Introduction to Superconductivity

251 Pages·1978·3.36 MB·English

by  A.C. Rose-Innes (Eds.)

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PATTERN OF INDIVIDUAL FLUXONS IN A TYPE-II SUPERCONDUCTOR
This photograp h shows the triangular pattern of fluxons in a type-II superconducto r
(see Chapter 12). The pattern is revealed by allowing very small (500 A) ferromagneti c
particles to settle on the surface of a magnetized specimen (lead—indium alloy). The
particles locate themselves where the magnetic flux intersects the surface. The photo-
graph was obtained by electron microscopy of the deposited particles. (Photograp h by
courtesy of V. Essmann and H. Trauble, Max Plank Institut fur Metallforschung. )
INTRODUCTIO N TO
SUPERCONDUCTIVIT Y
BY
A. C. ROSE-INNES
Professor of Physics and Electrical Engineering
AND
Å. H. RHODERICK
Professor of Solid-State Electronics
University of Manchester Institute of Science and Technology
U.K.
SECON D EDITIO N
PERGAMON
U.K. Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington,
Oxford OX5 1GB, England
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JAPAN Elsevier Science Japan, Tsunashima Building Annex,
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Tokyo 113, Japan
Copyright © 1978 Pergamon Press pic
The cover illustration is reproduced with permission from J. I. Castro
and A. Lopez, Symmetries of Superconductor Micronetworks, Solid
State Commun. 82, 787 (1992).
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,
electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise,
without permission in writingfrom the publishers.
First edition 1969
Reprinted with corrections 1976
Second edition 1978
Reprinted 1980,1986,1988 (twice)
Reprinted with corrections 1994
Library of Congress Cataloging in Publication Data
Rose-Innes, Alistair Christopher.
Introduction to superconductivity.
(International series in solid state physics; v.6)
Includes index
I. Superconductivity. I. Rhoderick, Å. H., joint author.
II. Title.
QC612.S8R6 1977 573.6'23 77-4811
ISBN 0-08-021651-X Hardcover
ISBN 0-08-021652-8 Flexicover
Printed in Great Britain by BPC Wheatons, Exeter
PREFACE TO THE SECOND EDITION
THIS edition differs from the first edition chiefly in Chapter 11, which
has been almost completely rewritten to give a more physically-based
picture of the effects arising from the long-range coherence of the
electron-waves in superconductors and the operation of quantum inter-
ference devices. We are very grateful to Dr. J. Lowell for reading and
commenting on the draft of this rewritten chapter. There are a number
of other relatively minor changes throughout the book which we hope
will improve the presentation.
We must also thank Dr Lucjan Sniadower for pointing out a number
of errors, Miss Dorothy Denton for typing the manuscript of this second
edition, and Nicholas Rose-Innes for help in checking the manuscript
and proofs.
Uç iversity ofManchester Å. Ç. R.
Institute of Science and Technology A. C. R. -I.
December 1976
NOTE ON THE REVISED SECOND EDITION
IN this revised second edition we have made some further modifications
to the text and added a short extra chapter dealing with 'high-tempera-
ture' superconductors. A vast amount of research has been carried out on
these since their discovery in 1986 but the results, both theoretical and
experimental, have often been contradictory, and seven years later there
remains little understanding of their behaviour. We have therefore been
very selective and have included only material which we are confident
will have permanent validity.
We are grateful to Dr Geoffrey Ross for comments on the draft of
Chapter 14.
E.H.R.
May 1993 A.C.R.-I.
ix
PREFACE TO THE SECOND EDITION
THIS edition differs from the first edition chiefly in Chapter 11, which
has been almost completely rewritten to give a more physically-based
picture of the effects arising from the long-range coherence of the
electron-waves in superconductors and the operation of quantum inter-
ference devices. We are very grateful to Dr. J. Lowell for reading and
commenting on the draft of this rewritten chapter. There are a number
of other relatively minor changes throughout the book which we hope
will improve the presentation.
We must also thank Dr Lucjan Sniadower for pointing out a number
of errors, Miss Dorothy Denton for typing the manuscript of this second
edition, and Nicholas Rose-Innes for help in checking the manuscript
and proofs.
Uç iversity ofManchester Å. Ç. R.
Institute of Science and Technology A. C. R. -I.
December 1976
NOTE ON THE REVISED SECOND EDITION
IN this revised second edition we have made some further modifications
to the text and added a short extra chapter dealing with 'high-tempera-
ture' superconductors. A vast amount of research has been carried out on
these since their discovery in 1986 but the results, both theoretical and
experimental, have often been contradictory, and seven years later there
remains little understanding of their behaviour. We have therefore been
very selective and have included only material which we are confident
will have permanent validity.
We are grateful to Dr Geoffrey Ross for comments on the draft of
Chapter 14.
E.H.R.
May 1993 A.C.R.-I.
ix
PREFACE TO T HE F I R ST E D I T I ON
THIS book is based to a large extent on lectures we have given to
