1 The Phenomenon: Occurrence and Characteristics ............... 1
1.1 Marching Towards Absolute Zero .......................... 1
1.2 Discovery of Superconductivity .......................... 2
1.3 Occurrence of Superconductivity ......................... 3
1.3.1 Elemental Superconductivity ...................... 3
1.3.2 Alloys ........................................... 3
1.3.3 Binary Compounds (A-15 Materials) ................ 3
1.3.4 Heavy Fermion Superconductors .................... 4
1.3.5 Organic Superconductors .......................... 4
1.3.6 C60-Based Superconductors ........................ 6
1.4 The Superconducting State ............................... 7
1.5 Phase Coherence ......................................... 9
1.6 Coherence Length ....................................... 10
1.6.1 Pippard's Equation and Coherence Length ......... 11
1.6.2 The Size of an Electron Pair .................... 12
1.6.3 Analogy Between Long Range Spatial Order in
a Solid and Phase-Order in a Superconductor ..... 13
1.7 Critical Magnetic Field ................................ 13
1.8 Meissner Effect ........................................ 14
1.9 Comparison Between a Superconductor and a Very Good
(or Ideal) Conductor ................................... 15
1.10 Isotope Effect ......................................... 17
1.11 Isotope Effect in HTSCs ................................ 18
1.11.1 Optical Behaviour Study ........................ 18
1.11.2 Elastic and Ultrasonic Studies ................. 18
1.12 The Energy Gap ......................................... 19
1.13 Thermodynamics of Superconductors ...................... 21
1.13.1 Latent Heat of Superconducting Transitions ...... 24
1.13.2 Heat Capacity of Superconductors ................ 24
1.13.3 Strong Coupling Case ............................ 26
1.14 London Equations and Penetration Depth ................. 27
1.15 Ginzberg-Landau Theory ................................. 29
1.16 Type-I and Type-II Superconductors ..................... 32
1.16.1 How a Normal Core is Formed in Mixed State? ..... 35
1.17 Why Materials with High Tc Tend to Fall in Type-II
Category? .............................................. 37
1.18 Why It is Extremely Difficult to Obtain Higher Tc? ..... 38
References ............................................. 39
2 Crystal Structure of High Temperature Superconductors ....... 41
2.1 Introduction ........................................... 41
2.1.1 Perovskite Structure ............................ 41
2.2 The Structure of YBa2Cu3O7-x ............................ 41
2.2.1 Variation of Tc with Oxygen Stoichiometry ....... 43
2.3 The Structure of Lа2-xMxСuO4 ............................ 46
2.4 The Structure of Bi-Based Cuprate Superconductors ...... 46
2.5 Structure of Thallium-Based Cuprate Superconductors .... 48
2.5.1 Comparison of Bismuth and Thallium Based
Cuprates ........................................ 49
2.6 Mercury Based Cuprate Superconductors .................. 51
2.7 Characteristics of High Temperature Superconductors .... 53
2.7.1 Resemblance Between HTSC and Conventional
Superconductors ................................. 54
2.7.2 Unusual Properties of HTSCs ..................... 54
2.8 Fermi Energy and Fermi Velocity of Superconductors ..... 55
2.9 Comparison of High Tc Cuprates with Typical Metals
in Relation to Normal State Resistivity ................ 57
References ............................................. 57
3 Critical Current ............................................ 59
3.1 Introduction ........................................... 59
3.2 Critical Current of a Wire ............................. 60
3.3 Critical Current in Mixed State ........................ 61
3.4 Flux Pinning ........................................... 61
3.4.1 Role of Inhomogeneties .......................... 62
3.4.2 Flux Pinning (Pinning of Flux-Vortices in
Conventional Superconductors) ................... 63
3.5 Depinning of Flux Vortices ............................. 63
3.6 Critical Current in High Temperature Superconductors ... 65
3.6.1 Effect of Structure ............................. 65
3.7 RSJ Model of an HTSC (High Tc Superconductor) .......... 66
3.8 Effect of Granularity on Superconductivity ............. 68
3.9 Measurement for Jc ..................................... 69
3.10 Flux Flow and Defining Jc .............................. 70
3.11 Anisotropies in High Tc Superconductors ................ 71
3.12 Flux Pinning in High Temperature Superconductors ....... 73
