Composite fermions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 543 S. graph. Darst. |
| ISBN: | 9780521862325 0521862329 |
Internformat
MARC
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| 020 | |a 9780521862325 |9 978-0-521-86232-5 | ||
| 020 | |a 0521862329 |c (hbk.) : £50.00 |9 0-521-86232-9 | ||
| 035 | |a (OCoLC)232346722 | ||
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| 100 | 1 | |a Jain, Jainendra K. |d 1960- |e Verfasser |0 (DE-588)173927149 |4 aut | |
| 245 | 1 | 0 | |a Composite fermions |c Jainendra K. Jain |
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XVI, 543 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Fermions | |
| 650 | 7 | |a Fermions |2 ram | |
| 650 | 7 | |a Hall quantique, Effet |2 ram | |
| 650 | 7 | |a Hall, Effet |2 ram | |
| 650 | 4 | |a Fermions | |
| 650 | 0 | 7 | |a Quanten-Hall-Effekt |0 (DE-588)4124013-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fermion |0 (DE-588)4121256-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Composite fermion |0 (DE-588)4598966-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Composite fermion |0 (DE-588)4598966-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Quanten-Hall-Effekt |0 (DE-588)4124013-3 |D s |
| 689 | 1 | 1 | |a Fermion |0 (DE-588)4121256-3 |D s |
| 689 | 1 | |5 DE-604 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015470078 | ||
Datensatz im Suchindex
| _version_ | 1804136258952232960 |
|---|---|
| adam_text | Contents
Preface
page
xiii
List of symbols and abbreviations
xv
1
Overview
1
1.1
Integral quantum Hall effect
1
1.2
Fractional quantum Hall effect
2
4
5
7
7
9
10
12
12
14
17
19
21
22
23
26
27
28
29
32
33
34
36
37
1.3
Strongly correlated state
1.4
Composite
fermions
1.5
Origin of the FQHE
1.6
The composite fermion quantum fluid
1.7
An ideal theory
1.8
Miscellaneous remarks
Quantum Hall effect
2.1
The Hall effect
2.2
Two-dimensional electron system
2.3
The
von Klitzing
discovery
2.4
The
von
Klitzing constant
2.5
The Tsui-Stormer-Gossard discovery
2.6
Role of technology
Exercises
Landau levels
3.1
Gauge
invariance
3.2
Landau gauge
3.3
Symmetric gauge
3.4
Degeneracy
3.5
Filling factor
3.6
Wave functions for filled Landau levels
3.7
Lowest Landau level projection of operators
3.8
Gauge independent treatment
Contents
3.9
Magnetic
translation
operator
40
3.10
Spherical geometry
42
3.11
Coulomb matrix elements
52
3.12
Disk geometry/parabolic quantum dot
61
3.13
Torus geometry
65
3.14
Periodic potential: the
Hofstadter
butterfly
67
3.15
Tight binding model
69
Exercises
71
Theory of the IQHE
77
4.1
The puzzle
77
4.2
The effect of disorder
78
4.3
Edge states
81
4.4
Origin of quantized Hall plateaus
81
4.5
IQHE in a periodic potential
96
4.6
Two-dimensional Anderson localization in a magnetic field
97
4.7
Density gradient and R^
101
4.8
The role of interaction
102
Foundations of the composite fermion theory
105
5.1
The great FQHE mystery
105
5.2
The Hamiltonian
106
5.3
Why the problem is hard
109
5.4
Condensed matter theory: solid or squalid?
no
5.5
Laughlin s theory
113
5.6
The analogy
115
5.7
Particles of condensed matter
116
5.8
Composite fermion theory
118
5.9
Wave functions in the spherical geometry
138
5.10
Uniform density for incompressible states
141
5.11
Derivation of v* and B*
141
5.12
Reality of the effective magnetic field
145
5.13
Reality of the
Λ
levels
146
5.14
Lowest Landau level projection
146
5.15
Need
f
or other formulations
153
5.16
Composite fermion Chern-Simons theory
154
5.17
Other CF based approaches
164
Exercises
173
Microscopic verifications
174
6.1
Computer experiments
174
6.2
Relevance to laboratory experiments
175
6.3
A caveat regarding variational approach
176
Contents ix
6.4 Qualitative
tests
176
6.5 Quantitative
tests
181
6.6
What computer experiments prove
187
6.7
Inter-composite fermion interaction
188
6.8
Disk geometry
192
6.9
A small parameter and perturbation theory
197
Exercises
199
7
Theory of the FQHE
201
7.1
Comparing the IQHE and the FQHE
201
7.2
Explanation of the FQHE
203
7.3
Absence of FQHE at
v
= 1/2 206
7.4
Interacting composite
fermions:
new fractions
206
7.5
FQHE and spin
213
7.6
FQHE at low fillings
213
7.7
FQHE in higher Landau levels
213
7.8
Fractions
ad infinitum!
