Superconductivity (eBook)
XVI, 390 Seiten
Springer-Verlag
978-3-319-50527-5 (ISBN)
This book proposes a thorough introduction for a varied audience. The reader will master London theory and the Pippard equations, and go on to understand type I and type II superconductors (their thermodynamics, magnetic properties, vortex dynamics, current transport...), Cooper pairs and the results of BCS theory. By studying coherence and flux quantization he or she will be lead to the Josephson effect which, with the SQUID, is a good example of the applications. The reader can make up for any gaps in his knowledge with the use of the appendices, follow the logic behind each model, and assimilate completely the underlying concepts. Approximately 250 illustrations help in developing a thorough understanding.
This volume is aimed towards masters and doctoral students, as well as advanced undergraduates, teachers and researchers at all levels coming from a broad range of subjects (chemistry, physics, mechanical and electrical engineering, materials science...). Engineers working in industry will have a useful introduction to other more applied or specialized material.
Philippe Mangin is emeritus professor of physics at Mines Nancy Graduate School of Science, Engineering and Management of the University of Lorraine, and researcher at the Jean Lamour Institute in France. He is the former director of both the French neutron scattering facility, Léon Brillouin Laboratory in Orsay, and the Material Physics Laboratory in Nancy, and has taught superconductivity to a broad audience, in particular to engineering students.
Rémi Kahn is a retired senior research scientist of the French Alternative Energies and Atomic Energy Commission (CEA-Saclay). He worked at the Léon Brillouin Laboratory and was in charge of the experimental areas of INB 101 (the Orphée research reactor).
This work responded to the need to bring an accessible account suitable for a wide spectrum of scientists and engineers.
Philippe Mangin, now Emeritus Professor, is the author of 130 papers in solid state physics: amorphous materials, thin films, magnetism, neutron scattering, rare earths.
He directed during four years the 'Laboratoire de Physique des Matériaux' of Nancy and for four other years the 'Laboratoire Leon Brillouin' in Saclay, which is the French neutron scattering facility. He spent two 'one-year-periods' at the National Institute of Sciences and Technology in Gaithersburg MD (USA), became a member of various committees in the neutron scattering field, and a reviewer for many papers (PRL, PRB, etc.).
Rémi Kahn, expert in neutron scattering, worked in the bosom of the 'Laboratoire Léon Brillouin' for many years; he became the leader of the inelastic scattering group, then was in charge of the support groups and finally deputy-director responsible for the Orphée reactor's experimental areas. He authored around 100 papers in various solid state physics fields: phonons, magnetic critical transitions, vortex in superconductors, molecular dynamics in liquid and ad(ab)sorbed phases.
Philippe Mangin, now Emeritus Professor, is the author of 130 papers in solid state physics: amorphous materials, thin films, magnetism, neutron scattering, rare earths. He directed during four years the “Laboratoire de Physique des Matériaux” of Nancy and for four other years the “Laboratoire Leon Brillouin” in Saclay, which is the French neutron scattering facility. He spent two “one-year-periods” at the National Institute of Sciences and Technology in Gaithersburg MD (USA), became a member of various committees in the neutron scattering field, and a reviewer for many papers (PRL, PRB, etc.). Rémi Kahn, expert in neutron scattering, worked in the bosom of the “Laboratoire Léon Brillouin” for many years; he became the leader of the inelastic scattering group, then was in charge of the support groups and finally deputy-director responsible for the Orphée reactor’s experimental areas. He authored around 100 papers in various solid state physics fields: phonons, magnetic critical transitions, vortex in superconductors, molecular dynamics in liquid and ad(ab)sorbed phases.
