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.
Similar content being viewed by others
References
Klitzing, K. von, Dorda, G., Pepper, M.: Phys. Rev. Lett.45, 494 (1980)
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
Kubo, R., Miyake, S.J., Hashitsume, N.: Solid State Phys.17, 269 (1965)
Halperin, B.I.: Phys. Rev. B25, 2185 (1982)
Smrčka, L.: J. Phys. C17, L63 (1984)
Jonson, M.: Phys. Scr.32, 435 (1985)
Kuchar, F., Meisels, R., Weimann, G., Schlapp, W.: Phys. Rev. B33, 2965 (1986)
Johnston, R., Schweitzer, L.: Proceedings of the International Conference on Application of High Magnetic Fields in Semiconductor Physics, Würzburg, 1986 (to be published)
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)
A recent review was given by Ando, T.: Prog. Theor. Phys. Suppl.84, 69 (1985)
Bastin, A., Lewiner, C., Betbeder-Matibet, O., Nozieres, P.: J. Phys. Chem. Solids32, 1811 (1971)
Streda, P.: J. Phys. C15, L717 (1982)
Schweitzer, L., Kramer, B., MacKinnon, A.: Z. Phys. B — Condensed Matter59, 379 (1985)
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)
Teller, E.: Z. Phys.67, 311 (1931)
MacKinnon, A., Kramer, B., Schweitzer, L.: Proc. LITPIM Suppl. (PTB-PG-1), 314 (PTB Braunschweig, 1984)
Aoki, H.: J. Phys. C17, 1875 (1984)
Trugman, S.A.: Phys. Rev. B27, 7539 (1983)
Johnston, R., Kramer, B., MacKinnon, A., Schweitzer, L.: Surf. Sci.170, 256 (1986)
Heuser, M.: Diplomarbeit (Köln 1972); Heuser, M., Hajdu, J.: Z. Phys.270, 289 (1974)
Hajdu, J., Janßen, M., Viehweger, O.: Z. Phys. B — Condensed Matter (in press)
Hajdu, J., Gummich, U.: Solid State Commun.52, 985 (1984)
Apenko, S.M., Lozovik, Yu.E.: Sov. Phys. JETP62, 328 (1985)
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)
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01307258