214
Exercises
214
8
Incompressible ground states and their excitations
217
8.1
One-particle reduced density matrix
217
8.2
Pair correlation function
218
8.3
Static structure factor
220
8.4
Ground state energy
222
8.5
CF-quasiparticle and CF-quasihole
224
8.6
Excitations
226
8.7
CF masses
237
8.8
CFCS theory of excitations
245
8.9
Tunneling into the CF liquid: the electron spectral function
245
Exercises
250
9
Topology and quantizations
253
9.1
Charge charge, statistics statistics
253
9.2
Intrinsic charge and exchange statistics of composite
fermions
254
9.3
Local charge
255
9.4
Quantized screening
263
9.5
Fractionally quantized Hall resistance
264
9.6
Evidence for fractional local charge
266
9.7
Observations of the fermionic statistics of composite
fermions
268
9.8
Leinaas-Myrheim-Wilczek braiding statistics
269
9.9
Non-Abelian braiding statistics
279
9.10
Logical order
281
Exercises
281
Contents
10
Composite fermion
Fermi sea
286
10.1
Geometrie
resonances
287
10.2
Thermopower
297
10.3
Spin polarization of the
CF
Fermi sea
301
10.4 Magnetoresistance
at
v
= 1 /2 301
10.5
Compressibility
305
11
Composite
fermions
with spin
307
11.1
Controlling the spin experimentally
308
11.2
Violation of Hund s first rule
309
11.3
Mean-field model of composite
fermions
with a spin
311
11.4
Microscopic theory
314
11.5
Comparisons with exact results: resurrecting Hund s first rule
324
11.6
Phase diagram of the FQHE with spin
326
11.7
Polarization mass
331
11.8
Spin-reversed excitations of incompressible states
337
11.9
Summary
347
11.10
Skyrmions
348
Exercises
360
12
Non-composite fermion approaches
363
12.1
Hierarchy scenario
363
12.2
Composite boson approach
366
12.3
Response to Laughlin s critique
368
12.4
Two-dimensional one-component plasma (2DOCP)
370
12.5
Charged excitations at
v
=
í/m
372
12.6
Neutral excitations: Girvin-MacDonald-Platzman theory
377
12.7
Conti-Vignaie-Tokatly
continuum-elasticity theory
384
12.8
Search for a model interaction
386
Exercises
389
13
BilayerFQHE
394
13.1
Bilayer composite fermion states
395
13.2 1/2
FQHE
400
13.3
v
— 1:
interlayer phase coherence
403
13.4
Composite fermion drag
408
13.5
Spinful composite
fermions
in bilayers
409
Exercises
411
14
Edge physics
413
14.1
QHE edge
= 1
D
system
413
14.2
Green s function at the IQHE edge
414
14.3
Bosonization in one dimension
417
14.4
Wen s conjecture
429
Contents xi
14.5 Experiment 432
14.6
Exact
diagonalization
studies
437
14.7
Composite fermion theories of the edge
438
Exercises
441
15
Composite fermion crystals
442
15.1
Wigner crystal
442
15.2
Composite
fermions
at low
v
446
15.3
Composite fermion crystal
449
15.4
Experimental status
452
15.5
CF charge density waves
455
Appendixes
A Gaussian integral
458
В
Useful operator identities
460
С
Point flux tube
462
D
Adiabatic insertion of a point flux
463
E
Berry phase
465
F
Second quantization
467
G
Green s functions, spectral function, tunneling
477
H
Off-diagonal long-range order
482
/
Total energies and energy gaps
486
J
Lowest Landau level projection
490
К
Metropolis Monte Carlo
499
L
Composite fermion diagonalization
502
References
504
Index
540
|
| adam_txt |
Contents
Preface
page
xiii
List of symbols and abbreviations
xv
1
Overview
1
1.1
Integral quantum Hall effect
1
1.2
Fractional quantum Hall effect
2
4
5
7
7
9
10
12
12
14
17
19
21
22
23
26
27
28
29
32
33
34
36
37
1.3
Strongly correlated state
1.4
Composite
fermions
1.5
Origin of the FQHE
1.6
The composite fermion quantum fluid
1.7
An "ideal" theory
1.8
Miscellaneous remarks
Quantum Hall effect
2.1
The Hall effect
2.2
Two-dimensional electron system
2.3
The
von Klitzing
discovery
2.4
The
von
Klitzing constant
2.5
The Tsui-Stormer-Gossard discovery
2.6
Role of technology
Exercises
Landau levels
3.1
Gauge
invariance
3.2
Landau gauge
3.3
Symmetric gauge
3.4
Degeneracy
3.5
Filling factor
3.6
Wave functions for filled Landau levels
3.7
Lowest Landau level projection of operators
3.8
Gauge independent treatment
Contents
3.9
Magnetic
translation
operator
40
3.10
Spherical geometry
42
3.11
Coulomb matrix elements
52
3.12
Disk geometry/parabolic quantum dot
61
3.13
Torus geometry
65
3.14
Periodic potential: the
Hofstadter
butterfly
67
3.15
Tight binding model
69
Exercises
71
Theory of the IQHE
77
4.1
The puzzle
77
4.2
The effect of disorder
78
4.3
Edge states
81
4.4
Origin of quantized Hall plateaus
81
4.5
IQHE in a periodic potential
96
4.6
Two-dimensional Anderson localization in a magnetic field
97
4.7
Density gradient and R^
101
4.8
The role of interaction
102
Foundations of the composite fermion theory
105
5.1
The great FQHE mystery
105
5.2
The Hamiltonian
106
5.3
Why the problem is hard
109
5.4
Condensed matter theory: solid or squalid?
