Quantum Hall Effects: Field Theoretical Approach and Related Topics

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World Scientific, 2008 - 706 pages
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The quantum Hall effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. Tremendous theoretical and experimental developments are still being made in this sphere. In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. This new edition includes many novel ideas according to recent progress. Fantastic phenomena associated with the interlayer phase coherence and SU(4) quantum Hall ferromagnets in the bilayer system are extensively reviewed. The microscopic theory of the QHE is formulated based on noncommutative geometry, the underlying mathematical structure. Quasiparticles are described as noncommutative solitons. The coverage also includes the recent development of the unconventional QHE in graphene (a single atomic layer graphite), where the electron dynamics can be treated as relativistic Dirac fermions and even the supersymmetric quantum mechanics plays a key role. An instructive and comprehensive overview of the QHE, this book is also suitable as an introduction to quantum field theory with vivid applications. Only a knowledge of quantum mechanics is assumed.
 

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Table des matières

Quantum Mechanics
3
Quantum Field Theory
20
Canonical Quantization
31
Spontaneous Symmetry Breaking
47
Electromagnetic Field
67
Dirac Field
94
Topological Solitons
113
Anyons
144
Stripes and Bubbles in Higher Landau Levels
325
Quantum Hall Effects in Graphene
335
Overview of Bilayer QH Systems
369
SU2 Pseudospin Structure
383
BilayerLocked States
400
Interlayer Coherence
409
SU4 Quantum Hall Ferromagnets
428
Bilayer Quantum Hall Systems at ν 2
454

Overview of Monolayer QH Systems
163
Landau Quantization
177
Quantum Hall Effects
204
Quasiparticles and Activation Energy
215
Field Theory of Composite Particles
227
Composite Bosons and Semiclassical Analysis
246
Quantum Hall Ferromagnets
261
Spin Textures
274
Hierarchy of Fractional QH States
291
Edge Effects
307
Bilayer QuantumHall Junction
485
Overview of Microscopic Theory
523
Noncommutative Geometry
534
Landau Level Projection
562
Noncommutative Solitons
584
Exchange Interactions and Effective Theory
607
Appendices
643
References
681
Index
699
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