The Quantum Hall Effect

By: Daijiro Yoshioka

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Hardcover | 26 February 2002

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224 Pages

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22.86 x 15.24 x 1.27

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Today, more than 20 years after the discovery of the quantum Hall effect, the number of publications in this field, at more than one paper per day, is still increasing. This remarkable fact requires some explanation. It also poses, but perhaps also answers, the question of why a new monograph entitled 'The Quantum Hall Effect' is a highly desirable addition to the literature. Originally the quantum Hall effect (QHE) was a term coined to describe the unexpected observation of a fundamental electrical resistance, with a value independent of the microscopic details of the semiconductor device. The simplest explanation of this phenomenon was based on an independent electron picture. The subsequent discovery of the fractional quantum Hall ef- fect demonstrated that a many-body wave function and a more global view of the system is necessary to incorporate and explain interesting new aspects. Today, the quantum Hall effect has become a pseudonym for many differ- ent phenomena observed in high magnetic fields, with connections not only to solid state physics but also to theoretical descriptions in plasma physics, astrophysics, atomic physics, and high energy physics. There are even spec- ulations that a higher-dimensional generalization of the QHE may be useful for discussing questions related to the basic properties of space.

Industry Reviews

From the reviews:

In this monograph Daijiro Yoshioka has done a marvelous job.

--The Physicist

"This book will provide a nice starting point for ideas that an experienced solid state physics educator may use for an in-depth introduction to the fundamentals of both the integral and fractional Quantum Hall effect. ... this volume does provide a useful introduction to this exciting field in one rather small but excellently produced volume. Rather nicely, each chapter has a few exercises to challenge the reader." (Gary J. Long and Fernande Grandjean, Physicalia, Vol. 25 (3), 2003)

"In this monograph Daijiro Yoshioka has done a marvelous job. ... he gives an excellent pedagogic description of both integral and fractional QHEs. ... This book would be a good reference for a post-graduate course in Condensed Matter Physics. Those interested enough to learn the subject from scratch, are recommended to buy personal copies." (Mukunda Das, The Physicist, Vol. 39 (5), 2002)

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Discovery of the Quantum Hall Effect	p. 1
Realization of Two-Dimensional Electron Systems	p. 1
The Quantum Hall Effect	p. 7
Two-Dimensional Electrons in a Magnetic Field	p. 17
Electron Motion in Classical Mechanics	p. 17
Motion of an Electron in Quantum Mechanics	p. 20
Electrons in External Fields	p. 28
Localization by Impurities	p. 31
The Integer Quantum Hall Effect	p. 37
Laughlin's Gedankenexperiment	p. 37
Buttiker's Theory	p. 41
Edge Current vs. Bulk Current	p. 47
Deviations from the Quantized Value	p. 49
The Fractional Quantum Hall Effect	p. 53
General Considerations	p. 53
Investigation by the Exact-Diagonalization Method	p. 59
Investigation by the Variational Method	p. 65
Comparison Between the Exact Ground State and the Laughlin State	p. 72
Properties of the FQHE State	p. 74
Comparison with Experiment	p. 85
Order Parameter and Long-Range Order	p. 90
Composite-Particle Mean-Field Theory	p. 95
Berry Phase and Statistics of Quasiparticles	p. 95
Composite-Boson Mean-Field Theory	p. 102
Chern-Simons Ginzburg-Landau Theory	p. 105
Composite-Fermion Mean-Field Theory	p. 112
Spin and Pseudospin Freedom	p. 117
The Ground State in the Presence of Spin Degeneracy	p. 117
Excited States	p. 122
Skyrmions	p. 125
Bilayer Systems and Pseudospin Representation	p. 130
Ground State of a Bilayer System	p. 132
Even-Denominator States	p. 139
Anomalous Phenomena at v = 1/2	p. 139
Composite-Fermion Theory	p. 142
Experimental Verification	p. 143
A Remaining Problem: the Essence of the State at v = 1/2	p. 148
Electron States at the Sample Edge	p. 151
Edge States - Effect of the Long-Range Coulomb Interaction	p. 151
Idealized Edge States - the Effect of Electron Correlation	p. 155
Higher Landau Levels	p. 173
New Ground States in Higher Landau Levels	p. 173
The Hamiltonian in Higher Landau Levels	p. 176
Pair States	p. 178
Charge Density Wave States	p. 181
Answers to Exercises	p. 189
References	p. 201
Index	p. 205
Table of Contents provided by Blackwell. All Rights Reserved.

The Quantum Hall Effect

At a Glance

Hardcover

Industry Reviews

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