no
5.5
Laughlin's theory
113
5.6
The analogy
115
5.7
Particles of condensed matter
116
5.8
Composite fermion theory
118
5.9
Wave functions in the spherical geometry
138
5.10
Uniform density for incompressible states
141
5.11
Derivation of v* and B*
141
5.12
Reality of the effective magnetic field
145
5.13
Reality of the
Λ
levels
146
5.14
Lowest Landau level projection
146
5.15
Need
f
or other formulations
153
5.16
Composite fermion Chern-Simons theory
154
5.17
Other CF based approaches
164
Exercises
173
Microscopic verifications
174
6.1
Computer experiments
174
6.2
Relevance to laboratory experiments
175
6.3
A caveat regarding variational approach
176
Contents ix
6.4 Qualitative
tests
176
6.5 Quantitative
tests
181
6.6
What computer experiments prove
187
6.7
Inter-composite fermion interaction
188
6.8
Disk geometry
192
6.9
A small parameter and perturbation theory
197
Exercises
199
7
Theory of the FQHE
201
7.1
Comparing the IQHE and the FQHE
201
7.2
Explanation of the FQHE
203
7.3
Absence of FQHE at
v
= 1/2 206
7.4
Interacting composite
fermions:
new fractions
206
7.5
FQHE and spin
213
7.6
FQHE at low fillings
213
7.7
FQHE in higher Landau levels
213
7.8
Fractions
ad infinitum!
214
Exercises
214
8
Incompressible ground states and their excitations
217
8.1
One-particle reduced density matrix
217
8.2
Pair correlation function
218
8.3
Static structure factor
220
8.4
Ground state energy
222
8.5
CF-quasiparticle and CF-quasihole
224
8.6
Excitations
226
8.7
CF masses
237
8.8
CFCS theory of excitations
245
8.9
Tunneling into the CF liquid: the electron spectral function
245
Exercises
250
9
Topology and quantizations
253
9.1
Charge charge, statistics statistics
253
9.2
Intrinsic charge and exchange statistics of composite
fermions
254
9.3
Local charge
255
9.4
Quantized screening
263
9.5
Fractionally quantized Hall resistance
264
9.6
Evidence for fractional local charge
266
9.7
Observations of the fermionic statistics of composite
fermions
268
9.8
Leinaas-Myrheim-Wilczek braiding statistics
269
9.9
Non-Abelian braiding statistics
279
9.10
Logical order
281
Exercises
281
Contents
10
Composite fermion
Fermi sea
286
10.1
Geometrie
resonances
287
10.2
Thermopower
297
10.3
Spin polarization of the
CF
Fermi sea
301
10.4 Magnetoresistance
at
v
= 1 /2 301
10.5
Compressibility
305
11
Composite
fermions
with spin
307
11.1
Controlling the spin experimentally
308
11.2
Violation of Hund's first rule
309
11.3
Mean-field model of composite
fermions
with a spin
311
11.4
Microscopic theory
314
11.5
Comparisons with exact results: resurrecting Hund's first rule
324
11.6
Phase diagram of the FQHE with spin
326
11.7
Polarization mass
331
11.8
Spin-reversed excitations of incompressible states
337
11.9
Summary
347
11.10
Skyrmions
348
Exercises
360
12
Non-composite fermion approaches
363
12.1
Hierarchy scenario
363
12.2
Composite boson approach
366
12.3
Response to Laughlin's critique
368
12.4
Two-dimensional one-component plasma (2DOCP)
370
12.5
Charged excitations at
v
=
í/m
372
12.6
Neutral excitations: Girvin-MacDonald-Platzman theory
377
12.7
Conti-Vignaie-Tokatly
continuum-elasticity theory
384
12.8
Search for a model interaction
386
Exercises
389
13
BilayerFQHE
394
13.1
Bilayer composite fermion states
395
13.2 1/2
FQHE
400
13.3
v
— 1:
interlayer phase coherence
403
13.4
Composite fermion drag
408
13.5
Spinful composite
fermions
in bilayers
409
Exercises
411
14
Edge physics
413
14.1
QHE edge
= 1
D
system
413
14.2
Green's function at the IQHE edge
414
14.3
Bosonization in one dimension
417
14.4
Wen's conjecture
429
Contents xi
14.5 Experiment 432
14.6
Exact
diagonalization
studies
437
14.7
Composite fermion theories of the edge
438
Exercises
441
15
Composite fermion crystals