PREFACE 6
CONTENTS 8
1INTRODUCTION 18
1.1 - A history of women and men 18
1.2 - Experimental signs of superconductivity 18
1.2.1 - The discovery of superconductivity: the critical temperature 18
1.2.2 - The magnetic behavior of superconductors 20
1.2.3 - Critical current 20
1.2.4 - The isotope effect 21
1.2.5 - JOSEPHSON currents and fluxquantization 21
1.3 - Phenomenological models 22
1.3.1 - LONDON theory 22
1.3.2 - The thermodynamic approach 23
1.3.3 - GINZBURG-LANDAU 23
1.3.4 - Vortices 24
1.4 - The microscopic BCS theory 25
1.5 - Tunnelling effects 26
1.6 - A great diversity of superconducting materials 26
1.7 - “Unconventional” superconductors 27
1.8 - Numerous spectacular applications 28
1.9 - Superconductivity in the history of mankind 29
2LONDON THEORY 30
2.1 - MAXWELL’s equations 30
2.2 - The behavior expected for a perfect conductor 31
2.2.1 - Electrical conduction in a normal conductor 31
2.2.2 - Electrical conduction in a perfect conductor 32
2.2.3 - Magnetic fields in a perfect conductor 33
2.3 - Superconductor versus perfect conductor 36
2.3.1 - Cooling in zero field followed by application of a field 36
2.3.2 - Application of the magnetic field when T > Tc followed by cooling in the field
2.4 - The LONDON equations 39
2.4.1 - “Superconducting electrons” 39
2.4.2 - First LONDON equation 39
2.4.3 - Second LONDON equation 40
2.4.4 - Superconducting slab in an applied magnetic field 40
2.5 - The LONDON penetration depth 42
2.5.1 - Experimental measurement of ? L 42
2.5.2 - Temperature dependence of the LONDON penetration depth 43
2.6 - Applications to superconducting wires 43
2.6.1 - A wire in magnetic field 43
2.6.2 - A current-carrying wire 46
2.6.3 - Thin current-carrying wire 47
2.6.4 - Generalized response of the wire 47
2.7 - The OCHSENFELD experiment 48
2.8 - Non-simply-connected superconductor 49
2.8.1 - Sequence 1: cooling in zero field 50
2.8.2 - Sequence 2: field cooling 50
2.8.3 - Conclusion 51
2.9 - Analysis from the point of view of energy 51
2.9.1 - Energetic interpretation of the LONDON penetration depth 51
2.9.2 - The second LONDON equation by a variational method 52
2.10 - Description of superconductivity in fluid-mechanical terms 54
2.11 - The LONDON moment 55
2.11.1 - Intuitive approach 55
2.11.2 - Calculating the LONDON moment 56
2.12 - The LONDON equation in the LONDON gauge 58
2.12.1 - The concept of gauge 58
2.12.2 - The LONDON gauge 59
2.12.3 - The second LONDON equation in the LONDON gauge 60
2.12.4 - Momentum p and the LONDON equation 60
2.12.5 - Non-simply-connected superconductors 61
3THE NON-LOCAL PIPPARD EQUATIONS 66
3.1 - Origin of the non-local equations 66
3.2 - Non-locality in pure superconductors 67
3.3 - Penetration depth of the magnetic field 68
3.4 - FOURIER analysis of the PIPPARD equations 69
3.5 - “Dirty” superconductors 72
4THERMODYNAMICS OF TYPE I SUPERCONDUCTORS 75
4.1 - Thermodynamic description 76
4.2 - The thermodynamic variables of superconductivity 77
4.2.1 - The relation between LONDON currents and magnetization 77
4.2.2 - Thermodynamic systems 78
4.2.3 - Interpreting the levitation of type I superconductors 80
4.3 - Thermodynamic functions of superconductivity 81
4.4 - Thermodynamic data 82
4.4.1 - Equations of state 83
4.4.2 - Specific heat 83
4.4.3 - Phase diagram - The critical field line 85
4.5 - The transition between superconducting and normal states 86
4.5.1 - Free enthalpy of condensation 86
4.5.2 - Relation between the specific heat and the slope of the transition line 88
4.5.3 - Latent heat of transformation 90
4.5.4 - Order of the phase transitions 91
Appendix 4 93
Magnetic media 93
A4.1 - Fields in magnetized materials The equivalence magnetization - distribution of AMPÈRE currents 93
A4.2 - Work performed in the magnetization of matter 100
5THE INTERMEDIATE STATE OF TYPE I SUPERCONDUCTORS 102
