. Phys. C 11, 925 (1978).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. T. Ando: J. Phys. Soc. Jpn. 52, 1893 (1983)

    Article  MathSciNet  Google Scholar 

  12. T. Ando: J. Phys. Soc. Jpn. 53, 3101 (1983)

    Article  ADS  Google Scholar 

  13. T. Ando: J. Phys. Soc. Jpn. 53, 3126 (1983).

    Article  ADS  Google Scholar 

  14. T. Ando and H. Aoki: J. Phys. Soc. Jpn. 54, 2238 (1985).

    Article  ADS  Google Scholar 

  15. L. Schweitzer, B. Kramer and A. MacKinnon: J. Phys. C 17, 4111 (1984).

    Article  ADS  Google Scholar 

  16. T. Ando, Y. Matsumoto, Y. Uemura, M. Kobayashi and K.F. Komatsubara: J. Phys. Soc. Jpn. 32, 859 (1972).

    Article  ADS  Google Scholar 

  17. S. Kawaji and J. Wakabayashi: Surf. Sci. 58, 238 (1976).

    Article  ADS  Google Scholar 

  18. H. Levine, S.B. Libby and A.M.M. Pruisken, Phys. Rev. Lett. 51, 1915 (1983); Nucl. Phys. B 240, 30; 49; 71 (1984).

    Google Scholar 

  19. T. Ando: Surf. Sci. 170, 243 (1986).

    Article  ADS  Google Scholar 

  20. T. Ando: J. Phys. Soc. Jpn. 55, No.9 (1986).

    Google Scholar 

  21. H. Aoki and T. Ando, Surf. Sci. 170, 249 (1986).

    Article  ADS  Google Scholar 

  22. S. Kawaji: Prog. Theor. Phys. Suppl. 94, 178 (1986).

    Google Scholar 

  23. H.P. Wei, A.M. Chang, D.C. Tsui, A.M.M. Pruisken and M. Razeghi: Surf. Sci. 170, 238 (1986).

    Article  ADS  Google Scholar 

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© 1987 Springer-Verlag Berlin Heidelberg

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Ando, T. (1987). Localization in Landau Levels of 2D Systems and the Quantum Hall Effect. In: Landwehr, G. (eds) High Magnetic Fields in Semiconductor Physics. Springer Series in Solid-State Sciences, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83114-0_1

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  • DOI: https://doi.org/10.1007/978-3-642-83114-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83116-4

  • Online ISBN: 978-3-642-83114-0

  • eBook Packages: Springer Book Archive

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