442
15.1
Wigner crystal
442
15.2
Composite
fermions
at low
v
446
15.3
Composite fermion crystal
449
15.4
Experimental status
452
15.5
CF charge density waves
455
Appendixes
A Gaussian integral
458
В
Useful operator identities
460
С
Point flux tube
462
D
Adiabatic insertion of a point flux
463
E
Berry phase
465
F
Second quantization
467
G
Green's functions, spectral function, tunneling
477
H
Off-diagonal long-range order
482
/
Total energies and energy gaps
486
J
Lowest Landau level projection
490
К
Metropolis Monte Carlo
499
L
Composite fermion diagonalization
502
References
504
Index
540 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Jain, Jainendra K. 1960- |
| author_GND | (DE-588)173927149 |
| author_facet | Jain, Jainendra K. 1960- |
| author_role | aut |
| author_sort | Jain, Jainendra K. 1960- |
| author_variant | j k j jk jkj |
| building | Verbundindex |
| bvnumber | BV022259410 |
| callnumber-first | Q - Science |
| callnumber-label | QC793 |
| callnumber-raw | QC793.5.F42 |
| callnumber-search | QC793.5.F42 |
| callnumber-sort | QC 3793.5 F42 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 5110 |
| ctrlnum | (OCoLC)232346722 (DE-599)BVBBV022259410 |
| dewey-full | 539.721 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics |
| dewey-raw | 539.721 |
| dewey-search | 539.721 |
| dewey-sort | 3539.721 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV022259410 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:42:20Z |
| indexdate | 2024-07-09T20:53:33Z |
| institution | BVB |
| isbn | 9780521862325 0521862329 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015470078 |
| oclc_num | 232346722 |
| open_access_boolean | |
| owner | DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 DE-83 DE-384 DE-20 |
| owner_facet | DE-703 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-11 DE-83 DE-384 DE-20 |
| physical | XVI, 543 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Jain, Jainendra K. 1960- Verfasser (DE-588)173927149 aut Composite fermions Jainendra K. Jain Cambridge [u.a.] Cambridge Univ. Press 2007 XVI, 543 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Fermions Fermions ram Hall quantique, Effet ram Hall, Effet ram Quanten-Hall-Effekt (DE-588)4124013-3 gnd rswk-swf Fermion (DE-588)4121256-3 gnd rswk-swf Composite fermion (DE-588)4598966-7 gnd rswk-swf Composite fermion (DE-588)4598966-7 s DE-604 Quanten-Hall-Effekt (DE-588)4124013-3 s Fermion (DE-588)4121256-3 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015470078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jain, Jainendra K. 1960- Composite fermions Fermions Fermions ram Hall quantique, Effet ram Hall, Effet ram Quanten-Hall-Effekt (DE-588)4124013-3 gnd Fermion (DE-588)4121256-3 gnd Composite fermion (DE-588)4598966-7 gnd |
| subject_GND | (DE-588)4124013-3 (DE-588)4121256-3 (DE-588)4598966-7 |
| title | Composite fermions |
| title_auth | Composite fermions |
| title_exact_search | Composite fermions |
| title_exact_search_txtP | Composite fermions |
| title_full | Composite fermions Jainendra K. Jain |
| title_fullStr | Composite fermions Jainendra K. Jain |
| title_full_unstemmed | Composite fermions Jainendra K. Jain |
| title_short | Composite fermions |
| title_sort | composite fermions |
| topic | Fermions Fermions ram Hall quantique, Effet ram Hall, Effet ram Quanten-Hall-Effekt (DE-588)4124013-3 gnd Fermion (DE-588)4121256-3 gnd Composite fermion (DE-588)4598966-7 gnd |
| topic_facet | Fermions Hall quantique, Effet Hall, Effet Quanten-Hall-Effekt Fermion Composite fermion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015470078&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT jainjainendrak compositefermions |