The quantum Hall effect:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Springer series in solid state sciences
133 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 207 S. graph. Darst. |
| ISBN: | 3540431152 |
Internformat
MARC
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| 100 | 1 | |a Yoshioka, Daijiro |d 1949- |e Verfasser |0 (DE-588)123454190 |4 aut | |
| 245 | 1 | 0 | |a The quantum Hall effect |c Daijiro Yoshioka |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XII, 207 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Springer series in solid state sciences |v 133 | |
| 490 | 0 | |a Physics and astronomy online library | |
| 650 | 7 | |a Efeito hall |2 larpcal | |
| 650 | 4 | |a Hall quantique, Effet | |
| 650 | 4 | |a Quantum Hall effect | |
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Datensatz im Suchindex
| _version_ | 1806142871707844608 |
|---|---|
| adam_text |
Contents
1. Discovery
of the
Quantum Hall
Effect
. 1
1.1
Realization of Two-Dimensional Electron Systems
. 1
1.1.1
Si
MOS
Systems and GaAs-AlGaAs Heterojimctions
. 1
1.1.2
Surface of Liquid Helium
. 6
1.2
The Quantum Hall Effect
. 7
1.2.1
Diagonal and Hall Resistances
. 7
1.2.2
The Discovery of the Integer Quantum Hall Effect
. 9
1.2.3
Discovery of the Fractional Quantum Hall Effect
. 13
Exercises
. 15
2.
Two-Dimensional Electrons in a Magnetic Field
. 17
2.1
Electron Motion in Classical Mechanics
. 17
2.1.1
Motion in a Magnetic Field
. 17
2.1.2
Motion in the Presence of a Magnetic Field
and an Electric, Field
. 19
2.2
Motion of an Electron in Quantum Mechanics
. 20
2.2.1
Hamiltonian for a Free Electron
. 20
2.2.2
Momentum and Angular Momentum
. 20
2.2.3
Gauge
Invariance
. 21
2.2.4
Landau Levels
. 22
2.2.5
Quantization Condition and Aharonov
-Bohm
Phase
. 25
2.2.6
Abrikosov Lattice
. 26
2.3
Electrons in External Fields
. 28
2.3.1
Motion in a Uniform Electric Field
. 28
2.3.2
Motion at the Edge of the System
. 29
2.4
Localization by Impurities
. 31
2.4.1
Anderson Localization at
В
= 0. 31
2.4.2
Localization in a Strong Magnetic Field
. 33
Exercises
. 35
3.
The Integer Quantum Hall Effect
. 37
3.1
Laughliiťs
Gedankenexperiment. 37
3.2
Buttikeťs
Theory
. 41
3.2.1
Nonequilibrium Occupation of the Edge States
. 41
X
Contents
3.2.2
Fermi Level and Current
. 43
3.2.3
Behavior of Current at the Electrodes
. 45
3.3
Edge Current vs. Bulk Current
. 47
3.4
Deviations from the Quantized Value
. 49
3.4.1
Effect of Temperature
. 49
3.4.2
Breakdown due to Large Current
. 49
4.
The Fractional Quantum Hall Effect
. 53
4.1
General Considerations
. 53
4.1.1
Impurity Potential and Electron-Electron Interaction
. 53
4.1.2
Limit of Strong Magnetic Field
. 55
4.1.3
Electron-Hole Symmetry
. 55
4.1.4
Definition of the Problem
. 57
4.1.5
Possibility of a Wigner Crystal
. 57
4.2
Investigation by the Exact-Diagonalization Method
. 59
4.2.1
Representation of the Hamiltonian in a Matrix Form
. . 59
4.2.2
Ground State
. 61
4.2.3
Excitation Spectrum
. 64
4.3
Investigation by the Variational Method
. 65
4.3.1
Laughlin's Wave Function
. 65
4.3.2
The Filling Factor of the Landau Level
. 66
4.3.3
Zero Points
. 69
4.3.4
Exact Hamiltonian
. 70
4.4
Comparison Between the Exact Ground State
and the Laughlin State
. 72
4.4.1
Comparison of the Wave Functions
. 72
4.4.2
Comparison of the Interactions
. 73
4.5
Properties of the FQHE State
. 74
4.5.1
Quasiparticles
. 74
4.5.2
Collective Excitations
. 77
4.5.3
Hierarchy
. 83
4.6
Comparison with Experiment
. 85
4.6.1
Fractional Quantization
. 85
4.6.2
Excitation Energy
. 86
4.6.3
Fractional Charge
. 88
4.7
Order Parameter and Long-Range Order
. 90
4.7.1
Off-Diagonal Long-Range Order
. 90
4.7.2
Order in the Fractional Quantum Hall Effect
. 91
Exercises
. 94
5.
Composite-Particle Mean-Field Theory
. 95
5.1
Berry Phase and Statistics of Quasiparticles
. 95
5.1.1
Berry Phase
. 95
5.1.2
Anyone
. 98
5.1.3
Statistics of the Quasiparticles
. 100
Contents
XI
5.1.4
Hierarchy Theory in
Termy
of Anyons
.101
5.2
Composite-Boson Mean-Field Theory
.102
5.3
Chern-Simons Ginzburg-Landau Theory
.105
5.3.1
Ginzburg-Landau Equation
.105
5.3.2
Mean-Field Solution
.107
5.3.3
Properties of the Uniform Solution
.108
5.4
Composite-Fermion Mean-Field Theory
.112
Exercises
.115
6.
