Theory of Conventional and Unconventional Superconductivity in the High-Tc Cuprates and Other Systems

360 Pages·2013·5.672 MB·English

by  Dzhumanov Safarali

PHYSICS RESEARCH AND TECHNOLOGY

T C
HEORY OF ONVENTIONAL
U
AND NCONVENTIONAL
S
UPERCONDUCTIVITY
H -T C
IN THE IGH UPRATES
C
O S
AND THER YSTEMS

No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or
by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no
expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No
liability is assumed for incidental or consequential damages in connection with or arising out of information
contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in
rendering legal, medical or any other professional services.
P R T
HYSICS ESEARCH AND ECHNOLOGY

Additional books in this series can be found on Nova’s website
under the Series tab.

Additional e-books in this series can be found on Nova’s website
under the e-book tab.
PHYSICS RESEARCH AND TECHNOLOGY

T C
HEORY OF ONVENTIONAL
U
AND NCONVENTIONAL
S
UPERCONDUCTIVITY
H -T C
IN THE IGH UPRATES
C
O S
AND THER YSTEMS

DZHUMANOV SAFARALI

New York
Copyright © 2013 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or
transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical
photocopying, recording or otherwise without the written permission of the Publisher.

For permission to use material from this book please contact us:
Telephone [phone]; Fax [phone]
Web Site: http://www.novapublishers.com

NOTICE TO THE READER

The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or
implied warranty of any kind and assumes no responsibility for any errors or omissions. No
liability is assumed for incidental or consequential damages in connection with or arising out of
information contained in this book. The Publisher shall not be liable for any special,
consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or
reliance upon, this material. Any parts of this book based on government reports are so indicated
and copyright is claimed for those parts to the extent applicable to compilations of such works.

Independent verification should be sought for any data, advice or recommendations contained in
this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage
to persons or property arising from any methods, products, instructions, ideas or otherwise
contained in this publication.

This publication is designed to provide accurate and authoritative information with regard to the
subject matter covered herein. It is sold with the clear understanding that the Publisher is not
engaged in rendering legal or any other professional services. If legal or any other expert
assistance is required, the services of a competent person should be sought. FROM A
DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE
AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS.

Additional color graphics may be available in the e-book version of this book.

LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA

Theory of conventional and unconventional superconductivity in the High-Tc cuprates and other
systems / editor, Dzhumanov Safarali.
p. cm.
Includes bibliographical references and index.
ISBN: (cid:28)(cid:26)(cid:27)(cid:16)(cid:20)(cid:16)(cid:25)(cid:21)(cid:19)(cid:27)(cid:20)(cid:16)(cid:24)(cid:27)(cid:21)(cid:16)(cid:22) (eBook)
1. Copper oxide superconductors. I. Safarali, Dzhumanov.
QC611.98.C64T46 2011
537.6'23--dc23
2012011768

