Fundamental Problems of Mesoscopic Physics: Interactions and Decoherence

386 Pages·2004·4.537 MB·English

by  Igor V. Lerner, Boris L. Altshuler, Yuval Gefen

Fundamental Problems of Mesoscopic Physics
Interactions and Decoherence
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Series II: Mathematics, Physics and Chemistry – Vol. 154
Fundamental Problems of
Mesoscopic Physics
Interactions and Decoherence
edited by
Igor V. Lerner
University of Birmingham,
Birmingham, United Kingdom
Boris L. Altshuler
Princeton University and NEC Research Institute,
Princeton, New Jersey, U.S.A.
and
Yuval Gefen
The Weizmann Institute of Science,
Rehovot, Israel
KLUWER ACADEMIC PUBLISHERS
NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW
eBook ISBN: 1-4020-2193-3
Print ISBN: 1-4020-2192-5
©2004 Springer Science + Business Media, Inc.
Print ©2004 Kluwer Academic Publishers
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Contents
Preface xi
PartI DecoherenceandDephasing
1
ElectronDephasinginMesoscopicMetalWires 3
NormanO.BirgeandF.Pierre
1 Introduction 3
2 τφinpureAuandAgsamples 5
3 Possibleexplanationsforsaturationofτφ 7
4 Aharonov-BohmexperimentsinlargeCurings 10
5 Conclusions 13
2
DecoherenceeffectsintheJosephsoncurrentofaCooperpairshuttle 17
AlessandroRomitoandRosarioFazio
1 Introduction 17
2 Themodel 18
3 Results 20
4 CooperpairshuttlewithSQUIDloops 29
3
Dephasingindisorderedmetalswithsuperconductivegrains 33
M.A.Skvortsov,A.I.Larkin,M.V.Feigel’man
1 Introduction 33
2 Descriptionoftheformalism 36
3 Dynamicsofthephase 37
4 Phasetransition 38
5 Cooperonself-energy 40
6 Dephasingtime 42
7 Magnetoresistance 44
8 Discussion 45
4
49
DecoherenceinDisorderedConductorsatLowTemperatures: theeffect
ofSoftLocalExcitations
Y.Imry,Z.OvadyahuandA.Schiller
1 Introduction 50
v
vi FUNDAMENTALPROBLEMSOFMESOSCOPICPHYSICS
2 ThevanishingofthedephasingrateasT →0: theory 51
3 Experimentalresults 55
4 Atunnellingmodelforlooselyboundheavyimpurities 58
5 Conclusions 61
5
Quantumprecursorofshuttleinstability 65
D.Fedorets,L.Y.Gorelik,R.I.ShekhterandM.Jonson
1 Introduction 65
2 Theoreticalmodel 66
3 Analysisandresults 69
6
Dephasinganddynamiclocalizationinquantumdots 75
V.E.Kravtsov
1 Introduction 75
2 Weakdynamiclocalization 78
3 Roleofelectroninteractionondynamiclocalizationinclosedquan-
tumdots. 91
4 Dynamic localization in an open quantum dot and the shape of the
Coulombblockadepeak. 93
5 Summary 97
7
99
Mesoscopic Aharonov-Bohmoscillationsinmetallicrings
T.LudwigandA.D.Mirlin
1 Introduction 100
2 Low-temperaturelimit: fullycoherentsample 100
3 Dephasingbyelectron-electroninteraction 104
4 Summary 112
8
Influence Functional forDecoherence of Interacting Electrons inDisor- 115
deredConductors
J.vonDelft
1 Introduction 115
2 Mainresultsofinfluencefunctionalapproach 118
3 OriginofthePaulifactor 121
4 Calculatingτϕ`alaGZ 122
5 DysonequationandCooperonselfenergy 125
6 Vertexcontributions 127
7 Discussionandsummary 130
Appendix 131
1 Outlineofderivationofinfluencefunctional 132
2 Cooperonselfenergybeforedisorderaveraging 135
3 Thermalaveraging 136
Contents vii
PartII EntanglementandQubits
9
Low-frequencynoiseasasourceofdephasingofaqubit 141
Y.M.Galperin,B.L.AltshulerandD.V.Shantsev
1 Introductionandmodel 142
2 Resultsforasinglefluctuator 150
3 Summationovermanyfluctuators 154
4 Simulations 158
5 Comparisonwiththenoiseintherandomfrequencydeviation 162
6 Applicabilityrangeofthemodel 162
7 Conclusions 163
10
Entanglementproductioninachaoticquantumdot 167
