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The Physics of Solids$
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J. B. Ketterson

Print publication date: 2016

Print ISBN-13: 9780198742906

Published to Oxford Scholarship Online: December 2016

DOI: 10.1093/acprof:oso/9780198742906.001.0001

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The Quantum Hall Effects

The Quantum Hall Effects

(p.958) 48 The Quantum Hall Effects
The Physics of Solids

J. B. Ketterson

Oxford University Press

This chapter first analyses the integer quantum Hall effect, covering an electron in two dimensions in a magnetic field; a two-dimensional electron gas in a magnetic field; motion under orthogonal electric and magnetic fields; the quantization of the Hall voltage; an electron in two dimensions in a magnetic field; edge states; and localized states. The chapter then turns to the fractional quantum Hall effect, discussing a semi-empirical accounting for observed filling fractions; many-body ground states for non-interacting electrons in the lowest Landau level; adding flux tubes to the non-interacting many-body ground state wave function; and trial ground states for the fractional quantum Hall effect. Sample problems are also provided at the end of the chapter.

Keywords:   integer quantum Hall effect, electrons, magnetic field, electric field, edge state, localized state, fractional quantum Hall effect, ground state, flux tube

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