Bennemann K.H., Ketterson J.B. Superconductivity: Volume 1: Conventional and Unconventional Superconductors; Volume 2: Novel Superconductors

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Superconductivity

K.H. Bennemann, J.B. Ketterson: Superconductivity

Volume 1: Conventional and Unconventional Superconductors

Volume 2: Novel Superconductors

K.H. Bennemann

J.B. Ketterson

Editors

Superconductivity

Novel Superconductors

Volume 2

123

Professor Dr. K.H. Bennemann

FU Berlin

Department of Physics

Arnimallee 14

14195 Berlin, Germany

e-mail: khb@physik.fu-berlin.de

Professor Dr. John B. Ketterson

Northwestern University

Department of Physics & Astronomy

Sheridan Road 2145

60208-3112 Evanston, USA

e-mail: j-ketterson@nwu.edu

ISBN 978-3-540-73252-5

DOI 10.1007/978-3-540-73253-2

e-ISBN 978-3-540-73253-2

Library of Congress Control Number: 2008926416

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Preface

Superconductivity is a classical problem of physics.

Since the discovery by Kamerlingh–Onnes in 1911

it has undergone tremendous advances in recent

years. Complimentary theoretical and experimen-

tal studies have advanced our understanding of sys-

tems with strong electronic correlations and the as-

sociated superconducting phase transitions. New ex-

perimental techniques and field-theoretical meth-

ods have emerged. The symmetry of the supercon-

ducting order-parameter in certain material classes

seems different from the usual singlet, s-wave form

found in conventional superconductors. There is

strong evidence of a Cooper-pairing mechanism dif-

fering from the conventional one arising from the

electron–phonon interaction. In view of the simulta-

neous occurrence of an enhanced magnetic response

in many novel superconductors (cuprates, ruthen-

ates and heavy-fermion metals), pairing due to ex-

change of spin-excitations has been proposed and

studied.Withthis mechanism,triplet Cooper-pairing

can also occur, inaddition to singlet Cooper-pairing.

This may be the case in Sr

RuO

and heavy-fermion

metals like UPt

Most notable of course was the discovery of high

temperature superconductivity in the cuprates. This

discovery resulted in an enormous activity. Combin-

ing this with the discovery of superconductivity in

other materials such as heavy-Fermion metals,MgB

various organics, fullerenes, magnetic metals under

pressure, and presumably non s-symmetry triplet

Cooper-pairing in ruthenates (Sr

RuO

)wehavean

enrichment of the phenomenon superconductivity.

Many of the new superconductorsare being called

unconventional, either with respect to the pairing

mechanism or the symmetry of the underlying order

parameter. A central problem is the definite iden-

tification of the pairing mechanism. Yet in spite of

the new superconductors continuing studies of con-

ventional electron–phonon based superconductivity

remain interesting.

With the aid of historical hindsight,we expect the

field to continueto advance in unexpected directions.

Nonetheless it is our view that a state-of-the-art trea-

tise on superconductivityis justified at this time,not

only to summarize the present understanding, but

also to introduce newcomers to the field, as was the

case with the two justly-famous 1968 “bibles of su-

perconductivity” by our former colleague R.D. Parks

for an earlier generation. It is hoped that the present

book will help to point the way for future work, re-

search and discoveries.

The treatise starts with a historical introduction

and with the basic phenomenological and micro-

scopic theory of conventional superconductors. This

should be particularly useful for students and be-

ginning researchers. This and the following chap-

ters reﬂect the somewhat refined present state of

the understanding of phonon-mediated supercon-

ductivity. However, many of the results, in partic-

ular the Cooper-pairing theory itself, have much

wider validity. The phenomenological models and

many-body theories are also useful for the study

of other pairing mechanisms. As an example see

the treatise on electron–phonon superconductivity,

studies using Ginzburg–Landau theory and ﬂuc-

tuation phenomena. Note that appropriately gen-

eralized Ginzburg–Landau theories are useful for

analyzing multi-component and competing order

parameters in unconventional superconductors and

for non-equilibrium behavior in general.

VI Preface

Several chapters discuss recent developments of

superconductors containing impurities. Of particu-

lar interest are nanostructured superconductors.The

important interplayof magnetism and superconduc-

tivity is also discussed. Later chapters (see Volume

II) focus on novel superconductors, in particular on

cuprate superconductivity with its almost univer-

sally accepted d-wave symmetry order parameter. A

wide variety of important experimental results on

high superconductivity are described. In particular,

experiments determining the symmetry of the su-

perconducting order-parameter are discussed. The

theory analyses the pairing mechanism, important

properties and in particular vortices in high-T

su-

perconductors. Note that the study of vortex matter

is also of interest for applications. Several chapters

present a theory for cuprate superconductivity as-

suming Cooper-pairing due to the exchange of spin-

excitations. A critical comparison with experiments

is presented. Moreover, superconductivity in vari-

ous novel superconductors like ruthenates, heavy-

Fermions and organics is discussed. Many of the

properties involve an interesting interplay of mag-

netic and superconducting excitations and interac-

tions. The use of neutrons is very important for the

analysis of the elementary excitations and of mag-

netic activity, in particular regarding novel super-

conductors. Still important open problems are dis-

cussed. This should stimulate in particular current

and future research.

The theoretical studies illustrate our present un-

derstanding of novel superconductors and should be

helpful for further theoretical development towards

a general theory that plays the role of the BCS the-

ory in the past. The connections with superﬂuid

He,

the best understood unconventional Fermion super-

ﬂuid, and with Bose–Einstein condensation are also

discussed.