Published by Nova Science Publishers, Inc. † New York
Contents
Preface xi
1 ConventionalSuperconductors 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ClassificationofSolidsonElectricalConductivity . . . . . . . . . . . . . . 2
1.3 One-ElectronBandTheoryofSolids . . . . . . . . . . . . . . . . . . . . . 3
1.4 SimpleMetals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 BasicPropertiesofConventionalSuperconductors. . . . . . . . . . . . . . 14
1.5.1 ElectromagneticProperties . . . . . . . . . . . . . . . . . . . . . . 14
1.5.2 ThermalProperties . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5.3 ThermodynamicsofSuperconductors . . . . . . . . . . . . . . . . 19
1.5.4 TheIsotopeEffect . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.5.5 OpticalProperties. . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 PhenomenologicalTheories
ofSuperconductivity 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 LandauCriterionforSuperfluidity . . . . . . . . . . . . . . . . . . . . . . 30
2.3 LondonEquationsforaSuperconductorandPenetrationDepth . . . . . . . 32
2.4 QuantizationofMagneticField,VortexState
andJosephsonEffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Ginzburg-LandauTheoryandCoherenceLength . . . . . . . . . . . . . . 40
2.6 CriticalMagneticFieldsandMixedState . . . . . . . . . . . . . . . . . . 44
2.7 MeissnerEffectandTypeIISuperconductivity . . . . . . . . . . . . . . . 47
2.8 CriticalCurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.9 FluctuationEffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3 MicroscopicTheoryofConventionalSuperconductivity 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 LandauFermi-LiquidTheory . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Electron-PhononInteractioninMetals . . . . . . . . . . . . . . . . . . . . 62
3.4 CooperPairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5 TheBCSPairingTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5.1 TheBCSGroundandExcitedStatesAtZeroTemperature . . . . . 71
3.5.2 TheBCSGroundandExcitedStatesatFiniteTemperatures . . . . 74
vi Contents
3.5.3 DensityofStates . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5.4 ThermodynamicPropertiesofConventionalSuperconductors . . . 79
3.5.5 MagneticPropertiesofConventionalSuperconductors . . . . . . . 81
3.5.6 BogoliubovandEliashberg-McMillanPairingTheories . . . . . . . 85
4 High-T andOther UnconventionalSuperconductors 91
C
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.2 ResistiveTransitions,CrystalStructure,andPhase
DiagramsoftheCuprates . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3 Normal-StatePropertiesofHigh-T Cuprates . . . . . . . . . . . . . . . . 94
c
4.3.1 OpticalPropertiesandPseudogapFeatures . . . . . . . . . . . . . 95
4.3.2 ThermalProperties . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.3 Metal-insulatorTransitions,ChargeTransport,PhaseSeparation
andStripeFormation . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.4 MagneticProperties . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.5 ElasticProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4 SuperconductingStatePropertiesofHigh-T Cuprates . . . . . . . . . . . . 105
c
4.4.1 SuperconductingOrderParameter, Low-lyingExcitations
andZero-biasConductancePeak . . . . . . . . . . . . . . . . . . . 105
4.4.2 CoexistenceofthePseudogapandSuperconductingGap . . . . . . 107
4.4.3 ThermodynamicPropertiesandλ-likeSuperconductingProperties . 108
4.4.4 Electrodynamic Properties: Penetration Depth, Critical Magnetic
FieldsandMixedState . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4.5 VortexStates,IntegerandHalf-IntegerMagneticFluxQuantization 111
4.4.6 CriticalCurrentandSuperfluidDensity . . . . . . . . . . . . . . . 112
4.4.7 GaplessandTypeIIandIIISuperconductivity . . . . . . . . . . . 113
4.4.8 One- and Two-bell-shaped Doping Dependences of T with the
c
PlateauorLocalMinimumbetweenTwoSuperconductingDomes . 114
4.5 IsotopeEffectontheSuperconductingTransition
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.6 BasicPhysicalPropertiesofHeavy-Fermion
Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.7 BasicPhysicalPropertiesofOrganicSuperconductors. . . . . . . . . . . . 117
5 DifferentTheoreticalApproaches... 127
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.2 BipolaronicMechanismofSuperconductivity . . . . . . . . . . . . . . . . 128
5.3 ElectronicMechanismsofBCS-likePairing . . . . . . . . . . . . . . . . . 130
5.4 BCS-Bose-Einstein-CondensationCrossoverApproach . . . . . . . . . . . 131
5.5 Boson-FermionModels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.6 ResonatingValenceBondModel . . . . . . . . . . . . . . . . . . . . . . . 134
5.7 SuperconductingFluctuationApproach . . . . . . . . . . . . . . . . . . . 136
5.8 TheMarginalandNearlyAntiferromagneticFermi-LiquidModels . . . . . 139
5.9 BCS-likes-, p-andd-wavePairingMechanisms . . . . . . . . . . . . . . . 141
Contents vii
6 TheoryoftheElectronicStructure
ofUndoped andDopedCuprates 151
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.2 One-ElectronBandTheory . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6.3 StrongElectronCorrelationsintheUndopedCuprates . . . . . . . . . . . 154
6.4 One-andThree-BandHubbardModels... . . . . . . . . . . . . . . . . . . 156
6.5 Electron-Defect-PhononandDefect(Impurity)-AssistedSelf-Trapping... . 158
6.5.1 FormationoftheShallowHydrogen-likeDefectsStates. . . . . . . 162
6.5.2 FormationoftheNon-hydrogen-likeLocalizedDefectStates . . . . 163
