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The Quantum Hall Effects

  • Chapter
Quantum Coherence in Mesoscopic Systems

Part of the book series: NATO ASI Series ((NSSB,volume 254))

Abstract

The quantum Hall effect [1] occurs in two-dimensional electronic systems (2 DES) [2] in strong perpendicular magnetic fields. It differs from many of the phenomena which are being discussed at this ASI in that it does not depend directly on quantum coherence for its occurrence. Quantum coherence plays an important supporting role rather that a starring role in this drama. At low temperatures and strong magnetic fields the magnetoresistance of two-dimensional (2D) metals becomes extremely small and the Hall resistance nearly constant over certain ranges of carrier density and magnetic field strength. Although this effect seemed quite mysterious at the time of its discovery, the principle elements of the physics which is responsible are now understood. In these notes I hope to explain these elements and to point out some aspects of our current theoretical picture of the phenomenon which seem to be incomplete.

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Authors and Affiliations

  1. Department of Physics, Indiana University, Bloomington, IN, 47405, USA

    Allan H. MacDonald

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  1. Allan H. MacDonald
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  1. Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Braunschweig, Germany

    B. Kramer

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MacDonald, A.H. (1991). The Quantum Hall Effects. In: Kramer, B. (eds) Quantum Coherence in Mesoscopic Systems. NATO ASI Series, vol 254. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3698-1_13

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  • DOI: https://doi.org/10.1007/978-1-4899-3698-1_13

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