TEXTBOOK ON Superconductivity and Josephson Effect: Physics ...

Table of content
Preface: ......................................................................................................................................... 2
Definitions and abbreviations ....................................................................................................... 7
Lecture-1........................................................................................................................................... 8
1. Introduction............................................................................................................................... 8
1.1. Superconductivity: Historical overview and basic experimental facts............................ 12
1.2. The Meissner effect.......................................................................................................... 18
1.3. Magnetic flux quantization .............................................................................................. 19
1.4. Josephson effect............................................................................................................... 20
1.5 Development of the theory of superconductivity.............................................................. 20
Lecture-2: Magnetic and thermodynamic properties of superconductors ...................................... 25
Type-I and II superconductors.................................................................................................... 25
2.1 Magnetic properties of type-I superconductors ................................................................ 25
2.2 Intermediate state in type- I superconductors ................................................................... 26
2.3 Magnetic properties of type-II superconductors............................................................... 28
Thermodynamics of superconductors ......................................................................................... 29
2.4 Thermodynamic critical field............................................................................................ 30
2.5 Entropy of type-I superconductors.................................................................................... 31
2.6 Specific heat of superconductors ...................................................................................... 32
Problems to Lecture - 2............................................................................................................... 33
Lecture-3......................................................................................................................................... 34
Two-fluid model and linear electrodynamics of superconductors.............................................. 34
3.1 The London equations....................................................................................................... 34
3.2 London penetration depth ................................................................................................. 35
3.3 Quantum generalization of the 2-nd London equation. .................................................... 37
3.4. Magnetic flux quantization in superconductors............................................................... 37
3.5 Application of London equations for calculation of static magnetic field and current
distributions in superconductors ............................................................................................. 38
3.6. The image method for finding field distributions............................................................ 40
3.7. The short-circuit principle................................................................................................ 42
3.8 Free energy in the London model ..................................................................................... 43
Problems to lecture-3 .................................................................................................................. 44
Lecture 4 ......................................................................................................................................... 45
High frequency properties of superconductors........................................................................... 45
4.1 Kinetic inductance ............................................................................................................ 46
4.2. Normal skin effect............................................................................................................ 48
4.3. High frequency conductivity of superconductors............................................................ 48
4.4. Surface impedance........................................................................................................... 50
4.5. Superconducting transmission line .................................................................................. 52
4.6 Nonlocal Electrodynamics of Superconductors................................................................ 55
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Problems to lecture-4 .................................................................................................................. 56
Lecture 5 ......................................................................................................................................... 57
Ginzburg-Landau Theory............................................................................................................ 57
5.1 Landau’s theory of second order phase transition ............................................................ 57
5.2 Ginzburg-Landau formalism in zero magnetic field......................................................... 58
5.3 Ginzburg-Landau free energy density .............................................................................. 60
5.4 Derivation of Ginzburg-Landau (GL) equations .............................................................. 60
5.5 Gauge invariance of GL theory......................................................................................... 62
5.6 Two characteristic lengths ................................................................................................ 63
5.7 The proximity effect ......................................................................................................... 64
5.8 Relation between the microscopic and the Ginzburg-Landau theory............................... 66
5.9 Energy of a Normal metal-Superconductor interface ....................................................... 67
5.10 Critical current of a thin film .......................................................................................... 70
5.11 Critical field of a thin film .............................................................................................. 71
Problems to lecture 5 .................................................................................................................. 73
Lecture 6 ......................................................................................................................................... 75
Microscopic foundations of superconductivity........................................................................... 75
6.1 Electron - Phonon interaction ........................................................................................... 75
6.2 The ground state of a superconductor............................................................................... 76
6.3 Energy of the ground state. ............................................................................................... 79
6.4 Energy gap in the spectrum of elementary excitations ..................................................... 81
6.5. Density of states of elementary excitations ..................................................................... 82
6.6 The coherence length ........................................................................................................ 82
6.7 Temperature dependence of the energy gap ..................................................................... 83
6.8 Persistent currents ............................................................................................................. 84
Problems to Lecture 6 ................................................................................................................. 86
Lecture-7......................................................................................................................................... 87
Vortices in type-II superconductors............................................................................................ 87
7.1 Introduction....................................................................................................................... 87
7.2 Structure of an isolated Abrikosov vortex ........................................................................ 87
7.3 Vortex energy and the lower critical field Hc1.................................................................. 90
7.4 Vortex interaction ............................................................................................................. 91
7.5 The Upper Critical Field ................................................................................................... 92
7.6 Lorentz force..................................................................................................................... 93
7.7 Magnus force .................................................................................................................... 93
7.8 The viscous damping force ............................................................................................... 94
7.9 Flux-flow resistance.......................................................................................................... 96
7.10 The entropy force............................................................................................................ 97
7.11 Surface superconductivity and the third critical field ..................................................... 97
7.12 Reversible Magnetization of a Type-II Superconductor................................................. 98
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