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

  • H. Aoki
  • T. Ando
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 71)


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.


Landau Level Quantise Hall Effect Hall Conductivity Flux Quantum Kubo Formula 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • H. Aoki
    • 1
  • T. Ando
    • 2
  1. 1.Institute of Materials ScienceUniversity of TsukubaIbarakiJapan
  2. 2.Institute for Solid State PhysicsUniversity of TokyoTokyoJapan

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