Preface ......................................................... v
Acknowledgments ................................................ ix
List of Contributors .......................................... xxi
Credit Lines ................................................ xxiii
1 From Single- to Bipolarons with Jahn-Teller Character
and Metallic Cluster-Stripes in Hole-Doped Cuprates ........ 1
K.A. Müller
1.1 The Original Jahn-Teller Polaron Concept and Its
Shortcomings ............................................... 1
1.2 Recent Experiments Probing Delocalized Properties .......... 2
1.3 Probing of Local Properties ................................ 4
1.4 The Intersite JT-Bipolaron Concept Derived from EXAFS,
EPR, and Neutron Scattering ................................ 5
1.5 Two-Component Scenario ..................................... 7
1.6 JT-Bipolarons as the Elementary Quasiparticles to
Understand the Phase Diagram and Metallic Clusters or
Stripes .................................................... 9
1.7 Substantial Oxygen Isotope Effects ........................ 12
1.8 Concluding Remarks ........................................ 17
Bibliography .............................................. 17
2 Tunneling Measurements of the Cuprate Superconductors ..... 19
J.R. Kirtley and F. Tafuri
2.1 Introduction .............................................. 19
2.2 General Concepts .......................................... 20
2.2.1 Types of Junction Structures ....................... 20
2.2.2 Generalized Junction Conductance ................... 22
2.2.3 The Tunnel and Proximity Effects ................... 22
2.2.4 Andreev Reflection and Bound States ................ 25
2.2.5 The Josephson Effect: General Features ............. 27
Andreev Reflection in SNS Junctions ................ 28
2.3 Means of Preparing Tunnel Junctions ....................... 32
2.3.1 Junctions with Single Crystals ..................... 32
2.3.2 Grain Boundary Junctions ........................... 32
Bicrystal Junctions ................................ 32
Biepitaxial Junctions .............................. 33
Step-Edge Junctions ................................ 34
Electron Beam Junctions ............................ 34
2.3.3 Junctions with Artificial Barriers ................. 35
Noble Metal Barriers ............................... 35
Perovskite and Layered Materials Barriers .......... 36
2.3.4 Interface-Engineered Junctions ..................... 37
2.3.5 Junctions with HTS Rather than YBCO ................ 37
La1.85Sr0.15CuO4-Based Trilayer with
One-Unit-Cell-Thick Barrier ........................ 37
Electron Doped HTS ................................. 38
Ca and Co Doped YBCO: Insights into the Overdoped
Regime ............................................. 38
Ultra-Thin Films and Superlattices ................. 38
Intrinsic Stacked Junctions ........................ 38
2.4 π-Rings and 0 - π-Junctions ................................. 39
2.5 Tunneling Spectroscopy .................................... 44
2.5.1 Superconducting Gap ................................ 44
General Features ................................... 44
Temperature Dependence ............................. 50
Momentum Dependence ................................ 53
Doping Dependence .................................. 57
Macroscopic Quantum Effects ........................ 59
2.5.2 Pseudogap .......................................... 60
Temperature Dependence ............................. 60
Magnetic Field Dependence .......................... 62
2.5.3 Linear Conduction Background ....................... 64
2.5.4 Zero-Bias Anomalies ................................ 65
2.5.5 Atomically Resolved Conductivity Modulation
Effects ............................................ 69
2.5.6 Strong Coupling Effects ............................ 72
Electron-Phonon .................................... 73
Electron-Magnon .................................... 74
2.6 Conclusions ............................................... 75
Bibliography .............................................. 75
3 Angle-Resolved Photoemission Spectroscopy on Electronic
Structure and Electron-Phonon Coupling in Cuprate
Superconductors ........................................... 87
X.J. Zhou, Т. Cuk, T. Devereaux, N. Nagaosa, and
Z.-X. Shen
3.1 Introduction .............................................. 87
3.2 Angle-Resolved Photoemission Spectroscopy ................. 88
3.2.1 Principle .......................................... 88
3.2.2 Technique .......................................... 90
3.3 Electronic Structures of High Temperature
Superconductors ........................................... 95