undergraduate and first-year postgraduate students. We intend that it
should indeed be an introduction to superconductivity and have selected
and presented our material with this in mind. We do not intend the con-
tents to be read as a definitive and exhaustive treatment of superconduc-
tivity; several such texts are already published and it has not been our
intention to compete with these. Rather our object has been to explain as
clearly as possible the basic phenomena and concepts of superconduct-
ivity in a manner which will be understood by those with no previous
knowledge of superconductivity and only a modest acquaintance with
solid-state physics.
In this book we have concentrated on the physics of superconductivity
and, though we occasionally mention applications, we have not treated
these in any detail. We hope, nevertheless, that this book will be useful
both to "pure" physicists and to those interested in practical
applications. With this in mind, we have used the rationalized MKS
system throughout. Many of those interested in practical applications
will be engineers brought up on the MKS system and, furthermore,
MKS units are increasingly used in physics teaching. It seemed to us
that someone should take the plunge and write a book on superconduc-
tivity using the MKS system. The MKS approach has involved us in
some thought about the meaning of  and Ç in superconductors, a point
which is discussed in Appendix A.
We have, of course, drawn on other texts on the subject and, in par-
ticular, we have made frequent use of Shoenberg's classic monograph
Superconductivity. Because our book is an introduction, we have not
attempted to include a complete list of references, but have referred to
some of the key papers where this seemed appropriate.
We are grateful to Professor G. Rickayzen and to Mr. Ê . E. Osborne
for discussing the contents of Chapter 9 and 11, and to those authors
who allowed us to use the original copies of figures from their
xi
xii PREFACE
publications. We must also thank Mrs. Shirley Breen, who typed the
manuscript and who, like Maxwell's daemon, made order where none
was before. Our wives and children deserve gratitude for their
forebearance during the time this book was being written.
University of Manchester E.H.R.
Institute of Science and Technology A.C.R.-I.
July 1968
SYMBOLS
THROUGHOUT this book there is employed, as far as possible, a
consistent set of symbols. The following list includes definitions of most
of the symbols used.
a half-thickness of a slab
"i coefficient of wavefunction 0(p/t, —p/ 0 in pair wavefunction
A magnetic vector potential, defined by  = curl A
si area
 magnetic flux density
B flux density of applied magnetic field (§ 2.1)
0
B critical flux density ( = ìïÇ )
c €
c specific heat of normal phase
n
C specific heat of superconducting phase
s
electronic contribution to specific heat
lattice contribution to specific heat
Qatt
d thickness of a plate
e electronic charge
Å energy or electric field strength
E energy gap of superconductor ( = 2Ä)
g
gn Gibbs free energy per unit volume of normal phase
gs Gibbs free energy per unit volume of superconducting phase
G Gibbs free energy of specimen in normal state
n
G Gibbs free energy of specimen in superconducting state
s
ç Planck's constant -5- 2ð
hi probability that pair state (p/t, —p/i) is occupied in BCS
ground state
Ç magnetic field strength
H applied magnetic field strength (see p. 16)
a
H field strength inside specimen or field strength due to transport
t
current
H thermodynamic critical magnetic field strength
c
xiii
XIV SYMBOLS
H' enhanced critical magnetic field of a thin specimen
c
H critical magnetic field strength at 0°K
0
H lower critical field of type-II superconductor
cl
H upper critical field of type-II superconductor
c2
i current
i critical current
c
i supercurrent, current of electron-pairs
s
J magnetization (magnetic moment per unit volume) or current
J current or current per unit width
j surface current density per unit length
J volume current density per unit area (= magnitude of current
density vector J )
J critical current density
c
J current density due to normal electrons
n
J current density due to superconducting electrons
s
k Boltzmann's constant or effective susceptibility of plate [eqn.
(8.4)]
l electron mean free-path in normal state
e
L self-inductance or latent heat
m electronic mass or number of turns/unit length of solenoid
Ì mutual inductance or total magnetic moment of specimen
ç demagnetizing factor [defined by eqn. (6.2)] or any integer
n density of superelectrons
s
Jr (å) density of states for electrons with kinetic energy å
p momentum of an electron or pressure
p Fermi momentum [ = ^(2ôçåñ)]
F
Ñ total momentum of a Cooper pair
q electric charge or momentum of a phonon
R resistance of specimen in normal state
n
R' flow resistance of a type-II superconductor in the mixed state
s entropy density or velocity of sound
T transition temperature in zero field (or critical temperature)
c
u internal energy per unit volume
v velocity of superelectrons
s
V volume or matrix element of scattering interaction or voltage
difference
W kinetic energy
x thickness of normal lamina in intermediate state
n
x thickness of superconducting lamina in intermediate state
s
a surface energy per unit area or a parameter = ôç/ì çâ2 (Chap. 3)
¼ 5