Mourachkine A. Room-Temperature Superconductivity

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x ROOM-TEMPERATURE SUPERCONDUCTIVITY

4.2 The Meissner effect 42

4.3 Flux quantization 42

4.4 The Josephson effects 45

4.5 Energy gap in the excitation spectrum 50

4.6 Thermodynamic properties 55

4.7 Proximity effect 59

4.8 Isotope effect 61

4.9 Type-II superconductors: Properties of the mixed state 62

4.10 Suppression of the superconducting state 69

5 Universal theory of the superconducting state 71

3. SUPERCONDUCTING MATERIALS 81

1 First group of superconducting materials 82

2 Second group of superconducting materials 83

2.1 A-15 superconductors 83

2.2 Metal oxide Ba

1−x

BiO

2.3 Magnesium diboride MgB

2.4 Binary compounds 88

2.5 Semiconductors 90

3 Third group of superconducting materials 90

3.1 Chevrel phases 91

3.2 Copper oxides 94

3.3 Charge transfer organics 104

3.4 Fullerides 109

3.5 Graphite intercalation compounds 113

3.6 Polymers 115

3.7 Carbon nanotubes and DNA 116

3.8 Heavy-fermion systems 117

3.9 Nickel borocarbides 121

3.10 Strontium ruthenate 122

3.11 Ruthenocuprates 123

3.12 MgCNi

124

3.13 Cd

125

3.14 Hydrides and deuterides 126

3.15 Oxides 127

4. PRINCIPLES OF SUPERCONDUCTIVITY 129

1 First principle of superconductivity 129

2 Second principle of superconductivity 131

Contents xi

3 Third principle of superconductivity 134

4 Fourth principle of superconductivity 135

5 Proximity-induced superconductivity 137

5. FIRST GROUP OF SUPERCONDUCTORS: MECHANISM

OF SUPERCONDUCTIVITY 141

1 Introduction 141

2 Interaction of electrons through the lattice 142

3 Main results of the BCS theory 146

3.1 Instability of the Fermi surface 146

3.2 Electron-electron attraction via phonons 148

3.3 The ground state of a superconductor 149

3.4 Energy gap 152

3.5 Density of states of elementary excitations 154

3.6 Critical temperature 155

3.7 Condensation energy 156

3.8 Coherence length 157

3.9 Speciﬁc-heat jump 158

3.10 The BCS and Ginzburg-Landau theory 158

4 Extensions of the BCS theory 159

4.1 Critical temperature 159

4.2 Strength of the electron-phonon interaction 160

4.3 Tunneling 161

4.4 Effect of impurities on

162

4.5 High-frequency residual losses 163

6. THIRD GROUP OF SUPERCONDUCTORS: MECHANISM

OF SUPERCONDUCTIVITY 165

1 Systems with strongly-correlated electrons 166

2 General description of the mechanism 167

3 Detailed description of the mechanism 169

3.1 Structural phase transitions 169

3.2 Phase separation and the charge distribution into the

CuO

planes 172

3.3 The striped phase 177

3.4 Phase diagram 180

3.5 Pseudogap 184

3.6 Soliton-like excitations on charge stripes 188

3.7 Cooper pairs 196

xii ROOM-TEMPERATURE SUPERCONDUCTIVITY

3.8 Phonons 207

3.9 Mechanism of phase coherence along the

c axis 210

3.10 Energy gaps

∆

and ∆

224

3.11 Quantum critical point and the condensation energy 229

3.12 Effective mass anisotropy 229

3.13 Penetration depth 230

3.14 Critical ﬁelds and current 230

3.15 Coherence length and the size of a Cooper pair 232

3.16 Resistivity and the effect of the magnetic ﬁeld 234

3.17 Crystal structure and

236

3.18 Effect of impurities 238

3.19 Chains in YBCO 239

3.20 Superconductivity in electron-doped cuprates 239

3.21 Superconductivity in alkali-doped C

240

3.22 Future theory 242

3.23 Two remarks 242

3.24 Tunneling in unconventional superconductors 243

7. SECONDGROUP OFSUPERCONDUCTORS: MECHANISM

OF SUPERCONDUCTIVITY 247

1 General description of the mechanism 247

1.1 Effect of isotope substitution on

249

1.2 Effect of impurities on

249

1.3 Magnetic-ﬁeld effect on resistivity 249

2 MgB

250

8. COOPER PAIRS AT ROOM TEMPERATURE 253

1 Mechanism of electron pairing at room temperature 254

1.1 Electrons versus holes 254

2 Selection process by Nature 254