5.1 - Criteria for the occurrence of a S/N transition 102
5.2 - S/N transition of an infinite cylinder 103
5.3 - Transition in small samples 104
5.3.1 - Thin slab 104
5.3.2 - Thin wire 105
5.4 - Effects of sample shape 106
5.4.1 - Reminder of relevant results in magnetism 106
5.4.2 - Application to superconductors 106
5.5 - Intermediate state for a sphere 108
5.5.1 - First approach 108
5.5.2 - More realistic structures 110
5.6 - Intermediate state of a thin plate 112
5.6.1 - Laminar model 112
5.6.2 - Energy balance 113
5.6.3 - Structure of the intermediate state of the plate 115
5.7 - Avoiding confusion 116
5.8 - Wire carrying a current (model of the intermediate state) 117
5.8.1 - Formulation of the problem 117
5.8.2 - Model for the intermediate state 119
5.8.3 - A thin wire 121
5.9 - Critical current of a wire in a magnetic field 121
5.9.1 - General case 121
5.9.2 - Magnetic field applied parallel to the axis of the wire 122
5.9.3 - Magnetic field applied perpendicular to the axis of the wire 123
6TYPE II SUPERCONDUCTORS 125
6.1 - Two types of magnetic behavior 125
6.1.1 - The emergence of type II superconductors 125
6.1.2 - Magnetic behavior of type II superconductors 126
6.1.3 - Classification of superconducting materials 127
6.2 - Surface magnetic free enthalpy 128
6.2.1 - Surface magnetic free enthalpy density 128
6.2.2 - A first step toward vortices 130
6.3 - Surface free enthalpy of condensation 132
6.3.1 - Coherence length 132
6.3.2 - Geometric interpretation of the coherence length 132
6.3.3 - Surface free enthalpy density of condensation 134
6.4 - Total surface free enthalpy 134
6.5 - Vortices and type II superconductors 135
6.5.1 - Description of a vortex 135
6.5.2 - Stability of vortices 137
6.5.3 - Quantization of the flux carried by a vortex 139
6.5.4 - Results of “GLAG” theory 140
6.6 - Vortex lattice 141
6.6.1 - ABRIKOSOV lattice 141
6.6.2 - Imaging vortex lattices 143
6.7 - Critical field 145
6.8 - Elements of the structure and dynamics of vortices 146
6.8.1 - Penetration of vortices 147
6.8.2 - Phase diagrams of vortices 148
6.9 - Electric transport in type II superconductors 150
6.9.1 - The problem of type II superconductors 150
6.9.2 - Distribution of the current density 150
6.9.3 - Critical current density 151
6.10 - Levitation in the presence of vortices 152
6.11 - A few illustrations of the diverse behavior of vortices 153
6.11.1 - Effect of the demagnetizing field 154
6.11.2 - Crystal growth by transported current 154
6.11.3 - Repulsion by surfaces 155
6.11.4 - Trapping vortex lines by depressions in thin films 156
6.11.5 - Effects of confinement 156
7FIELDS AND CURRENTS IN TYPE II SUPERCONDUCTORS MODELS OF THE CRITICAL STATE 160
7.1 - Forces acting on vortices 160
7.1.1 - Force exerted on a vortex by a transported current 161
7.1.2 - Interaction forces between vortices 161
7.2 - Energy dissipation by vortex displacement 163
7.2.1 - Model of vortex flow 163
7.2.2 - Induced electric field 164
7.2.3 - The BARDEEN-STEPHEN model 165
7.3 - Critical current density in type II superconductors 165
7.3.1 - Pinning force 165
7.3.2 - Critical current density 166
7.3.3 - Return to the flux-flow resistivity 166
7.3.4 - Vortex jumps 168
7.3.5 - Vortex flux creep 168
7.3.6 - Other behavior 169
7.4 - Models of the critical state 169
7.4.1 - Critical state 169
7.4.2 - Laws of behavior 170
7.5 - The BEAN model 171
7.5.1 - Increasing field: vortex penetration 171
7.5.2 - Decreasing field: field profile and the vortex distribution 173
7.5.3 - Rules for the profile of magnetic field and current density (in planar geometry) 174
7.6 - Magnetization of a type II superconducting plate 175
7.6.1 - Geometry and magnetization 175
7.6.2 - Initial magnetization curve (BEAN model) 176
7.6.3 - Hysteresis loop in the BEAN model 178
7.6.4 - Hysteresis loop in the KIM-JI model 179
7.7 - Magnetization in cylindrical geometry (BEAN model) 181
