Superconductivity: Physics and Applications

430 Pages·2004·3.488 MB·English

by  Kristian Fossheim, Asle Sudboe

Superconductivity
Physics and Applications
Kristian Fossheim and Asle Sudbø
The Norwegian University of Science and Technology
Trondheim, Norway
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Fossheim,K.(Kristian)
Superconductivity:physicsandapplications/KristianFossheimandAsleSudbo.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN0-470-84452-3(alk.paper)
1. Superconductivity. I.Sudbo,Asle.II.Title.
QC611.92.F672004
(cid:2)
537.623–dc22
2004002271
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Contents
Preface xi
Acknowledgements xiii
I BASIC TOPICS 1
1 What is superconductivity? A brief overview 3
1.1 Some introductory, historical remarks 3
1.2 Resistivity 6
1.3 The Meissner effect: perfect diamagnetism 10
1.4 Type I and type II superconductors 13
1.5 Vortex lines and flux lines 17
1.6 Thermodynamics of the superconducting state 18
1.7 Demagnetization factors and screening 23
2 Superconducting materials 27
2.1 Introductory remarks 27
2.2 Low-T superconductors 27
c
2.2.1 Superconducting elements 27
2.2.2 Binary alloys and stoichiometric compounds 29
2.3 Organic superconductors 31
2.3.1 Polymer and stacked molecular type 31
2.3.2 Fullerene superconductors 34
2.4 Chevrel phase materials 35
2.5 Oxide superconductors before the cuprates 35
2.6 High-T cuprate superconductors 37
c
2.6.1 The discovery of cuprate superconductors 37
2.6.2 Composition and structure 40
2.6.3 Making high T materials 41
c
2.6.4 Phase diagrams and doping 42
2.6.5 Some remarks on the original idea which led to the
discovery of cuprate superconductors 47
2.6.6 Thermal fluctuations of the superconducting conden-
sate. A preliminary discussion 48
vi CONTENTS
2.7 Heavy fermion superconductors 52
2.8 MgB superconductor 53
2
2.9 Summarizing remarks 55
3 Fermi-liquids and attractive interactions 57
3.1 Introduction 57
3.2 The non-interacting electron gas 59
3.3 Interacting electrons, quasiparticles and Fermi-liquids 61
3.4 Instability due to attractive interactions 66
3.4.1 Two electrons with attractive interaction 66
3.4.2 Phonon-mediated attractive interactions 71
3.4.3 Reduction of the effective Hamiltonian 75
4 The superconducting state – an electronic condensate 79
4.1 BCS theory: a magnetic analogue 79
4.2 Derivation of the BCS gap equation 81
4.3 Transition temperature T and the energy gap (cid:1) 87
c
4.4 Generalized gap equation, s-wave and d-wave gaps 89
4.5 Quasi-particle tunnelling and the gap 94
4.5.1 Introductory remarks 94
4.5.2 The tunnelling principle 95
4.5.3 Single-particle NIN tunnelling 97
4.5.4 NIS quasiparticle tunnelling 99
4.5.5 SIS quasiparticle tunnelling 102
4.6 BCS coherence factors versus quasiparticle-effects:
ultrasound and NMR 103
4.6.1 Introductory remarks 103
4.6.2 Transition rates in ultrasound propagation and NMR 104
4.6.3 Longitudinal ultrasonic attenuation 105
4.6.4 Transverse ultrasound 108
4.6.5 Nuclear magnetic resonance relaxation below T 113
c
4.7 The Ginzburg–Landau theory 115
4.7.1 Some remarks on Landau theory 115
4.7.2 Ginzburg–Landau theory for superconductors 117
4.7.3 Flux quantization 121
5 Weak Links and Josephson Effects 123
5.1 Weak links, pair tunnelling, and Josephson effects 123
5.1.1 Introductory remarks 123
5.1.2 DC Josephson effect: the Feynman approach 125
5.2 AC Josephson effect 128
5.2.1 Alternative derivation of the AC Josephson effect 129
5.3 Josephson current in a magnetic field 131
CONTENTS vii
5.4 The SQUID principle 134
5.5 The Ferrell–Prange equation 136
5.6 The critical field H of a Josephson junction 138
c1
5.7 Josephson vortex dynamics 139
5.8 Josephson plasma in cuprate high-T superconductors 140
c
6 London Approximation to Ginzburg–Landau Theory
(|ψ| constant) 141
6.1 The London equation and the penetration depth λ 141
L
6.1.1 Early electrodynamics and the London hypothesis 141
6.1.2 Derivation of the London equation
from the free energy 146
6.2 The energy of a single flux line 148
6.2.1 Energy of a flux line: alternative derivation.
An exercise 151
6.3 Interacting flux lines: the energy of an arbitrary flux
line lattice 154
6.4 Self energy of a single straight flux line
in the London approximation 160
6.5 Interaction between two parallel flux lines 162
6.6 Interaction between two flux lines at angle α 164
6.7 General flux-line lattice elastic matrix
