Superconductivity Physics and Applications Kristian Fossheim and Asle Sudbø The Norwegian University of Science and Technology Trondheim, Norway www.com Copyright c 2004 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.uk Visit our Home Page on www.com or www.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.uk, or faxed to (+44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered.
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Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Fossheim, K. (Kristian) Superconductivity : physics and applications / Kristian Fossheim and Asle Sudbo. Includes bibliographical references and index.6 23 – dc22 2004002271 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-84452-3 Typeset in 10.5/13pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Biddles Ltd, King’s Lynn This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.com Contents Preface xi Acknowledgements xiii I BASIC TOPICS 1 1 What is superconductivity? A brief overview 3 1.1 Some introductory, historical remarks 3 1.3 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 2.2 Low-Tc superconductors 27 2.2 Binary alloys and stoichiometric compounds 29 2.1 Polymer and stacked molecular type 31 2.4 Chevrel phase materials 35 2.5 Oxide superconductors before the cuprates 35 2.6 High-Tc cuprate superconductors 37 2.1 The discovery of cuprate superconductors 37 2.2 Composition and structure 40 2.3 Making high Tc materials 41 2.4 Phase diagrams and doping 42 2.5 Some remarks on the original idea which led to the discovery of cuprate superconductors 47 2.6 Thermal fluctuations of the superconducting conden- sate.
A preliminary discussion 48 www.com vi CONTENTS 2.7 Heavy fermion superconductors 52 2.9 Summarizing remarks 55 3 Fermi-liquids and attractive interactions 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 3.1 Two electrons with attractive interaction 66 3.2 Phonon-mediated attractive interactions 71 3.3 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 Tc and the energy gap 87 4.4 Generalized gap equation, s-wave and d-wave gaps 89 4.5 Quasi-particle tunnelling and the gap 94 4.2 The tunnelling principle 95 4.3 Single-particle NIN tunnelling 97 4.4 NIS quasiparticle tunnelling 99 4.5 SIS quasiparticle tunnelling 102 4.6 BCS coherence factors versus quasiparticle-effects: ultrasound and NMR 103 4.2 Transition rates in ultrasound propagation and NMR 104 4.3 Longitudinal ultrasonic attenuation 105 4.5 Nuclear magnetic resonance relaxation below Tc 113 4.7 The Ginzburg–Landau theory 115 4.1 Some remarks on Landau theory 115 4.2 Ginzburg–Landau theory for superconductors 117 4.3 Flux quantization 121 5 Weak Links and Josephson Effects 123 5.1 Weak links, pair tunnelling, and Josephson effects 123 5.2 DC Josephson effect: the Feynman approach 125 5.2 AC Josephson effect 128 5.1 Alternative derivation of the AC Josephson effect 129 5.3 Josephson current in a magnetic field 131 www.com CONTENTS vii 5.4 The SQUID principle 134 5.5 The Ferrell–Prange equation 136 5.6 The critical field Hc1 of a Josephson junction 138 5.7 Josephson vortex dynamics 139 5.8 Josephson plasma in cuprate high-Tc superconductors 140 6 London Approximation to Ginzburg–Landau Theory (|ψ| constant) 141 6.1 The London equation and the penetration depth λL 141 6.1 Early electrodynamics and the London hypothesis 141 6.2 Derivation of the London equation from the free energy 146 6.2 The energy of a single flux line 148 6.1 Energy of a flux line: alternative derivation.