Spin and Pseudospin Freedom
.117
6.1
The Ground State in the Presence of Spin Degeneracy
.117
6.1.1
Halperin's Trial Wave Function
.118
6.1.2
Ferromagnetic State
.119
6.1.3
Spin Singlet State
.119
6.2
Excited States
.122
6.2.1
Spin Waves
.122
6.2.2
Quasiparticles
.123
6.3
Skyrmions
.125
6.3.1
Small Skyrmions
.126
6.3.2
Large Skyrmions
.127
6.3.3
Experimental Evidence for Skyrmioiis
.128
6.3.4
Comparison with the Hubbard Model
.129
6.4
Bilayer Systems and Pseudospin Representation
.130
6.4.1
Parameters Which Specify the Bilayer
.130
6.4.2
Pseudospin Representation of a Bilayer System
.132
6.5
Ground State of a Bilayer System
.132
6.5.1
The Case
d
> 0
and
ЛЅАЅ
= 0 .133
6.5.2
The case
d
> 0
and ASAS
> 0.135
Exercise
.137
7.
Even-Denominator States
.139
7.1
Anomalous Phenomena at
v
= 1/2.139
7.1.1
Anomaly in
д„
.139
7.1.2
Anomaly in Surface Acoustic Waves
.140
7.2
Composite-Fermion Theory
.142
7.3
Experimental Verification
.143
7.3.1
Measurement of the Fermi Wave Number
.143
7.3.2
Effective Mass
.146
7.4
A Remaining Problem: the Essence of the State at
v
= 1/2 . 148
8.
Electron States at the Sample Edge
. 151
8.1
Edge States Effect of the Long-Range Coulomb Interaction.
151
8.1.1
Steep Confining Potential
. 151
8.1.2
Slowly Varying Confining Potential
. 153
8.2
Idealized Edge States
--
the Effect of Electron Correlation
. 155
XII Contents
8.2.1 Tomonaga-Luttinger Liquid.155
8.2.2 Chiral Tomonaga-Luttinger Liquid.161
8.2.3
Experimental
Confirmation.
169
Exercises
.171
9. Higher Landau
Levels .
173
9.1 New
Ground
States in Higher Landau
Levels
.173
9.1.1
The Second Lowest
Landau Level .173
9.1.2
The Third Lowest
and Higher Landau
Levels .
175
9.2 The Hamiltonian in Higher Landau
Levels
.176
9.3
Pair
States.178
9.3.1 New
Ingredients: Spin Degree of Freedom and Pairing
. 178
9.3.2
Spin Singlet Pair State
.179
9.3.3
Pairing of Spin-Polarized
Fermions
.179
9.3.4
Ground State at
v
= 5/2.181
9.4
Charge Density Wave States
.181
9.4.1
Mean-Field Theory of the CDW States
.181
9.4.2
Exact-Diagonalization and DMRG Studies
of the CDW States
.185
Exercises
.187
Answers to Exercises
.189
References
.201
Index
.205 |
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| author | Yoshioka, Daijiro 1949- |
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| genre | 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV014096022 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T00:27:48Z |
| institution | BVB |
| isbn | 3540431152 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009657116 |
| oclc_num | 248747655 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-11 DE-188 |
| physical | XII, 207 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in solid state sciences |
| series2 | Springer series in solid state sciences Physics and astronomy online library |
| spelling | Yoshioka, Daijiro 1949- Verfasser (DE-588)123454190 aut The quantum Hall effect Daijiro Yoshioka Berlin [u.a.] Springer 2002 XII, 207 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid state sciences 133 Physics and astronomy online library Efeito hall larpcal Hall quantique, Effet Quantum Hall effect Hall-Effekt (DE-588)4023028-4 gnd rswk-swf Quanten-Hall-Effekt (DE-588)4124013-3 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Quanten-Hall-Effekt (DE-588)4124013-3 s DE-604 Hall-Effekt (DE-588)4023028-4 s 2\p DE-604 Erscheint auch als Online-Ausgabe 978-3-662-05016-3 Springer series in solid state sciences 133 (DE-604)BV000016582 133 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009657116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Yoshioka, Daijiro 1949- The quantum Hall effect Springer series in solid state sciences Efeito hall larpcal Hall quantique, Effet Quantum Hall effect Hall-Effekt (DE-588)4023028-4 gnd Quanten-Hall-Effekt (DE-588)4124013-3 gnd |
| subject_GND | (DE-588)4023028-4 (DE-588)4124013-3 (DE-588)4143413-4 |
| title | The quantum Hall effect |
| title_auth | The quantum Hall effect |
| title_exact_search | The quantum Hall effect |
| title_full | The quantum Hall effect Daijiro Yoshioka |
| title_fullStr | The quantum Hall effect Daijiro Yoshioka |
| title_full_unstemmed | The quantum Hall effect Daijiro Yoshioka |
| title_short | The quantum Hall effect |
| title_sort | the quantum hall effect |
| topic | Efeito hall larpcal Hall quantique, Effet Quantum Hall effect Hall-Effekt (DE-588)4023028-4 gnd Quanten-Hall-Effekt (DE-588)4124013-3 gnd |
| topic_facet | Efeito hall Hall quantique, Effet Quantum Hall effect Hall-Effekt Quanten-Hall-Effekt Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009657116&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016582 |
| work_keys_str_mv | AT yoshiokadaijiro thequantumhalleffect |