A Phase Transition Approach to High Temperature Superconductivity
432 pages, parution le 01/07/2000
Résumé
During the past decade, a great deal of experimental data
has been gathered on the superconductivity of cuprates.
Although the fundamental mechanisms are still unclear, the
authors feel that the overall experimental situation is
cleat enough to present a graduate-level textbook from the
phase transition point of view. They survey and identify
thermal and quantum fluctuation effects, identify material
independent universal properties, and provide constraints
for the microscopic description of the various phenomena.
Brief introductory chapters offer background information on
the theory of thermal and quantum critical phenomena.
Distributed by World Scientific. Annotation c. Book News,
Inc., Portland, OR (booknews.com)
Table of Contents
| Preface | V | |
| 1 | Introduction | 1 |
| 1.1 | Cuprate superconductors | 1 |
| 1.1.1 | Structure | 2 |
| 1.1.2 | Doping | 3 |
| 1.1.3 | Effective mass anisotropy and spatial dimensionality | 7 |
| 1.1.4 | Pseudogap | 10 |
| 1.1.5 | Symmetry of the order parameter | 13 |
| 1.1.6 | Importance of critical fluctuations | 15 |
| 1.2 | Universal critical properties of continuous phase transitions | 18 |
| 1.2.1 | Static critical properties at finite temperature | 18 |
| 1.2.2 | Dynamic critical properties at finite temperature | 23 |
| 1.2.3 | Quantum critical properties | 25 |
| 1.3 | Finite size effect and corrections to scaling | 32 |
| 2 | Ginzburg - Landau phenomenology | 37 |
| 2.1 | London phenomenology | 37 |
| 2.2 | Ginzburg - Landau functional | 46 |
| 2.3 | Mean-field treatment | 48 |
| 2.3.1 | Meissner phase | 49 |
| 2.3.2 | Length scales: London penetration depth and correlation length | 51 |
| 2.3.3 | Classification of superconductors | 55 |
| 2.3.4 | Upper critical field | 57 |
| 2.4 | Flux quantization | 59 |
| 2.5 | London model and first flux penetration field | 61 |
| 2.6 | Effective mass anisotropy | 64 |
| 2.6.1 | 3D anisotropic London model | 67 |
| 3 | Gaussian thermal fluctuations | 73 |
| 3.1 | Gaussian fluctuations around the mean field solution | 73 |
| 3.2 | Gaussian order parameter fluctuations | 74 |
| 3.3 | Gaussian vector potential fluctuations | 79 |
| 3.4 | Relevance of vector potential fluctuations | 80 |
| 3.5 | Helicity modulus | 82 |
| 3.6 | Effective mass anisotropy | 85 |
| 3.7 | Fluctuation induced diamagnetism | 88 |
| 3.7.1 | Isotropic system | 88 |
| 3.7.2 | Effective mass anisotropy | 94 |
| 3.7.3 | Magnetic torque | 96 |
| 4 | Superfluidity and the n-vector model | 99 |
| 4.1 | Ideal Bose gas | 101 |
| 4.2 | Charged Bose gas subjected to a magnetic field | 109 |
| 4.3 | Weakly interacting Bose gas | 111 |
| 4.4 | Hydrodynamic approach | 114 |
| 4.5 | The n-vector model | 118 |
| 5 | Universality and scaling theory of classical critical phenomena at finite temperature | 125 |
| 5.1 | Static critical phenomena in isotropic systems | 125 |
| 5.2 | Superconductors with effective mass anisotropy | 136 |
| 5.3 | Dimensional analysis | 149 |
| 5.3.1 | Static critical properties | 149 |
| 5.3.2 | Classical dynamic critical phenomena | 151 |
| 5.4 | Implications of the universal critical amplitude relations | 153 |
| 6 | Experimental evidence for classical critical behavior | 157 |
| 6.1 | Critical behavior close to optimum doping | 157 |
| 6.1.1 | Specific heat in zero field | 157 |
| 6.1.2 | Temperature dependence of the penetration depth | 169 |
| 6.1.3 | Corrections to scaling | 171 |
| 6.1.4 | Temperature dependence of the diamagnetic susceptibility | 175 |
| 6.1.5 | Scaling of the magnetization | 175 |
