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Ten Years of the Quantum Hall Effect: Development and Present State of the Theory

  • Conference paper
High Magnetic Fields in Semiconductor Physics III

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 101))

Abstract

Shortly after the discovery of the Quantum Hall Effect had been announced /1/, a number of approaches were suggested to explain this surprising phenomenon:

  • The semi-phenomenological approach by Aoki and Ando /2/

  • The gauge argument by Laughlin /3/

  • The single point impurity model by Prange /4/

  • The Streda formula /5/

  • The lattice model by Thouless et al. /6/ (Preliminary form of the topological approach).

  • Semi-classical percolation models by Allen and Tsui /7/, Iordansky /8/ and Ono /9/.

In this survey I will try to sketch the development of these approaches and to show their place in the present state of the theory. Furthermore, I would like to make a few comments on some recent investigations and to mention a few still unsolved problems.

All of the approaches listed above refer to independent electrons (no Coulomb interaction). That a two-dimensional system of independent electrons moving in a random potential (impurities) and a strong perpendicular magnetic field indeed shows a QHE was confirmed by Ando in an early numerical analysis /10/. (A survey of the numerical work will be given by Professor Aoki in this conference).

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicherstr. 77, W-5000, Köln 41, Germany

    J. Hajdu

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  1. J. Hajdu
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  1. Physikalisches Institut, Universität Würzburg, Am Hubland, W-8700, Würzburg, Fed. Rep. of Germany

    Gottfried Landwehr

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Hajdu, J. (1992). Ten Years of the Quantum Hall Effect: Development and Present State of the Theory. In: Landwehr, G. (eds) High Magnetic Fields in Semiconductor Physics III. Springer Series in Solid-State Sciences, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84408-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-84408-9_1

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