Skip to main content
Log in

The hall conductivity of a two-dimensional confined system

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The Hall conductivity of a two-dimensional system of free, independent electrons is calculated using linear response theory. Emphasis is on the influence of the edge states introduced by a confining potential. It is shown that within the Kubo formalism the quantized values of the Hall conductivity may be described by bulk states as well as by edge states only. The influence of a random potential is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Google Scholar 

  2. Hajdu, J., Landwehr, G., In: Strong and ultrastrong magnetic fields and their applications. Topics in Applied Physics. herlach, F. (ed.), Vol. 57, p. 17. Berlin, Heidelberg, New York: Springer Verlag 1985

    Google Scholar 

  3. Kubo, R., Miyake, S.J., Hashitsume, N.: Solid State Phys.17, 269 (1965)

    Google Scholar 

  4. Halperin, B.I.: Phys. Rev. B25, 2185 (1982)

    Google Scholar 

  5. Smrčka, L.: J. Phys. C17, L63 (1984)

    Google Scholar 

  6. Jonson, M.: Phys. Scr.32, 435 (1985)

    Google Scholar 

  7. Kuchar, F., Meisels, R., Weimann, G., Schlapp, W.: Phys. Rev. B33, 2965 (1986)

    Google Scholar 

  8. Johnston, R., Schweitzer, L.: Proceedings of the International Conference on Application of High Magnetic Fields in Semiconductor Physics, Würzburg, 1986 (to be published)

  9. Bliek, L., Hein, G., Kose, V., Niemeyer, J., Weimann, G., Schlapp, W.: Preprint. Proceedings of the International Conference on the Application of High Magnetic Fields in Semiconductor Physics, Würzburg 1986 (to be published)

  10. A recent review was given by Ando, T.: Prog. Theor. Phys. Suppl.84, 69 (1985)

    Google Scholar 

  11. Bastin, A., Lewiner, C., Betbeder-Matibet, O., Nozieres, P.: J. Phys. Chem. Solids32, 1811 (1971)

    Google Scholar 

  12. Streda, P.: J. Phys. C15, L717 (1982)

    Google Scholar 

  13. Schweitzer, L., Kramer, B., MacKinnon, A.: Z. Phys. B — Condensed Matter59, 379 (1985)

    Google Scholar 

  14. Pruisken, A.M.M., In: Localization, interaction, and transport phenomena. Springer Series in Solid State Science. Kramer, B., Bergmann, G., Bruynseraede, Y. (eds.), Vol. 61, p. 188. Berlin, Heidelberg, New York: Springer Verlag 1985; Nucl. Phys. B235, FS[11], 277 (1984)

    Google Scholar 

  15. Teller, E.: Z. Phys.67, 311 (1931)

    Google Scholar 

  16. MacKinnon, A., Kramer, B., Schweitzer, L.: Proc. LITPIM Suppl. (PTB-PG-1), 314 (PTB Braunschweig, 1984)

  17. Aoki, H.: J. Phys. C17, 1875 (1984)

    Google Scholar 

  18. Trugman, S.A.: Phys. Rev. B27, 7539 (1983)

    Google Scholar 

  19. Johnston, R., Kramer, B., MacKinnon, A., Schweitzer, L.: Surf. Sci.170, 256 (1986)

    Google Scholar 

  20. Heuser, M.: Diplomarbeit (Köln 1972); Heuser, M., Hajdu, J.: Z. Phys.270, 289 (1974)

  21. Hajdu, J., Janßen, M., Viehweger, O.: Z. Phys. B — Condensed Matter (in press)

  22. Hajdu, J., Gummich, U.: Solid State Commun.52, 985 (1984)

    Google Scholar 

  23. Apenko, S.M., Lozovik, Yu.E.: Sov. Phys. JETP62, 328 (1985)

    Google Scholar 

  24. A preliminary discussion is given in: B. Kramer, to be published in Proceedings of the International Conference on Application of High Magnetic fields in Semiconductor Physics, Würzburg (1986)

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ono, Y., Kramer, B. The hall conductivity of a two-dimensional confined system. Z. Physik B - Condensed Matter 67, 341–347 (1987). https://doi.org/10.1007/BF01307258

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01307258

Keywords

Navigation