in the London approximation 166
7 Applications of Ginzburg–Landau Theory
(|ψ| spatially varying) 171
7.1 The temperature-dependent order parameter |ψ(T)| 171
7.2 The coherence length ξ 172
7.2.1 Relations between λ, ξ and H 174
c
7.3 Two types of superconductors 175
7.4 The structure of the vortex core 180
7.5 The length ξ and the upper critical field B 182
c2
7.5.1 Isotropic systems 182
7.5.2 B ,ξ, and λ in anisotropic superconductors 184
c2
7.6 Ginzburg–Landau–Abrikosov (GLA) predictions for B /B 188
c2 c1
7.7 Surface superconductivity and B 190
c3
8 More on the Flux-line System 199
8.1 Elementary pinning forces and simple models 199
8.1.1 The concept of a pinning force 199
8.1.2 Pinning force and flux gradient 200
8.2 Critical state and the Bean model 201
viii CONTENTS
8.3 Flux-line dynamics, thermal effects, depinning, creep
and flow 204
8.3.1 TAFF, flow and creep: Definitions 204
8.3.2 Flux flow 205
8.3.3 Thermally activated flux creep: Anderson model 206
8.4 Single particle TAFF 207
8.5 FLL elasticity and pinning 208
8.5.1 Collective effects 208
8.5.2 Collective creep: inverse power law U(J) 212
8.5.3 Logarithmic U(J) 213
8.5.4 The vortex solid–liquid transition 215
8.5.5 Lindemann criterion and melting of a clean flux-line
system 218
8.5.6 Modelling non-linear vortex diffusion 224
8.6 Flux-line entry at B : thermodynamic and geometric
c1
restrictions 228
8.6.1 The critical field B 228
c1
8.6.2 The Bean–Livingston barrier 229
8.6.3 Geometric barriers 232
8.7 Critical current issues 233
8.7.1 Critical current in the Meissner state 233
8.7.2 Depairing critical current 234
8.7.3 Reduction of J at grain boundaries 235
c
8.7.4 Relaxation of magnetic moment
and the irreversibility line 236
8.7.5 How can J be increased? 242
c
II ADVANCED TOPICS 247
9 Two-dimensional superconductivity. Vortex-pair unbinding 249
9.1 Introduction 249
9.2 Ginzburg–Landau description 250
9.3 Critical fluctuations in two-dimensional superfluids 251
9.4 Vortex–antivortex pairs 255
9.5 Mapping to the 2D Coulomb gas 257
9.6 Vortex-pair unbinding and Kosterlitz–Thouless transition 264
9.7 Jump in superfluid density 271
10 Dual description of the superconducting phase transition 279
10.1 Introduction 279
10.2 Lattice formulation of the Ginzburg–Landau theory 282
10.2.1 Lattice Ginzburg–Landau model in a frozen gauge
approximation 284
CONTENTS ix
10.3 Preliminary results 286
10.4 Vortex-loops as topological defects of the order parameter 289
10.5 Superconductor–superfluid duality in d =3 295
10.6 Zero-field vortex-loop blowout 298
10.6.1 Definitions 299
10.7 Fractal dimension of a vortex-loop tangle 306
10.8 Type I versus type II, briefly revisited 309
III SELECTED APPLICATIONS 315
11 Small scale applications 317
11.1 More JJ-junction and SQUID basics 318
11.1.1 Introductory remarks 318
11.1.2 RSJ – the resistively shunted Josephson junction 318
11.1.3 Further modelling of the Josephson junction 322
11.1.4 The autonomous DC SQUID 323
11.1.5 Simplified model of the DC SQUID 325
11.2 SQUID applications 329
11.2.1 Biomagnetism: neuromagnetic applications 329
11.3 Superconducting electrodynamics in the two-fluid model 333
11.3.1 Frequency dependent conductivity
in the two fluid model 333
11.3.2 Surface impedance and AC loss 336
11.3.3 Surface resistance measurement 339
11.4 High-frequency radio technology 341
11.4.1 Microstrip filters and delay lines 341
11.4.2 Superconducting high-frequency devices 345
12 Superconducting Wire and Cable Technology 349
12.1 Low-T wire and cable 349
c
12.1.1 Introductory remarks 349
12.1.2 General design considerations 350
12.1.3 Basic superconductor properties 350
12.1.4 Design of technical superconductors 353
12.1.5 Stabilization 355
12.1.6 AC losses 358
12.1.7 Mechanical characteristics 359
12.1.8 Fabrication technology 359
12.2 High-T wire and cable 362
c
12.2.1 High-T wire and tape 362
c
12.2.2 Full-scale high-T cable 363
c
12.2.3 HTS induction heater 364
12.3 Magnet technology 366
x CONTENTS
IV TOPICAL CONTRIBUTIONS 369
13 Topical Contributions 371
13.1 Spin-Triplet superconductivity, by Y. Maeno 371
13.2 π-SQUIDs – realization and properties, by J. Mannhart 374
13.3 Doppler effect and the thermal Hall conductivity of quasipar-
ticles in d-wave superconductors, by N.P. Ong 376
13.4 Nanometer-sized defects responsible for strong flux pinningin
NEG123 superconductor at 77K, by M. Muralidhar and M.