2.1 Solitons and bisolitons in the living matter 255

3 Cooper pairs above room temperature 256

3.1 Pairing energy in a room-temperature superconductor 257

3.2 Pairing energy in the case

 450 K 259

4 Summary 259

9. PHASE COHERENCE AT ROOM TEMPERATURE 261

1 Mechanisms of phase coherence 261

1.1 The Josephson coupling 262

1.2 Spin ﬂuctuations 263

Contents

xiii

1.3 Other mechanisms of phase coherence 263

2 The magnetic mechanism 263

2.1 Antiferromagnetic or ferromagnetic? 264

2.2 Requirements to magnetic materials 264

2.3 Coherence energy gap 265

and the density of charge carriers 267

4 Transition temperature interval 269

10. ROOM-TEMPERATURE SUPERCONDUCTORS 271

1 Superconducting materials: Analysis 272

2 Requirements for high-T

materials 274

2.1 Electron pairing 275

2.2 Phase coherence 275

2.3 Structure 276

2.4 Materials 276

3 Three basic approaches to the problem 277

4 The ﬁrst approach 278

4.1 Materials for electron pairing 278

4.2 Materials for phase coherence 292

4.3 Materials containing water 294

5 The second approach 296

6 The third approach 297

7 Electrical contacts 300

References 303

Index

307

Preface

In spite of the fact that it is Nature’s “oversight,” superconductivity is a re-

markable phenomenon. Personally, I am fascinated by it. Superconductivity,

indeed, was a major scientiﬁc mystery for a large part of the last century: dis-

covered in 1911 by the Dutch physicist H. Kamerlingh Onnes and his assistant

Gilles Holst, it was completely understood only in 1957. Generally speaking,

superconductivity is a low-temperature phenomenon. As a result, it is com-

monly believed that it cannot occur at room temperature, T ∼ 300 K.

The main purpose of the book is twofold. First, to show that, under suitable

conditions, superconductivity can occur above room temperature. Second, to

present general guidelines how to synthesize a room-temperature supercon-

ductor. The principal point of this book is that, in order to synthesize a room-

temperature superconductor, we may use some of Nature’s experience (see the

prologue to the book).

The book is organized as follows. The ﬁrst seven chapters of the book

present an overview of the basic properties of the superconducting state and

the mechanisms of superconductivity in various compounds. Chapter 1 is a

historical review of major events related to the phenomenon of superconduc-

tivity. Chapter 2 gives an overview of the basic properties of the supercon-

ducting state. In all textbooks on superconductivity, the description of the su-

perconducting state is based on the Bardeen-Cooper-Schrieffer (BCS) theory,

assuming that the BCS model is the only possible mechanism of superconduc-

tivity (in fact, this is not the case). Contrary to this old tradition, Chapter 2

reviews the superconducting state independently of any speciﬁc mechanism.

Chapter 3 gives an overview of superconducting materials. The next chapter,

Chapter 4, presents the main principles of superconductivity as a phenomenon,

valid for every superconductor independently of its characteristic properties.

In various materials, the underlying mechanisms of superconductivity can be

different, but these principles must be satisﬁed. The following three chapters,

Chapters 5–7, describe the mechanisms of superconductivity in various com-

xvi ROOM-TEMPERATURE SUPERCONDUCTIVITY

pounds. The main purpose of Chapter 5 is to discuss the BCS mechanism of

superconductivity characteristic for conventional superconductors. Chapter 6

reviews the mechanism of unconventional superconductivity. The mechanism

of half-conventional superconductivityis discussed in Chapter 7. Thus, the ﬁrst

seven chapters make an introduction into the physics of the superconducting

state and superconducting materials and, therefore, can be used by students.

