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The conductivity of a two-dimensional electronic system of finite width in the presence of a strong perpendicular magnetic field and a random potential

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Zeitschrift für Physik B Condensed Matter

Abstract

Starting from the Kubo formula the conductivity tensor of a two-dimensional electronic system in a perpendicular magnetic field is evaluated. It is shown that at zero temperature only the states at the Fermi level contribute. The Hall conductivity of a purely periodic system of finite width is calculated and compared with earlier suggestions by Thouless et al. For a system described by a periodic and a random potential the Hall conductivity is calculated as a function of the electron density. The results emphasize the importance of disorder independent current carrying states for the Quantum Hall effect which extend along the boundaries of the system. The plateaux values of the Hall conductivity are related to the number of these states, and are independent of the existence of extended bulk states below the Fermi energy.

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Authors and Affiliations

  1. Physikalisch-Technische Bundesanstalt Braunschweig, Bundesallee 100, D-3300, Braunschweig, Germany

    L. Schweitzer & B. Kramer

  2. The Blackett Laboratory, Imperial College, Prince Consort Road, SW7 2BZ, London, UK

    A. MacKinnon

Authors
  1. L. Schweitzer
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  2. B. Kramer
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  3. A. MacKinnon
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Schweitzer, L., Kramer, B. & MacKinnon, A. The conductivity of a two-dimensional electronic system of finite width in the presence of a strong perpendicular magnetic field and a random potential. Z. Physik B - Condensed Matter 59, 379–384 (1985). https://doi.org/10.1007/BF01328845

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  • DOI: https://doi.org/10.1007/BF01328845

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