Murakami 378
13.5 Hybrid Magnets, by H. Schneider-Muntau 380
13.6 Magneto-Optical Imaging of Vortex Matter, by T.H. Johansen 385
13.7 Vortices seen by scanning tunneling spectroscopy, by Oystein
Fischer 388
13.8 Resistivity in Vortex State in High-T Superconductors, by K.
c
Kadowaki 392
13.9 Coated conductors: a developing application of high tempera-
ture superconductivity, by James R. Thompson, and David K.
Christen 395
References Chapter 13 397
V HISTORICAL NOTES 399
14 Historical notes on superconductivity: the Nobel laureates 401
Heike Kamerlingh Onnes 401
John Bardeen 402
Leon N. Cooper 403
J. Robert Schrieffer 404
Ivar Giaever 405
Brian D. Josephson 407
J. George Bednorz 408
K. Alex Mu¨ller 410
Alexei A. Abrikosov 411
Vitaly L. Ginzburg 413
Pierre-Gilles de Gennes 414
Philip W. Anderson 415
References 417
Author index 423
Subject index 425
Preface
Writing this textbook was motivated by the opinion of the authors that the
time has come for an updated look at the basics of superconductivity in the
aftermathofprogressduringthelastcoupleofdecades,boththroughthediscov-
eries of new superconductors, andtheensuing theoretical development. High-T
c
superconductor research since 1986 represents an almost unlimited source of
informationaboutsuperconductivity.Thisisanadvantageinthesensethatthere
is ample material with which to fill new books, but a disadvantage in the sense
that only a very small fraction of all the efforts that were made, and the results
that came out, can be discussed here. In this sense the situation is entirely new:
The older texts, like those of de Gennes and Tinkham could discuss or refer to
almost all aspects of superconductivity of importance in the 1960s and 1970s.
With tens of thousands of papers published after 1986, there is no possibility
to take such an approach any more. We apologize to the numerous researchers
in the field whose work we could not mention. This situation leaves it even
more to the taste of the authors to choose. First and foremost we have wanted
to review the basics of superconductivity to new students in the field. Secondly,
we wanted to allow those who take a serious interest in the subject at the PhD
level,tofollowtheideastooldheightslikeintheBCStheory,ortonewheights
like in the theory of the vortex system in high-T cuprates. Superconductivity
c
is now a far richer subject thanks to the discovery of high-T cuprates by Bed-
c
norz and Mu¨ller. Suddenly, superconductivity became an arena for the study
of critical behaviour in three-dimensional superconductors, an unthinkable sit-
uation in the low-T era. Our book seeks, among other things, to clarify this
c
new aspect of superconductivity. In addition, we wanted to respect the wish
of students to learn where physics meets the real life of applications. We have
concentrated the material here to the central topics, basically how to describe
and exploit the properties of Josephson junctions on the small scale, and on the
large scale to give some insight into the makings of wires and cables. A special
feature of this book is the inclusion of a chapter containing Topical Contribu-
tionsfromdistinguishedscientistsinvariousareasofsuperconductivityresearch
and development, from the smallest to the largest scale. Each of these scientists
were invited to contribute their leading edge knowledge to give a clear idea of
xii PREFACE
the state of the art in several important sub-fields as of September 2003 when
the writing of this book came to a conclusion.
Kristian Fossheim
National High Magnetic Field Laboratory, Tallahassee,
Florida and The Norwegian University of Science
and Technology Trondheim, Norway
Asle Sudbø
The Norwegian University of Science and Technology
Trondheim, Norway