3.13 Columnar Defects and Flux Pinning ...................... 74
3.13.1 Flux Pinning in HTSCs by Vortex Pancakes ........ 75
3.14 Experimental Results on Introduction of Flux Pinning
Centers in HTSCs ....................................... 77
3.14.1 Melt Textured Growth ............................ 77
3.14.2 Introduction of Second Phase (Chemical
Inhomogeneity) .................................. 78
3.14.3 Extended Defects (Columnar Defects) ............. 78
3.15 Magnetic Phase Diagrams of HTSCs ....................... 78
3.16 Melting of the FLL Because of Reduced Size of ξGL(T) ... 80
3.16.1 Effect of Reduced Size of ξGL(T) ................ 81
3.17 Kosterlitz-Thouless Berezinski Transition .............. 81
3.18 Anisotropy and Change Over from a 2D to 3D Behaviour ... 82
3.18.1 High Field Regime (B >> Bcr) ................... 83
3.18.2 Weak Field Region (B << Bcr) ................... 83
3.18.3 The Cross-Over Field Bcr ....................... 84
3.19 The Effect of Anisotropy Parameter γ on the Vortex
Phase Transitions ...................................... 84
3.20 Desired Microstructure Synthesis for High Critical
Current Density in High Tc Superconductors ............. 85
3.20.1 Some Inherent Problems (Weak-Links and "Flux
Lattice Melting") ............................... 85
3.20.2 Possible Ways Out of "Weak-Links" ............... 87
3.20.3 Provision of Flux Pinning Sites ................. 91
3.20.4 Desired Microstructure for High Jc .............. 93
3.21 High Tc Technology ..................................... 94
3.21.1 Advantage of Weak Pinning ....................... 95
3.22 Comparison Between Non-Uniform Order
in a Solid and that in a Superconductor ................ 95
References ............................................. 96
4 Synthesis of High Tc Superconductors ........................ 99
4.1 Synthesis of Y1Ba2Cu3O7 in Bulk Form .................... 99
4.2 Why Thin Films of High Tc Superconductors? ............ 100
4.3 Techniques for Thin Film Preparation .................. 101
4.3.1 Chemical Deposition Methods .................... 103
4.3.2 Chemical Vapour Deposition (CVD) ............... 103
4.3.3 Spray Pyrolysis ................................ 103
4.4 Basic Thin film Processes for HTSC Films .............. 104
4.5 Various Techniques for Deposition of Films of High
Temperature Superconductors ........................... 106
4.6 Preparation of Thin Films of HTSC-YBa2Cu307-x:
An Introduction ....................................... 108
4.6.1 Choice of the Substrate for Thin Film
Deposition ..................................... 108
4.6.2 YBCO Film/Substrate Interaction ................ 109
4.7 Techniques Employed for Synthesis of YBCO Thin
Films ................................................. 112
4.7.1 Electron Beam Evaporation ...................... 112
4.7.2 Molecular Beam Epitaxy ......................... 113
4.7.3 Sputter Deposition ............................. 114
4.7.4 Sputter Deposition of HTSC Films ............... 116
4.7.5 Pulsed Laser Deposition ........................ 118
4.7.6 Chemical Vapour Deposition ..................... 119
References ............................................ 120
5 Superconductivity in Cuprates .............................. 123
5.1 Mott Insulator ........................................ 123
5.2 The First Cuprate La2-X МxСuO4 ......................... 123
5.3 The Charge-Transfer Model of a High Tc Cuprate
Superconductor ........................................ 124
5.4 Electron and Hole Doping of СuO2 Layers ............... 125
5.4.1 Source of Hole (Carriers) in Various
Cuprate Families ............................... 126
5.5 The Conductions Plane in Cuprates ..................... 127
5.6 Octahedral Ligand Field ............................... 128
5.7 Jahn-Teller Effect .................................... 128
5.8 Energy levels for Copper .............................. 129
5.9 Comparison of Cu3+ and Cu2+ ions in the Oxide
Octahedron ............................................ 130
5.10 The Hamiltonian and the Relevant Energy Levels
in the Conduction Plane ............................... 130
5.11 Hole Superconductivity in Oxides ...................... 132
5.12 Two Band and One Band Hubbard Models .................. 134
5.13 The Electronic Structure of Cuprates .................. 134
5.14 Strong Electron Correlations .......................... 136
5.15 Charge Density Wave and Spin Density Wave ............. 137
5.16 Variation of Tc with Hole Concentration ............... 138