This treatise on superconductivity is a follow up

of the previous books on the physics of supercon-

ductors published a few years ago. Several important

new chapters are presented and most of the other

chapters have been largely rewritten, add new re-

sults and are generally updated. Thus it is hoped that

this book, like Park’s famous books on conventional

superconductors, describe our present more or less

definite knowledge on superconductivity one of the

most interesting problem in physics.

It is hoped that the book will remain useful for a

long time, as was the case with the Parks treatise. A

parallel goal is that the book will be helpful for both

students and researchers.

We wishto thank the authorsfor their careful work

andgreatpatience.Special thanks go to Christof Ben-

nemann for his essential help in preparing the book.

Finally we thank Dr.Ascheron from Springer for his

patience and help during editing.

Berlin, February 2008 K. H. Bennemann and J. B. Ketterson

K.H.Bennemann is Professor of Physics at the Physics Department FUB (Berlin,Germany), Sloan Fellow,and interna-

tionally known for his research on magnetism,superconductivity, and non-equilibrium phenomena.

J.B. Ketterson is Professor of Physics at Northwestern University (Evanston, Ill. USA), internationally known for his

research in the area of Solid State Physics, in particular of Low Temperature Physics, on Helium. Both are Editors of

the well-known books The Physics of Solid and Liquid Helium.

Contents

Volume I. Superconductivity: Conventional and Unconventional Superconductors

ListofContributors .................................................................................... XV

1 History of Superconductivity:Conventional, High-Transition Temperature

and Novel Superconductors

K. H. Bennemann and J. B. Ketterson ............................................................ 3

1.1 Introduction .................................................................................... 3

1.2 NovelSuperconductors.......................................................................... 9

1.3 GranularSuperconductors,MesoscopicSystems,JosephsonJunctions ........................... 18

1.4 Outlook ......................................................................................... 23

References ............................................................................................. 25

2 Phenomenology and Microscopic Theory: Theoretical Foundations

L. Pitaevskii .................................................................................... 27

2.1 Off-Diagonal Long-Range Order and Superﬂuidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.2 Off-Diagonal Long-Range Order in Superconductors . .. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.3 TheLondonEquation ........................................................................... 33

2.4 ThermodynamicsofSuperconductorsinaMagneticField....................................... 35

2.5 TheIntermediateStateofSuperconductors...................................................... 37

2.6 TheGinzburg–LandauTheory .................................................................. 38

2.7 SurfaceEnergyattheBoundaryBetweenNormalandSuperconductingPhases ................. 42

2.8 SuperconductorsoftheSecondKind ............................................................ 45

2.9 QuantizedVortexLines.......................................................................... 46

2.10 Vortex–VortexInteractions...................................................................... 49

2.11 CooperPairing.................................................................................. 52

2.12 EnergySpectrumofaSuperconductor .......................................................... 54

2.13 ThermodynamicPropertiesofSuperconductors ................................................ 57

2.14 ElementsoftheTheoryofGreen’sFunctions .................................................... 62

2.15 Green’sFunctionofaSuperconductor........................................................... 65

2.16 TemperatureGreen’sFunctions.................................................................. 68

2.17 TemperatureGreen’sFunctionsforaSuperconductor............................................ 70

References ............................................................................................. 71

VIII Contents

3 Electron–Phonon Superconductivity

F. Marsiglio and J. P. Carbotte ................................................................... 73

3.1 Introduction .................................................................................... 74

3.2 TheElectron–PhononInteraction:Overview .................................................... 74

3.3 ThePhonons .................................................................................... 92

3.4 TheCriticalTemperatureandtheEnergyGap................................................... 108

3.5 ThermodynamicsandCriticalMagneticFields.................................................. 118

3.6 ResponseFunctions ............................................................................. 122

3.7 Anisotropy and MgB

........................................................................... 139

3.8 Summary........................................................................................ 145

Appendix............................................................................................... 148

References ............................................................................................. 153

4 Coexistence of Singlet Superconductivity and Magnetic Order

in Bulk Magnetic Superconductorsand SF Heterostructures

M. L. Kuli´c and A. I. Buzdin ..................................................................... 163

4.1 Introduction .................................................................................... 164

4.2 FerromagneticSuperconductors................................................................. 169

4.3 AntiferromagneticSuperconductors(AFS) ...................................................... 180

4.4 MagneticSuperconductorsintheMagneticField................................................ 183

4.5 JosephsonEffectwithBulkMagneticSuperconductors .......................................... 188

4.6 Superconductor/FerromagnetHeterostructures ................................................. 189

4.7 Conclusion ...................................................................................... 196

Appendix............................................................................................... 197

References ............................................................................................. 199

5 Theory of SuperconductingAlloys

L. P. Gor’ko v ..................................................................................... 201

5.1 Introduction .................................................................................... 201

5.2 AveragesofGreenFunctionsOverImpurities ................................................... 202

5.3 SuperconductingAlloyswithaSmallGap ....................................................... 208

5.4 ParamagneticAlloysandGaplessSuperconductivity ............................................ 216

5.5 EilenbergerEquations........................................................................... 218

5.6 FinalRemark.................................................................................... 223

References ............................................................................................. 224

6 Impurity Nanostructures and Quantum Interference in Superconductors

D. K. Morr ...................................................................................... 225

6.1 Introduction .................................................................................... 225

6.2 Review: Single Impurity Effects in Conventional and Unconventional Superconductors . . . . . . . . . 228

6.3 Formalism ...................................................................................... 231

6.4 Quantum Interference and Quantum Imaging in s-waveSuperconductors....................... 234

6.5 Quantum Interference Phenomena in d

−y

-waveSuperconductors ............................. 244

6.6 Molecules on the Surface of d

−y

-waveSuperconductors ....................................... 250

6.7 Conclusions ..................................................................................... 253

References ............................................................................................. 256