C.W.J.Beenakker,M.Kindermann,C.M.Marcus,A.Yacoby
1 Introduction 167
2 Relationbetweenentanglementandtransmissioneigenvalues 169
3 Statisticsoftheconcurrence 171
4 RelationbetweenBellparameterandconcurrence 171
5 Relationbetweennoisecorrelatorandconcurrence 172
6 Bellinequalitywithouttunnelingassumption 173
7 Conclusion 175
11
Creationanddetectionofmobileandnon-localspin-entangledelectrons 179
P.Recher,D.S.SaragaandD.Loss
1 Sourcesofmobilespin-entangledelectrons 179
2 Superconductor-basedelectronspin-entanglers 180
3 Tripledotentangler 189
4 Detectionofspin-entanglement 193
5 Electron-holesentanglerswithoutinteraction 197
6 Summary 198
12
Berezinskii-Kosterlitz-ThoulesstransitioninJosephsonjunctionarrays 203
L.Capriotti,A.CuccoliandA.Fubini,V.TognettiandR.Vaia
1 Introduction 204
2 Themodel 205
3 Numericalsimulations 206
4 Results 208
5 Thephasediagram 212
6 Summary 214
Appendix: PIMCintheFourierspaceforJJA 215
PartIII InteractionsinNormalandSuperconductingSystems
13
Quantumcoherenttransportandsuperconductivityincarbonnanotubes 219
M.Ferrier,A.Kasumov,R.Deblock,M.Kociak,S.Gueron,B.ReuletandH.Bouchiat
1 Introduction 219
2 Proximityinducedsuperconductivityincarbonnanotubesasaprobe
ofquantumtransport 221
3 IntrinsicsuperconductivityinropesofSWNTonnormalcontacts 226
4 Conclusion 235
viii FUNDAMENTALPROBLEMSOFMESOSCOPICPHYSICS
14
Quantum Hall ferromagnets, cooperative transport anisotropy, and the 239
randomfieldIsingmodel
J.T.Chalker,D.G.Polyakov, F.Evers,A.D.Mirlin,andP.Wo¨lfle
1 Introduction 240
2 DomainformationandtherandomfieldIsingmodel 242
3 Transportanisotropyarisingfromdomainformation 244
4 Transportalongdomainwalls 247
5 Concludingremarks 249
15
Exoticproximityeffectsinsuperconductor/ferromagnetstructure 251
F.S.Bergeret,A.F.VolkovandK.B.Efetov
1 Introduction 252
2 ThecondensatefunctioninaF/S/Fsandwich 254
3 JosephsoncurrentinaF/S/F/S/Fstructure 259
4 Effectofspin-orbitinteraction 262
5 Inducedferromagnetisminthesuperconductor 263
6 Summary 270
16
TransportinLuttingerLiquids 275
T.Giamarchi,T.NattermannandP.LeDoussal
1 Introduction 275
2 Model 276
3 Transportatintermediatetemperatures 277
4 Creep 278
5 Variablerangehopping 280
6 Openissues 282
17
Interactioneffectsoncountingstatisticsandthetransmissiondistribution 285
M.Kindermann,YuliV.Nazarov
18
Variable–rangeHoppinginOne–dimensionalSystems 295
J.Prior,M.Ortun˜oandA.M.Somoza
1 Introduction 295
2 Model 297
3 Modelwithgeometricalfluctuationsonly 298
4 Hoppingmatrixelements 301
5 Quantummodel 304
6 Fluctuations 305
7 Summaryandconclusions 306
19
OntheElectron-ElectronInteractionsinTwoDimensions 309
V.M.Pudalov,M.GershensonandH.Kojima
1 Introduction 309
2 Renormalizedspinsusceptibility 311
3 Effectivemassandg-factor 318
4 Summary 324
Contents ix
20
Correlationsandspinintransportthroughquantumdots 329
M.Sassetti,F.Cavaliere,A.BraggioandB.Kramer
1 Introduction 329
2 Themodel 331
3 Thecharacteristicenergyscales 333
4 Sequentialtransport 335
5 Results 339
6 Discussionandconclusion 345
21
Interactionsinhigh-mobility2Delectronandholesystems 349
E.A.Galaktionov,A.K.Savchenko,S.S.Safonov,Y.Y.Proskuryakov,L.Li,M.Pepper,
M.Y.Simmons,D.A.Ritchie,E.H.Linfield,andZ.D.Kvon
1 Introduction 349
2 Ballisticregimeofelectron-electroninteraction 351
3 Interactioneffectsina2DholegasinGaAs 353
4 Electron-electroninteractionintheballisticregimeina2DEGinSi 361
5 Interactioneffectsintheballisticregimeina2DEGinGaAs. Long-
rangefluctuationpotential. 362
6 ComparisonofF0σ(rsψ)indifferent2Dsystems 364
7 Conclusion 367
Index 371