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 7.1 Relations between λ, ξ and Hc 174 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 Bc2 182 7.2 Bc2 , ξ , and λ in anisotropic superconductors 184 7.6 Ginzburg–Landau–Abrikosov (GLA) predictions for Bc2 /Bc1 188 7.7 Surface superconductivity and Bc3 190 8 More on the Flux-line System 199 8.1 Elementary pinning forces and simple models 199 8.1 The concept of a pinning force 199 8.2 Pinning force and flux gradient 200 8.2 Critical state and the Bean model 201 www.com viii CONTENTS 8.3 Flux-line dynamics, thermal effects, depinning, creep and flow 204 8.1 TAFF, flow and creep: Definitions 204 8.3 Thermally activated flux creep: Anderson model 206 8.4 Single particle TAFF 207 8.5 FLL elasticity and pinning 208 8.2 Collective creep: inverse power law U (J ) 212 8.4 The vortex solid–liquid transition 215 8.5 Lindemann criterion and melting of a clean flux-line system 218 8.6 Modelling non-linear vortex diffusion 224 8.6 Flux-line entry at Bc1 : thermodynamic and geometric restrictions 228 8.1 The critical field Bc1 228 8.2 The Bean–Livingston barrier 229 8.7 Critical current issues 233 8.1 Critical current in the Meissner state 233 8.2 Depairing critical current 234 8.3 Reduction of Jc at grain boundaries 235 8.4 Relaxation of magnetic moment and the irreversibility line 236 8.5 How can Jc be increased? 242 II ADVANCED TOPICS 247 9 Two-dimensional superconductivity. Vortex-pair unbinding 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 10.2 Lattice formulation of the Ginzburg–Landau theory 282 10.1 Lattice Ginzburg–Landau model in a frozen gauge approximation 284 www.com CONTENTS ix 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 10.7 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 11.2 RSJ – the resistively shunted Josephson junction 318 11.3 Further modelling of the Josephson junction 322 11.4 The autonomous DC SQUID 323 11.5 Simplified model of the DC SQUID 325 11.1 Biomagnetism: neuromagnetic applications 329 11.3 Superconducting electrodynamics in the two-fluid model 333 11.1 Frequency dependent conductivity in the two fluid model 333 11.2 Surface impedance and AC loss 336 11.3 Surface resistance measurement 339 11.4 High-frequency radio technology 341 11.1 Microstrip filters and delay lines 341 11.2 Superconducting high-frequency devices 345 12 Superconducting Wire and Cable Technology 349 12.1 Low-Tc wire and cable 349 12.2 General design considerations 350 12.3 Basic superconductor properties 350 12.4 Design of technical superconductors 353 12.2 High-Tc wire and cable 362 12.1 High-Tc wire and tape 362 12.2 Full-scale high-Tc cable 363 12.3 HTS induction heater 364 12.3 Magnet technology 366 www.com x CONTENTS IV TOPICAL CONTRIBUTIONS 369 13 Topical Contributions 371 13.1 Spin-Triplet superconductivity, by Y.2 π -SQUIDs – realization and properties, by J.3 Doppler effect and the thermal Hall conductivity of quasipar- ticles in d-wave superconductors, by N.4 Nanometer-sized defects responsible for strong flux pinning in NEG123 superconductor at 77 K, by M.5 Hybrid Magnets, by H.6 Magneto-Optical Imaging of Vortex Matter, by T.7 Vortices seen by scanning tunneling spectroscopy, by Oystein Fischer 388 13.8 Resistivity in Vortex State in High-Tc Superconductors, by K.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.
Robert Schrieffer 404 Ivar Giaever 405 Brian D. Alex Müller 410 Alexei A. Ginzburg 413 Pierre-Gilles de Gennes 414 Philip W. Anderson 415 References 417 Author index 423 Subject index 425 www.com 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 aftermath of progress during the last couple of decades, both through the discov- eries of new superconductors, and the ensuing theoretical development.
High-Tc superconductor research since 1986 represents an almost unlimited source of information about superconductivity. This is an advantage in the sense that there 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, to follow the ideas to old heights like in the BCS theory, or to new heights like in the theory of the vortex system in high-Tc cuprates.
Superconductivity is now a far richer subject thanks to the discovery of high-Tc cuprates by Bed- norz and Müller. Suddenly, superconductivity became an arena for the study of critical behaviour in three-dimensional superconductors, an unthinkable sit- uation in the low-Tc era. Our book seeks, among other things, to clarify this 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.