3.3.1 Basic Crystal Structure and Electronic Structure ... 95
3.3.2 Brief Summary of Some Latest ARPES Results ......... 98
3.4 Electron-Phonon Coupling in High Temperature
Superconductors ........................................... 98
3.4.1 Brief Survey of Electron-Phonon Coupling in High-
Temperature Superconductors ........................ 99
3.4.2 Electron-Phonon Coupling: Theory .................. 102
General ........................................... 102
Weak Coupling - Perturbative and Self-Energy
Description ....................................... 106
Strong Coupling - Polaron ......................... 110
3.4.3 Band Renormalization and Quasiparticle Lifetime
Effects ........................................... 111
El-Ph Coupling Along the (0,0)-(π, π) Nodal
Direction ......................................... 111
Multiple Modes in the Electron Self-Energy ........ 116
El-Ph Coupling Near the (π, 0) Antinodal Region ... 118
Anisotropic El - Ph Coupling ........................ 122
3.4.4 Polaronic Behavior ................................ 124
Polaronic Behavior in Parent Compounds ............ 124
Doping Dependence: From Z~0 Polaron to Finite Z
Quasiparticles .................................... 128
Doping Evolution of Fermi Surface: Nodal-
Antinodal Dichotomy ............................... 130
3.4.5 Electron-Phonon Coupling and High Temperature
Superconductivity ................................. 135
3.5 Summary .................................................. 137
Bibliography ............................................. 138
4 Microwave Electrodynamics of High Temperature
Superconductors .......................................... 145
D.A. Bonn and W.N. Hardy
4.1 Introduction ............................................. 145
4.2 Electrodynamics of Superconductors ....................... 146
4.2.1 London Theory ..................................... 146
4.2.2 Surface Impedance Approximation ................... 147
4.2.3 Non-local Electrodynamics ......................... 151
4.2.4 Excitation Spectrum of a d-Wave Superconductor .... 151
Phenomenological Pairing Model .................... 152
Effect of Impurities .............................. 154
4.3 Experimental Techniques .................................. 156
4.3.1 Penetration Depth Techniques - Single Crystals .... 158
Excluded Volume Techniques ........................ 158
Far Infrared Reflectivity: ǀRǀeiθ ................... 159
Measurement of Internal Field Distribution in
Mixed State ....................................... 160
Zero-Field Gadolinium ESR ......................... 161
4.3.2 Penetration Depth Techniques - Thin Films ......... 161
Low Frequency Mutual Inductance Techniques ........ 161
Thin Film Resonator Techniques .................... 161
Millimetre Wave Transmission ...................... 162
Far-Infrared Reflection ........................... 162
Slow Muon Beam Method ............................. 162
4.3.3 Penetration Depth Techniques - Powders ............ 162
4.4 Measurement of Surface Resistance Rs ..................... 163
4.4.1 Single Crystals ................................... 163
Cavity Perturbation ............................... 163
Broadband Bolometric Spectroscopy ................. 165
Thin Film Methods ................................. 165
4.5 Penetration Depth ........................................ 166
4.5.1 Complementary Roles of I and Rs ................... 166
4.5.2 YBa2Cu306+x ....................................... 167
4.5.3 Penetration Depth Anisotropy in YBa2Cu206+x ........ 170
4.5.4 Oxygen Doping Effects ............................. 171
4.5.5 Other Materials ................................... 174
Bi2Sr2CaCu2O8+δ .................................... 174
Tl2Ba2CaCu2O8 ...................................... 174
Тl2Ва2СuO6+δ ....................................... 174
La1-xSrxCuO4 ....................................... 175
HgBa2Ca2Cu3O8+δ .................................... 175
Electron Doped Thin Films and Single Crystals ..... 175
4.5.6 ĉ-Axis Penetration Depth .......................... 177
4.6 Surface Resistance ....................................... 179
4.6.1 YBa2Cu306+x aVPlane ................................ 180
4.6.2 Disorder and Quasiparticle Damping ................ 185
4.6.3 Other Materials - âb-Plane ........................ 187
4.6.4 Low Temperature Limit ............................. 193
4.6.5 Anisotropy ........................................ 200
4.7 Fluctuations ............................................. 202
Bibliography ............................................. 209
5 Magnetic Resonance Studies of High Temperature
Superconductors .......................................... 215