| 6.1.6 | Crossing point phenomenon | 177 |
| 6.1.7 | Magnetic torque and universal scaling function | 181 |
| 6.1.8 | Magnetic field tuned phase transitions: Melting transition | 189 |
| 6.1.9 | Magnetic field tuned phase transitions: Superconductor - normal conductor and insulator transitions | 194 |
| 6.1.10 | Evidence for a Kosterlitz - Thouless - Berezinskii transition in thin films | 201 |
| 6.1.11 | Temperature driven 2D to 3D crossover | 206 |
| 6.2 | Doping dependence of the critical behavior | 212 |
| 6.3 | Evidence for dynamic scaling | 219 |
| 6.4 | Vortex glass to vortex fluid transition | 220 |
| 6.5 | The (H,T) phase diagram of extreme type II superconductors emerging from Monte Carlo simulations | 224 |
| 7 | Quantum Phase Transitions | 233 |
| 7.1 | Scaling theory of quantum critical phenomena | 233 |
| 7.2 | Quantum critical phenomena: conventional superconductors | 242 |
| 7.3 | Quantum critical phenomena: cuprate superconductors | 248 |
| 7.3.1 | Doping and disorder tuned superconductor to insulator transition | 248 |
| 7.3.2 | Film thickness tuned superconductor to insulator transition | 256 |
| 7.3.3 | Doping dependence of the chemical potential | 260 |
| 7.3.4 | Magnetic field tuned transition | 261 |
| 7.3.5 | Nature of the non-superconducting phase | 265 |
| 7.3.6 | Superconductor to normal conductor transition | 268 |
| 8 | Implications | 273 |
| 8.1 | Interlayer tunneling model | 273 |
| 8.2 | Symmetry of the order parameter | 276 |
| 8.3 | Suppression of the transition temperature due to dimensional crossover and quantum fluctuations | 277 |
| 8.4 | Pseudogap features | 280 |
| 8.5 | Relationship between low frequency conductivity and zero temperature penetration depth | 284 |
| 8.6 | Doping and pressure dependences of critical amplitudes | 289 |
| 8.7 | Doping dependence of isotope and pressure coefficients | 295 |
| 8.8 | Bose gas approach | 298 |
| 8.9 | Effective pair mass | 299 |
| 8.10 | Emerging phase diagrams | 301 |
| A | Mean field treatment | 309 |
| A.1 | Ising Model | 309 |
| A.2 | XY Model | 315 |
| B | XY model | 319 |
| B.1 | 3D-2D Crossover in the XY model | 319 |
| B.1.1 | 2D-XY model | 320 |
| B.1.2 | 3D-XY model | 324 |
| B.1.3 | Layered XY model | 327 |
| B.1.4 | Anisotropic XY model | 331 |
| B.2 | Superconducting networks and films | 332 |
| B.2.1 | Models | 332 |
| B.2.2 | Uniform superconducting films | 335 |
| C | Quantum phase transitions | 337 |
| C.1 | The harmonic oscillator | 337 |
| C.2 | Large-n limit of a model for distortive phase transitions | 339 |
| C.3 | Onset of superfluidity in the ideal Bose gas | 343 |
| C.4 | Superconductors | 344 |
| D | BCS theory | 351 |
| D.1 | Cooper instability | 351 |
| D.2 | Electron-phonon interaction | 354 |
| D.3 | Ground state in the BCS approximation | 355 |
| D.4 | Thermodynamic properties in the BCS - approximation | 361 |
| D.5 | Simple model | 363 |
| E | Superconducting properties of the attractive Hubbard model | 367 |
| E.1 | BCS--BEC crossover | 367 |
| E.2 | BCS treatment of the attractive Hubbard model | 379 |
| E.3 | Phase diagram of the attractive Hubbard model on a lattice | 388 |
| E.4 | 2D-XY behavior and KT transition in the attractive Hubbard model | 400 |
| References | 411 | |
| Index | 427 |
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Imperial College Press |
| Auteur(s) | Thomas Schneider, J.M Singer |
| Parution | 01/07/2000 |
| Nb. de pages | 432 |
| Format | 16 x 22,4 |
| Couverture | Relié |
| Poids | 711g |
| Intérieur | Noir et Blanc |
| EAN13 | 9781860942419 |
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