6.5.3 BasicParametersofExtrinsicLargePolaronsandBipolarons. . . . 163
6.5.4 FormationofLargePolaronsandBipolarons . . . . . . . . . . . . 164
6.6 StrongElectron-PhononInteractionsandSelf-TrappingofCarriers... . . . 166
6.6.1 BasicParametersofLargePolaronsandBipolarons . . . . . . . . . 166
6.7 ExperimentalVerifications... . . . . . . . . . . . . . . . . . . . . . . . . 169
6.8 Low-EnergyElectronicStructureoftheDopedCuprates . . . . . . . . . . 170
6.8.1 SpecificCharge OrderingandFormationofDifferentSuperlattices
andIn-GapImpurityBands . . . . . . . . . . . . . . . . . . . . . 171
6.8.2 FormationoftheIn-GapPolaronicandBipolaronicBands . . . . . 173
6.9 Metal-InsulatorTransitionsinCrystalline
andNon-CrystallineSolids . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.10 PossibleMechanismsofMetal . . . . . . . . . . . . . . . . . . . . . . . . 176
6.10.1 TheMott-TypeMetal-InsulatorTransitions . . . . . . . . . . . . . 178
6.10.2 TheAnderson-TypeMetal-InsulatorTransitions . . . . . . . . . . . 180
6.10.3 TheNewMetal-InsulatorTransitions . . . . . . . . . . . . . . . . 181
6.11 TheAgreementoftheTheorywiththeExperiment . . . . . . . . . . . . . 183
7 TheoryofthePseudogapPhenomena,QuantumCriticality... 191
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
7.2 FormationofaLargeTemperature-IndependentNon-PairingPseudogap... 192
7.3 FormationofaSmallTemperature-IndependentPairingPseudogap... . . . 194
7.4 PrecursorBCS-LikePairingofLargePolaronsandFormation... . . . . . . 195
7.5 StripeFormationintheUnderdopedCuprates . . . . . . . . . . . . . . . . 202
7.5.1 TheChargeSegregationandOrderingDuetoInhomogeneousSpa-
tialDistributionofChargeCarriers . . . . . . . . . . . . . . . . . 203
7.5.2 FormationoftheStaticandDynamicStripesDuetotheCompeting
CarrierLocalizationandDelocalization . . . . . . . . . . . . . . . 204
7.6 QuantumCriticallyandPossibleQuantumCriticalPoints . . . . . . . . . . 206
7.6.1 Metal-insulatorCrossoverQuantumCriticalPoint . . . . . . . . . 206
7.6.2 StripeQuantumCriticalPoint . . . . . . . . . . . . . . . . . . . . 207
7.6.3 PseudogapQuantumCriticalPoint . . . . . . . . . . . . . . . . . . 207
7.7 PseudogapandStripeEffectsontheNormalStateProperties... . . . . . . 209
7.7.1 OpticalProperties. . . . . . . . . . . . . . . . . . . . . . . . . . . 209
7.7.2 ThermalProperties . . . . . . . . . . . . . . . . . . . . . . . . . . 219
7.7.3 ElectronicSpecificHeataboveT . . . . . . . . . . . . . . . . . . 220
∗
7.7.4 ElectronicSpecificHeatbelowT . . . . . . . . . . . . . . . . . . 221
∗
viii Contents
7.7.5 UnconventionalIsotopeEffectsonthePseudogapFormation
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
7.8 PseudogapPhenomenainOtherSystems . . . . . . . . . . . . . . . . . . . 230
7.8.1 PseudogapStateinOrganicSuperconductors . . . . . . . . . . . . 230
7.8.2 PossiblePseudogapStatesinHeavy-fermionSystems... . . . . . . 232
7.8.3 PseudogapStateinNuclearMatter . . . . . . . . . . . . . . . . . . 234
8 TheoryofUnconventionalSuperconductivity... 247
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
8.2 BosonizationofCooperPairsinHigh-T Cuprates . . . . . . . . . . . . . . 250
c
8.3 SuperfluidityoftheBCSCondensateofCooperPairs... . . . . . . . . . . 252
8.4 SuperfluidityofCompositeBosonicCooperPairs... . . . . . . . . . . . . 255
8.4.1 GroundStateofaBose-liquid . . . . . . . . . . . . . . . . . . . . 256
8.4.2 ThePairHamiltonianModel . . . . . . . . . . . . . . . . . . . . . 258
8.4.3 ChoiceofthePairInteractionModelPotential. . . . . . . . . . . . 260
8.4.4 Superfluid Single Particle and Pair Condensationin an Interacting
Three-dimensionalBoseGas . . . . . . . . . . . . . . . . . . . . . 260
8.4.5 Superfluid Single Particle and Pair Condensationin an Interacting
Two-dimensionalBose-gas . . . . . . . . . . . . . . . . . . . . . . 267
8.4.6 ConcentrationDependencesoftheSuperfluidTransition
TemperaturesinNonideal3Dand2DBoseGases . . . . . . . . . . 269
8.4.7 SpecificHeatofaSuperfluidBose-liquid . . . . . . . . . . . . . . 273
8.4.8 EntropyofaSFBose-liquid . . . . . . . . . . . . . . . . . . . . . 274
8.4.9 StabilityofAttractiveBoseSystems . . . . . . . . . . . . . . . . . 276
8.5 NovelSuperconductivityofChargedCompositeBosons... . . . . . . . . . 276
8.5.1 Gap-likeFeaturesofBosonicSuperconductor . . . . . . . . . . . . 277
8.5.2 GaplessSuperconductivityandKink-likeBehavior
oftheSuperconductingOrderParameter . . . . . . . . . . . . . . . 280
8.5.3 SpecificHeatandλ-likeSCPhaseTransitioninHigh-T Cuprates . 282
c
8.5.4 IntegerandHalf-integerMagneticFluxQuantizationEffects . . . . 283
8.5.5 LondonPenetrationDepth . . . . . . . . . . . . . . . . . . . . . . 284
8.5.6 CriticalMagneticFields . . . . . . . . . . . . . . . . . . . . . . . 285
8.5.7 CriticalCurrent,SoundVelocityandSuperfluidDensity . . . . . . 289
8.5.8 ElectronicPhaseDiagramofHigh-T CuprateSuperconductors . . 291
c
8.6 BasicPrinciplesofConventionalandUnconventional
Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
8.7 UnconventionalSuperconductivityandSuperfluidity
inOtherSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
8.8 NovelSuperconductivityinOrganicandHeavy-FermionSuperconductors . 294
8.9 Superfluidityof4He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
8.9.1 Superfluidityof3He . . . . . . . . . . . . . . . . . . . . . . . . . 297
8.9.2 SuperfluidityofNuclearMatter . . . . . . . . . . . . . . . . . . . 298
8.9.3 SuperfluidityoftheNeutronStarMatter . . . . . . . . . . . . . . . 300
8.9.4 NucleosynthesisintheEarlyUniverse . . . . . . . . . . . . . . . . 302