Charles P. Slichter
5.1 Introduction ............................................. 215
5.2 Basic NMR Theory and Experiment .......................... 216
5.2.1 The Resonance Spectrum ............................ 216
5.2.2 Exciting a Resonance .............................. 217
5.2.3 Spin-Lattice Relaxation ........................... 219
5.2.4 Double Resonance .................................. 220
5.2.5 NMR in Superconductors ............................ 221
5.3 NMR in Normal State Metals ............................... 221
5.4 NMR in Conventional BCS Superconductors .................. 223
5.5 The Cuprate Spin Hamiltonian ............................. 224
5.6 YBCO above Tc ............................................ 226
5.6.1 One or Two Components? ............................ 226
5.6.2 The Spin Pseudogap ................................ 227
5.6.3 The Spin-Lattice Relaxation Time .................. 227
5.6.4 Transverse Relaxation and T2G ..................... 232
5.6.5 Scaling Relationships ............................. 234
5.7 YBCO Below Tc: NMR Evidence About the Pairing State ...... 236
5.7.1 The Knight Shift .................................. 236
5.7.2 Spin-Lattice Relaxation ........................... 239
5.8 LSCO ..................................................... 240
5.8.1 The Spectrum ...................................... 240
5.8.2 One or Two Components ............................. 243
5.8.3 The Incommensurate State .......................... 244
5.8.4 Spatial Modulation ................................ 245
5.8.7 The High Temperature Properties ................... 248
5.8.6 The Low Temperature Properties: Wipeout ........... 248
5.9 Brief Review of EPR ...................................... 252
Bibliography ............................................. 254
6 Neutron Scattering Studies of Antiferromagnetic
Correlations in Cuprates ................................. 257
John M. Tranquada
6.1 Introduction ............................................. 257
6.2 Magnetic Excitations in Hole-Doped Superconductors ....... 259
6.2.1 Dispersion ........................................ 259
6.2.2 Spin Gap and "Resonance" Peak ..................... 262
6.2.3 Discussion ........................................ 263
6.3 Antiferromagnetism in the Parent Insulators .............. 264
6.3.1 Antiferromagnetic Order ........................... 264
6.3.2 Spin Waves ........................................ 267
6.3.3 Spin Dynamics at Г > TN ........................... 271
6.4 Destruction of Antiferromagnetic Order by Hole Doping .... 272
6.5 Stripe Order and Other Competing States .................. 274
6.5.1 Charge and Spin Stripe Order in Nickelates ........ 274
6.5.2 Stripes in Cuprates ............................... 276
6.5.3 Spin-Density-Wave Order in Chromium ............... 279
6.5.4 Other Proposed Types of Competing Order ........... 280
6.6 Variation of Magnetic Correlations with Doping and
Temperature in Cuprates .................................. 280
6.6.1 Magnetic Incommensurability vs. Hole Doping ....... 280
6.6.2 Doping Dependence of Energy Scales ................ 282
6.6.3 Temperature-Dependent Effects ..................... 283
6.7 Effects of Perturbations on Magnetic Correlations ........ 284
6.7.1 Magnetic Field .................................... 284
6.7.2 Zn Substitution ................................... 286
6.7.3 Li-Doping ......................................... 286
6.8 Electron-Doped Cuprates .................................. 286
6.9 Discussion ............................................... 288
6.9.1 Summary of Experimental Trends in Hole-Doped
Cuprates .......................................... 288
6.9.2 Theoretical Interpretations ....................... 289
Bibliography ............................................. 290
7 Optical Conductivity and Spatial Inhomogeneity in Cuprate
Superconductors .......................................... 299
J. Orenstein
7.1 Introduction ............................................. 299
7.1.1 Optical Conductivity of Superconductors ........... 299
7.1.2 Optical Conductivity and the Cuprates ............. 300
7.2 Low Frequency Optical Conductivity in the Cuprates ....... 301
7.2.1 YBCO Single Crystals: Success of the Two-Fluid
Model ............................................. 301
7.2.2 The BSCCO System: Failure of the Two-Fluid
Description ....................................... 303
7.2.3 Additional Examples ............................... 307
7.3 Optical Conductivity vs. Hole Concentration in BSCCO ..... 309
7.3.1 Systematics of the Conductivity Anomaly ........... 309
7.3.2 Quantitative Modeling of а (со, T) ................ 312
