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Adiabatic Transport in the Fractional Quantum Hall Effect Regime

  • Carlo W. J. Beenakker
Part of the NATO ASI Series book series (NSSB, volume 254)

Abstract

The quantum Hall effect (QHE) is the phenomenon that the Hall conductance Gh is quantized in units of e2/h, as expressed by the formula
$$ {G_H} = \frac{p}{q}\frac{{{e^2}}}{h} $$
(1)
(p and q being mutually prime integers). The integer QHE (q = 1) was discovered 10 years ago by von Klitzing, Dorda, and Pepper [1] in the two-dimensional electron gas (2 DEG) confined to a Si inversion layer. The fractional QHE (q > 1 and odd) was first observed by Tsui, Störmer, and Gossard [2] in the 2 DEG at the interface of a AxpGa1-xAs/GaAs heterostructure. Microscopically the two effects are entirely different. The integer QHE, on the one hand, can be explained satisfactorily in terms of the states of non-interacting electrons in a magnetic field (the Landau levels). The fractional QHE, on the other hand, exists only because of electron-electron interactions [3]. Phenomenologically, however, the integer and fractional QHE are quite similar. In an unbounded 2 DEG this similarity is understood from Laughlin’s general argument [4] that: (1) The Hall conductance shows a plateau as a function of magnetic field (or Fermi energy) whenever the quasi-particle excitations in the bulk of the 2 DEG are localized by disorder; and that: (2) The value of G H on the plateau is precisely an integer multiple p of ee*/h, where e* = e/q is the quasi-particle charge. (The product ee* appears because one e is needed to change the unit of conductance from Amperes per electron Volts to Amperes per Volts). Theory and experiment on the QHE in an unbounded 2 DEG have been reviewed in the books by Prange and Girvin [5] and by Chakraborty and Pietiläinen [6] (see also the article by MacDonald in the present volume).

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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Carlo W. J. Beenakker
    • 1
  1. 1.Philips Research LaboratoriesEindhovenThe Netherlands

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