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Localisation and Transport in One-Dimensional Disordered Systems

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Physics and Technology of Submicron Structures

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 83))

Abstract

The theory of localisation and transport in one-dimensional disordered systems is reviewed. The localisation length is calculated. It is shown that the dc-conductivity vanishes at the absolute zero of the temperature, if the Fermi energy lies in the region of localised states. The Landauer formula for the conductance of a system of finite length is derived. It is shown that the averages of the resistance and the conductance increase, and decrease exponentially with the length of the system, respectively. The distributions of the localisation length, the resistance, and the conductance are discussed. It is shown that the localisation length is the quantity which obeys the central limit theorem, whereas the width of the distributions of the resistance and the conductance increase with increasing size of the system faster than the averages of these quantities in the thermodynamic limit.

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Authors and Affiliations

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

    B. Kramer

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  1. B. Kramer
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Editor information

Editors and Affiliations

  1. Institut für Experimentalphysik, Universität Linz, A-4040, Linz, Austria

    Helmut Heinrich

  2. Institut für Physik, Montanuniversität Leoben, A-8700, Leoben, Austria

    Günther Bauer

  3. Institut für Festkörperphysik, Universität Wien, A-1090, Wien, Austria

    Friedemar Kuchar

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© 1988 Springer-Verlag Berlin Heidelberg

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Kramer, B. (1988). Localisation and Transport in One-Dimensional Disordered Systems. In: Heinrich, H., Bauer, G., Kuchar, F. (eds) Physics and Technology of Submicron Structures. Springer Series in Solid-State Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83431-8_13

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  • DOI: https://doi.org/10.1007/978-3-642-83431-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83433-2

  • Online ISBN: 978-3-642-83431-8

  • eBook Packages: Springer Book Archive

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