7.4 Collective Mode Contribution to Optical Conductivity ..... 314
7.4.1 Origin of the Collective Contribution ............. 314
7.4.2 Optical Conductivity in the Presence of
Inhomogeneity ..................................... 316
7.4.3 Extended Two-Fluid Model .......................... 316
7.4.4 Comparison of Model and Experiment ................ 320
7.5 Summary and Outlook ...................................... 321
7.5.1 Summary ........................................... 321
7.5.2 Outlook and Directions of Future Research ......... 321
Bibliography ............................................. 323
8 What Tc can Teach About Superconductivity ................ 325
Т.H. Geballe and G. Koster
8.1 Introduction ............................................. 325
8.2 Cuprate Superconductivity ................................ 326
8.2.1 Pairing and Tcs in the Cuprates ................... 327
The Cu Ion ............................................... 327
8.3 Interactions Beyond the Cu02 Layers ...................... 328
8.3.1 Pairing Centers in the Charge Reservoir Layer
Cuprates .......................................... 329
8.3.2 Negative-U Center Electronic Pairing in a Model
System ............................................ 330
8.3.3 The Chain-Layer Cuprates .......................... 334
8.3.4 Other Chain Layer Compounds ....................... 338
8.4 Superconductivity Originating in the CuO2 Layers ......... 339
8.5 Summary .................................................. 341
Bibliography ............................................. 341
9 High-Tc Superconductors: Thermodynamic Properties ........ 345
R.A. Fisher, J.E. Gordon, and N.E. Phillips
9.1 Introduction ............................................. 345
9.1.1 Scope and Organization of the Review .............. 345
9.1.2 Cuprate Superconductors: Occurrence; Structures;
Nomenclature; Phase Diagram; Characteristic
Parameters ........................................ 346
9.1.3 Magnetic Properties; Critical-Field Measurements .. 349
9.1.4 Specific-Heat Measurements ........................ 350
Specific Heat: Component Contributions; Field
and Temperature Dependences; Nomenclature ......... 350
Specific Heat: Experimental Techniques ............ 352
Specific Heat: Problems and Uncertainties in
Analysis of Data .................................. 353
9.2 Low-Temperature Specific Heat ............................ 353
9.2.1 Zero-Field "Linear" Term .......................... 354
9.2.2 Evidence for Line Nodes in the Energy Gap ......... 357
9.3 Chemical Substitutions ................................... 360
9.3.1 Rare-Earth Substitutions on the Y and La Sites .... 361
9.3.2 General Effects of Substitutions on the Cu Sites .. 362
9.3.3 Effects of Zn Substitution on the Cu Sites ........ 364
9.4 Stripes .................................................. 367
9.5 Specific-Heat Anomaly at Tc: Fluctuations; BCS
Transition, ВЕС .......................................... 372
9.5.1 Gaussian and Critical Fluctuations ................ 372
Fluctuations: Optimally-Doped Samples in Zero
Field ............................................. 373
Fluctuations: Optimally Doped Samples in Field .... 375
Fluctuations: Under- and Over-Doped Samples ....... 376
9.5.2 BCS to ВЕС ........................................ 376
9.6 Vortex-Lattice Melting ................................... 380
9.6.1 Introduction; Early Measurements on YBCO .......... 380
9.6.2 Other Measurements on YBCO ........................ 381
9.6.3 Measurements on Other HTS ......................... 386
9.7 Calorimetric Evidence for the Pseudogap .................. 386
9.7.1 Determination of the Electron Specific Heat of
YBa2Cu3O6.97 ...................................... 387
9.7.2 Use of the Differential Method to Obtain the
Conduction-Eiectron Specific Heat of YBa2Cu3O6+x
- A Simplified Discussion ........................ 388
9.7.3 Other Specific-Heat Results and Their
Interpretation .................................... 390
Bibliography ............................................. 390
10 Normal State Transport Properties ........................ 399
N.E. Hussey
10.1 Introduction ............................................. 399
10.2 Evolution of the In-Plane Resistivity with Doping ........ 400
10.2.1 Introduction ...................................... 400
10.2.2 Optimally Doped Cuprates .......................... 401
10.2.3 Underdoped Cuprates ............................... 404
10.2.4 Overdoped Cuprates ................................ 406
10.3 The Out-of-Plane Transport ............................... 406
10.3.1 Introduction ...................................... 406
10.3.2 Optimal Doped Cuprates ............................ 407
