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High Magnetic Fields in Semiconductor Physics pp 45–48Cite as

Quantum Hall Effect: From the Winding Number to the Flow Diagram

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

Abstract

To answer a query as to what extent the quantised Hall effect is universal, we show that (i) an exact proof for the quantisation of Hall conductivity is given by the topological invariant (winding number), (ii) there exists a definite distribution of winding numbers as a function of energy for given system size and degree of disorder giving rise to a well-behaved σxy for lattice systems with Landau-level mixing and (iii) the flow diagram for σxy vs σxx obtained by the Thouless number exhibits characteristic behaviours.

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References

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Author information

Authors and Affiliations

  1. Institute of Materials Science, University of Tsukuba, Sakura, Ibaraki, 305, Japan

    H. Aoki

  2. Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo, 106, Japan

    T. Ando

Authors
  1. H. Aoki
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  2. T. Ando
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Editor information

Editors and Affiliations

  1. Physikalisches Institut, Universität Würzburg, Röntgenring 8, D-8700, Würzburg, Fed. Rep.of Germany

    Gottfried Landwehr

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© 1987 Springer-Verlag Berlin Heidelberg

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Aoki, H., Ando, T. (1987). Quantum Hall Effect: From the Winding Number to the Flow Diagram. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-83114-0_6

  • 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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