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The Quantum Hall Effect: Novel Excitations And Broken Symmetries

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Aspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems

Part of the book series: Les Houches - Ecole d’Ete de Physique Theorique ((LHSUMMER,volume 69))

Abstract

The Quantum Hall Effect (QHE) is one of the most remarkable condensed-matter phenomena discovered in the second half of the 20th century. It rivals superconductivity in its fundamental significance as a manifestation of quantum mechanics on macroscopic scales. The basic experimental observation is the nearly vanishing dissipation σ xx → 0 (1.1) and the quantization of the Hall conductance

$$\sigma _{xy} = \nu \frac{{e^2 }}{h}$$
(1.2)

of a real (as opposed to some theorist’s fantasy) transistor-like device (similar in some cases to the transistors in computer chips) containing a two-dimensional electron gas subjected to a strong magnetic field. This quantization is universal and independent of all microscopic details such as the type of semiconductor material, the purity of the sample, the precise value of the magneticfield, and so forth. As a result, the effect is now used to mantain the standard of electrical resistance by metrology laboratories around the world. In addition, since the speed of light is now defined, a measurement of e 2/h equivalent to a measurement of the fine structure constant of fundamental importance in quantum electrodynamics.

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

    S. M. Girvin

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A. Comtet T. Jolicœur S. Ouvry F. David

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Girvin, S.M. (1999). The Quantum Hall Effect: Novel Excitations And Broken Symmetries. In: Comtet, A., Jolicœur, T., Ouvry, S., David, F. (eds) Aspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems. Les Houches - Ecole d’Ete de Physique Theorique, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46637-1_2

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