10.3.3 Underdoped Cuprates ............................... 408
10.3.4 Overdoped Cuprates ................................ 409
10.4 The Anomalous Hall Coefficient and Violation of
Kohler's Rule ............................................ 410
10.4.1 Introduction ...................................... 410
10.4.2 Magnitude of RH ................................... 410
10.4.3 The Inverse Hall Angle cot νH(T) .................. 411
10.4.4 Theoretical Modeling of ρab and RH(T) in
Cuprates .......................................... 412
10.4.5 In-Plane Magnetoresistance ........................ 414
10.5 Impurity Studies ......................................... 416
10.6 Thermal Transport ........................................ 417
10.6.1 Introduction ...................................... 417
10.6.2 Thermoelectric Power .............................. 418
10.6.3 Thermal Conductivity .............................. 418
10.6.4 Nernst-Ettinghausen Effect ........................ 419
10.7 Discussion and Summary .............................. 419
Bibliography ............................................. 422
11 High-Pressure Effects .................................... 427
J.S. Schilling
11.1 Introduction ............................................. 427
11.2 Elemental Superconductors ................................ 430
11.2.1 Simple Metals ..................................... 430
Nonalkali Metals ......................................... 430
Alkali Metals ............................................ 433
11.2.2 Transition Metals ................................. 436
11.3 Binary Superconductors ................................... 437
11.3.1 A-15 Compounds .................................... 437
11.3.2 A Special Case: MgB2 .............................. 438
11.3.3 Doped Fullerenes A3C60 ............................ 439
11.4 Multiatom Superconductors: High-Tc Oxides ................ 442
11.4.1 Nonhydrostatic Pressure Media ..................... 446
11.4.2 Structural Phase Transitions ...................... 446
11.4.3 Oxygen Ordering Effects ........................... 447
11.4.4 Intrinsic Pressure Dependence Tcintr(P) ............ 451
11.4.5 Uniaxial Pressure Results ......................... 453
11.5 Conclusions and Outlook .................................. 455
Bibliography 457
12 Superconductivity in Organic Conductors .................. 463
J.S. Brooks
12.1 Introduction ............................................. 463
12.2 Organic Building Blocks and Electronic Structure ......... 464
12.3 "Conventional" Properties of Organic Superconductors ..... 466
12.4 The "Standard Model" for Metallic, Insulating, and
Antiferromagnetic Ground States .......................... 475
12.4.1 Band Filling and Its Consequences ................. 475
12.4.2 Can Superconductivity Emerge From the "Standard
Model"? ........................................... 479
12.4.3 But What if it is Really Just Phonons? ............ 481
12.5 "Unconventional" Properties of Organic Superconductors ... 481
12.5.1 Q1D Materials and p-Wave Pairing .................. 481
12.5.2 Q2D Materials and d-Wave Pairing .................. 482
12.5.3 Magnetic Field Induced Superconductivity and
Possible FFLO States .............................. 483
12.6 Comparison of High Tc Superconductors with Organic
Conductors ............................................... 486
12.7 Summary and Future Prospects ............................. 488
Bibliography ............................................. 490
13 Numerical Studies of the 2D Hubbard Model ................ 495
D.J. Scalapino
13.1 Introduction ............................................. 495
13.2 Numerical Techniques ..................................... 496
13.2.1 Determinantal Quantum Monte Carlo ................. 497
13.2.2 The Dynamic Cluster Approximation ................. 499
13.2.3 The Density Matrix Renormalization Group .......... 501
13.3 Properties of the 2D Hubbard Model ....................... 503
13.3.1 The Antiferromagnetic Phase ....................... 504
13.3.2 d^ Pairing ........................................ 506
13.3.3 Stripes ........................................... 510
13.3.4 ThePseudogap ...................................... 512
13.4 The Structure of the Effective Pairing Interaction ....... 516
13.5 Conclusions .............................................. 522
Bibliography ............................................. 524
14 t-J Model and the Gauge Theory Description of Underdoped
Cuprates ................................................. 527
Patrick A. Lee
14.1 Introduction ............................................. 527