5.16.1 Role of CuO2 Planes (Effect on Tc) ............. 138
5.17 Defects in Bi Based Superconductors ................... 140
5.18 Effect of Oxygen Stoichiometry on Tc of HTSCs Bi
Based and Tl Based Superconductors .................... 140
5.19 Comparison of Bi- and Tl-Cuprates ..................... 141
5.20 Comparison of Mercury Based and Thallium Monolayer
Based Cuprate Superconductors ......................... 143
5.21 Mercury Based Superconductors ......................... 143
5.22 Mercury Doped Tl:2223 Superconductor .................. 144
References ............................................ 145
6 The Proximity and Josephson Effects ........................ 147
6.1 DC Josephson Effects .................................. 147
6.2 Some Types of Josephson Junctions ..................... 150
6.2.1 Typical Current Voltage Characteristics for
the Above Types of Junctions .................... 152
6.3 Equivalent Circuit of a Josephson Junction ............ 152
6.4 AC Josephson Effect ................................... 153
6.5 Giaever Tunnelling/Tunnelling of Quasi-Particles ...... 155
6.6 Superconductive Tunnelling in a S-I-S Junction ........ 159
6.7 Quasi-Particle Tunnelling for a Symmetric S-I-S
Junction .............................................. 162
6.7.1 Effect of Thickness of Insulator in S-I-S
Junction ....................................... 163
6.8 Properties of Josephson Junction ...................... 163
6.9 Flux Quantisation ..................................... 165
6.10 SQUIDs ................................................ 166
6.11 DC SQUID (A Superconducting Loop with Two Josephson
Junctions) ............................................ 167
6.11.1 The Characteristics of an Ideal DC SQUID ....... 170
6.12 The rf SQUID .......................................... 172
6.12.1 Principle ...................................... 172
6.12.2 Working ........................................ 173
6.13 Applications of SQUIDs ................................ 176
6.14 HTSC SQUIDs ........................................... 176
6.15 Some Practical rf SQUIDs .............................. 177
6.15.1 Break Junction rf SQUIDs ....................... 177
6.15.2 Two-and One-Hole rf SQUIDs ..................... 177
6.16 SQUIDs Fabricated From Films .......................... 178
6.16.1 SQUIDs using Polycrystalline Films ............. 179
6.16.2 SQUIDs using Epitaxial Films ................... 180
6.17 How SQUIDs are Used for Flux Measurements ............. 182
6.17.1 Superconducting Flux Transformers .............. 184
6.18 Design and Noise Aspects of SQUIDs .................... 186
6.18.1 Choice for Critical Current Ic of J.J .......... 186
6.18.2 Choice for the Inductance of the Ring .......... 186
6.18.3 Noise, Noise Energy and Energy Resolution of
SQUID .......................................... 187
6.19 Proximity Effect (Induced Superconductivity) .......... 190
6.19.1 S-I Junction ................................... 192
6.20 S-N Junction .......................................... 192
6.20.1 Fundamental Properties of S-N Contacts ......... 192
6.20.2 Boundary Conditions for Pair Amplitude (F) ..... 193
6.20.3 Effect of a Finite Boundary Resistance ......... 194
6.20.4 (Cuprate-S)/N Interface ........................ 195
6.21 Grain Boundary Junctions .............................. 195
6.22 Requirements for Josephson Devices .................... 197
6.22.2 Test for the ac Josephson Effect ............... 198
References ............................................ 198
7 Theories of Superconductivity .............................. 199
7.1 Microscopic Theory of Superconductivity (The BCS
Theory) ............................................... 200
7.1.1 Qualitative Ideas .............................. 201
7.1.2 The BCS Ground State ........................... 203
7.2 Anderson's Resonating Valence Bond Theory ............. 210
7.2.1 Anderson's Valence Bonds ....................... 210
7.3 Spin-Bag Theory ....................................... 214
7.3.1 Questions Which Remain ......................... 214
References ............................................ 214
8 Application of Superconductivity ........................... 215
8.1 Potential Applications ................................ 215
8.1.1 Superconducting Magnets ........................ 215
8.2 Applications of High-Tc Oxide Superconductors ......... 215
8.3 Applications of High Tc Films ......................... 217
Index ......................................................... 219
|