7.7.1 - Magnetization of a solid cylinder 181
7.7.2 - Magnetization of a thick-walled tube 183
7.8 - Experimental evidence for critical states 184
7.9 - Current transport in the SHUBNIKOV phase 186
7.9.1 - Current transport in the absence of applied magnetic field 186
7.9.2 - Current transport in an applied magnetic field 189
Appendix 7A 191
Different aspects of the “LORENTZ force” 191
A7A.1 - Introduction 191
A7A.2 - LORENTZ force 192
A7A.3 - LONDON force 192
A7A.4 - MAGNUS force 195
A7A.5 - Conclusions 197
Appendix 7B 198
Energy dissipated by a moving vortexThe BARDEEN-STEPHEN model 198
A7B.1 - Construction of the argument 198
A7B.2 - Current density 198
A7B.3 - Exterior electric field 198
A7B.4 - Charge density at the core surface 199
A7B.5 - Internal field 200
A7B.6 - Dissipated power and flux-flow resistivity 200
8COOPER PAIRS PRINCIPAL RESULTS OF BCS THEORY 202
8.1 - Free electron gas 202
8.1.1 - Free electron gas at 0 K 202
8.2 - Interacting electron gas 206
8.2.1 - Wave functions of two independent particles 206
8.2.2 - Interaction potential 207
8.2.3 - Interaction mediated by phonons 208
8.3 - The reference system 210
8.3.1 - One particle system 210
8.3.2 - Systems of pairs 214
8.4 - COOPER pairs 216
8.4.1 - The accessible pair states 216
8.4.2 - Redefinition of the zero of energy 217
8.4.3 - Bound state of the COOPER pair at 0 K 217
8.4.4 - Wave function, occupation probability 219
8.4.5 - Spatial extent of a COOPER pair 220
8.5 - Elements of BCS theory 220
8.5.1 - Collection of COOPER pairs 220
8.5.2 - Ground state 221
8.5.3 - Quasiparticles 223
8.6 - Consequences of the energy structure 225
8.6.1 - Critical temperature 225
8.6.2 - Nature of the superconducting gap 228
8.6.3 - Coherence length 228
8.6.4 - Critical field - Free enthalpy of condensation 229
8.6.5 - Electronic specific heat 230
8.6.6 - Critical current density 231
8.7 - Superconducting electrons and the LONDON penetration depth 235
Appendix 8 237
Matrix elements for the interaction potential between particles 237
9COHERENCE AND THE FLUX QUANTUM 238
9.1 - Current density and the LONDON equation 238
9.2 - Phase of the wave function 239
9. 3 - Flux quantization 240
9.3.1 - The fluxon 240
9.3.2 - Simply connected superconductor 241
9.3.3 - Multiply connected superconductor 242
9.3.4 - Experimental proof of the existence of COOPER pairs 242
9.4 - Back to gauges 244
9.4.1 - The second LONDON equation 244
9.4.2 - Simply connected superconductor 244
9.4.3 - Multiply connected superconductor 245
9. 5 - Flux quantization: application to vortices 245
9.5.1 - Fluxon carried by a single vortex 245
9.5.2 - Fluxon in the ABRIKOSOV lattice 246
9.5.3 - A confined vortex 247
9.5.4 - Current density around a vortex core 248
9.6 - Generalized LONDON equation in the presence of vortices 249
9.7 - Return to the LONDON moment 249
Appendix 9 251
Generalized momentum 251
A9.1 - Lagrangian and Hamiltonian mechanics 251
A9.2 - The passage to quantum mechanics 252
A9.3 - Gauges 253
10THE JOSEPHSON EFFECT 255
10.1 - JOSEPHSON equations in an SIS junction 255
10.1.1 - The ionized hydrogen molecule 256
10.1.2 - Transfer between superconducting blocks 256
10.2 - The d.c. JOSEPHSON effect 257
10.2.1 - The JOSEPHSON current 257
10.2.2 - Critical intensity of the JOSEPHSON current 259
10.3 - The a.c. JOSEPHSON effect 260
10.3.1 - The JOSEPHSON frequency 260
10.3.2 - Application: definition of the standard volt 260
10.4 - “Current-voltage” characteristics of an SIS JOSEPHSON junction 261
10.4.1 - Voltage-biased JOSEPHSON junction 261
10.4.2 - The RCSJ model 262
10.4.3 - Equations for the current-biased RCSJ system 263
10.4.4 - Mechanical analogy to the RCSJ model 264
10.4.5 - Characteristic frequencies 266
10.4.6 - Comparison of the response of the mechanical systems and RCSJ “biased” by a torque G or an intensity I 266