14.2 Basic Electronic Structure of the Cuprates ............... 528
14.3 Phenomenology of the Underdoped Cuprates ................. 531
14.4 Introduction to RVB and a Simple Explanation of the
Pseudogap ................................................ 534
14.5 Slave-Boson Formulation of t-J Model and Mean Field
Theory ................................................... 536
14.6 U(1) Gauge Theory of the URVB State ...................... 541
14.7 SU(2) Slave-Boson Theory of Doped Mott Insulators ........ 546
14.7.1 SU(2) Slave-Boson Mean-Field Theory at Finite
Doping ............................................ 547
14.7.2 Effect of Gauge Fluctuations: Enhanced (π, π)
spin Fluctuations in Pseudogap Phase .............. 550
14.7.3 σ-Model Effective Theory and New Collective
Modes in the Superconducting State ................ 551
14.7.4 Vortex Structure .................................. 554
14.7.5 Phase Diagram ..................................... 555
14.8 Spin Liquids, Deconfinement, and the Emergence of Gauge
Fields and Fractionalized Particles ...................... 557
14.9 Application of Gauge Theory to the High Tc
Superconductivity Problem ................................ 559
14.9.1 Spin Liquid, Quantum Critical Point, and the
Pseudogap ......................................... 560
14.9.2 Signature of the Spin Liquid ...................... 562
14.10 Summary and Outlook ..................................... 563
Bibliography ............................................ 565
15 How Optimal Inhomogeneity Produces High Temperature
Superconductivity ........................................ 570
Steven A. Kivelson and Eduardo Fradkin
15.1 Why High Temperature Superconductivity is Difficult ...... 570
15.2 Dynamic Inhomogeneity-Induced Pairing Mechanism of HTC ... 572
15.2.1 Pairing in Hubbard Clusters ....................... 573
15.2.2 Spin-Gap Proximity Effect ......................... 574
15.3 Superconductivity in a Striped Hubbard Model: A Case
Study .................................................... 576
15.3.1 Zeroth-Order Solution: Isolated two-Leg Ladders ... 578
15.3.2 Weak Inter-Ladder Interactions .................... 579
15.3.3 Renormalization-Group Analysis and Inter-Ladder
Mean Field Theory ................................. 580
15.3.4 Thex → 0 Limit ................................... 581
15.3.5 Relation to Superconductivity in the Cuprates ..... 582
15.4 Why There is Mesoscale Structure in Doped Mott
Insulators ............................................... 582
15.5 Weak Coupling Vs. Strong Coupling Perspectives ........... 584
15.6 What is so Special About the Cuprates? ................... 585
15.6.1 Is Charge Order, Or Fluctuating Charge Order,
Ubiquitous? ....................................... 585
15.6.2 Does the "Stuff" Between the Cu-O Planes Matter? .. 586
15.6.3 What About Phonons? ............................... 588
15.6.4 What About Magnetism? ............................. 588
15.6.5 Must We Consider Cu-0 Chemistry and the Three-
Band Model? ....................................... 589
15.6.6 Is d-Wave Crucial? ................................ 589
15.6.7 Is Electron Fractionalization Relevant? ........... 590
15.7 Coda: High Temperature Superconductivity is Delicate
But Robust ............................................... 590
Bibliography ............................................. 592
16 Superconducting States on the Border of Itinerant
Electron Magnetism ....................................... 597
Emma Pugh, Siddharth Saxena, and Gilbert Lonzarich
16.1 Introduction ............................................. 597
16.2 Uncharted Territory: The New Frontier .................... 597
16.3 Logarithmic Fermi Liquid ................................. 598
16.4 The Puzzle of MnSi ....................................... 599
16.5 Superconductivity on the Border of Magnetism ............. 600
16.6 Three Dimensional vs. Quasi-Two-Dimensional Structures ... 600
16.7 Density Mediated Superconductivity ....................... 601
16.8 The Search for Superconductivity on the Border of
Itinerant Ferromagnetism ................................. 602
16.9 Why Don't All Nearly Magnetic Materials Show
Superconductivity? ....................................... 605
16.10 From Weak to Strong Coupling ............................ 607
16.11 Superconductivity Without Inversion Symmetry ............ 608
16.12 Quantum Tuning .......................................... 608
16.13 Concluding Remarks ...................................... 611
Bibliography .................................................. 611
Index ......................................................... 615
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