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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

Chapter:
(p.958) 48 The Quantum Hall Effects
Source:
The Physics of Solids
Author(s):

J. B. Ketterson

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198742906.003.0048

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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