10.4.7 - Over-damped regime 268
10.4.8 - Graphical representations 270
10.4.9 - Weak and intermediate damping 272
10.4.10 - Some examples of SIS junctions 273
10.5 - Energy stocked in a JOSEPHSON junction (SIS) 274
10.6 - JOSEPHSON junction subject to an electromagnetic wave 275
10.6.1 - Resonance effects 275
10.6.2 - SHAPIRO steps 276
10.7 - SNS junctions 278
10.7.1 - Proximity effect, the ASLAMAZOV-LARKIN model 278
10.7.2 - JOSEPHSON current via the ANDREEV levels 279
10.7.3 - Examples of SNS junctions 283
10.7.4 - Signature of the JOSEPHSON effect 285
10.8 - ? -type JOSEPHSON junctions 285
10.8.1 - Definition and energy 285
10.8.2 - Families of JOSEPHSON ? junctions 287
10.8.3 - SFS junctions: mechanisms of ? junctions 288
10.9 - JOSEPHSON junction: a system with many states 291
10.9.1 - Electron on a chain of atoms 291
10.9.2 - Generalization 293
10.9.3 - Application to the JOSEPHSON effect 293
10.9.4 - A general property of BOSE-EINSTEIN condensates 296
Solution of the coupling equations 297
Appendix 10B 298
JOSEPHSON junction in the over-damped regime 298
Appendix 10C 300
JOSEPHSON junction subject to an alternating voltage 300
11SUPERCONDUCTING QUANTUM INTERFERENCE DEVICE ‘‘SQUID” 301
11.1 - Nature of the SQUID current 301
11.2 - rf-SQUID with vanishing inductance 304
11.2.1 - Single junction non-inductive rf-SQUID 304
11.2.2 - Non-inductive rf-SQUID with two junctions 305
11.3 - Inductive rf-SQUID 307
11.3.1 - Magnetic phase change and the external field flux 307
11.3.2 - Operation of the inductive rf-SQUID 309
11.4 - rf-SQUID with 311
junction 311
11.5 - Inductive single junction SQUID: energetic approach 312
11.6 - rf-SQUID with two JOSEPHSON junctions of different types 315
11.6.1 - 0-p rf-SQUID with zero inductance 315
11.6.2 - 0-p rf-SQUID of significant inductance 316
11.7 - Reading an rf-SQUID 318
11.8 - DC-SQUID (SQUID polarized by Direct Current) 318
11.8.1 - Principle of the DC-SQUID 318
11.8.2 - DC-SQUID in the over-damped regime 321
11.8.3 - Reading a DC-SQUID 321
11.8.4 - 0-p DC- SQUID 322
12JOSEPHSON JUNCTIONS IN A MAGNETIC FIELD 324
12.1 - Magnetic field on a short JOSEPHSON junction 325
12.2 - Current in a short JOSEPHSON junction under a magnetic field 326
12.3 - Short 0-?? junction in a magnetic field 332
12.4 - Introduction to the JOSEPHSON penetration depth 335
12.4.1 - General equations 335
12.4.2 - Behavior in very weak fields 336
12.5 - Long JOSEPHSON junction in a high magnetic field 339
12.5.1 - Mechanical analogy 339
12.5.2 - Special movements of the pendulum 341
12.5.3 - Long JOSEPHSON junction in the MEISSNER regime 344
12.5.4 - Long junction in the vortex regime 346
12.5.5 - Isolated JOSEPHSON vortex 348
12.6 - Current transport in a long JOSEPHSON junction 350
12.6.1 - Long junction carrying a current 350
12.6.2 - Long JOSEPHSON current subject to a magnetic field and carrying a current 352
12.7 - Half fluxon at the 0-? connectionof a hybrid JOSEPHSON junction 354
Appendix 12 357
Phase slip between the superconducting blockswithin an infinite 0-? junction 357
A12.1 - The equations governing the junction 357
A12.2 - Boundary conditions 357
A12.3 - Profile of the phase difference 358
NOTATION 360
General rules 360
SOME WORKS OF REFERENCE* 366
INDEX 368
| Erscheint lt. Verlag | 20.12.2016 |
|---|---|
| Zusatzinfo | XVI, 379 p. 241 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie |
| Technik ► Maschinenbau | |
| Schlagworte | high Tc superconductors • Levitation in Magnetic Fields • Meissner effect • Quantum Critical Behavior • Quantum Criticality • Superconductivity Book • Superconductor Quantum Interference Device • Type II Superconductors • Zero Electrical Resistance |
| ISBN-10 | 3-319-50527-0 / 3319505270 |
| ISBN-13 | 978-3-319-50527-5 / 9783319505275 |
| Haben Sie eine Frage zum Produkt? |
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