The last three chapters of the book are mainly addressed to specialists in ma-

terials science and in the ﬁeld of superconductivity. In Chapter 8, it is shown

that the Cooper pairs exist above room temperature in organic materials. The

main purpose of Chapter 9 is to discuss the onset of long-phase coherence in

a room-temperature superconductor. The chief aim of Chapter 10 is to con-

sider materials able to superconduct above room temperature. In the context

of practical application, Chapter 10 is the most important in the book. The

principal ideas of the last three chapters are based exclusively on experimen-

tal facts accumulated at the time of writing. Personally, I have no doubts that

in 2011 superconductivity will celebrate its 100

jubilee having a transition

temperature above 300 K. I hope that the present book will make a valuable

contribution to this event.

A few words about the history of this book: writing my ﬁrst book entitled

“High-Temperature Superconductivity in Cuprates: The Nonlinear Mechanism

and Tunneling Measurements,” I could add to the existing 12 chapters of the

book one chapter more. The title of this additional chapter would be similar to

the title of this book. However, I have decided to drop the additional chapter

and to realize this project by myself, even if it will take a few years to syn-

thesize a room-temperature superconductor. Unfortunately, I did not have a

possibility to start the project locally (still in Brussels). Then, I have proposed

this project to a few laboratories: I have sent a few e-mail messages. To my

surprise, I did not receive even one reply. This is how scientiﬁc relationships

function in our society: n ot even a simple “thank you for your proposal.”

In addition to a certain “culture” of relations among scientists, the disbelief

mentioned above, namely, that superconductivity cannot occur at room tem-

perature, was deﬁnitely the second reason why I did not get a reply. “Well,”

I said to myself, “Then I have no choice—if I cannot realize this project by

myself, I will write a new book about how to synthesize a room-temperature

superconductor.” This is it; the story is very short. In fact, some readers can

even thank these “nice” people to whom I have sent the proposal; otherwise,

this book would not exist.

I thank three professors of physics J. W. Turner, J. Wickens and D. Johnson,

and the publisher V. Riecansky for correcting English.

Andrei Mourachkine

Cambridge/Brussels, August 2003

Chapter 1

INTRODUCTION

What Nature created at the Big Bang—the spin of the electron—she later tried to “get

rid" of in the living matter.

—From Ref. [19]

1. What is the superconducting state?

The exact deﬁnition of the superconducting state will be given in the follow-

ing chapter. Here we discuss a bird’s-eye view of the superconducting state.

First, one question: would you be able to notice the difference in taste be-

tween two glasses of your preferred drink—soft or hard, whatever—in one of

which a 10

−4

part, i.e. 0.01%, is replaced by another drink? I do not think so.

However, it is not the case for a superconductor (not literally, of course).

In some metals for example, the superconducting state occurs due to the

presence of a 10

−4

fraction of “abnormal” electrons, while the other 99.99%

free (conduction) electrons remain absolutely normal. The correlated behav-

ior of the small fraction of these “abnormal” electrons overwhelms the rest.

Amazing, is it not? Due to the presence of these “abnormal” electrons, the

metal is no longer a metal but a superconductor, losing its ability to resist to a

small-magnitude electrical current. The presence of normal (conduction) elec-

trons is completely masked by that of the “abnormal” electrons, as if the normal

electrons were not existing at all. (Of course, we talk only about electron trans-

port properties of a metal; the crystal structure of a metal is almost unchanged

below the critical temperature, i.e. when a metal becomes superconducting.)

What is even more interesting is that Nature had no intention at all to create

the superconducting state. Superconductivity is rather Nature’s oversight—it

2 ROOM-TEMPERATURE SUPERCONDUCTIVITY

is an instability,ananomaly. What does the superconducting state literally

mean? In the superconducting state, THERE IS NO FRICTION. In the real

world, what does it mean? If friction were absent, Earth would be ideally

round, no buildings, no clothes, and I am afraid that the living matter, including

us, would not exist at all. Deﬁnitely, it was not Nature’s intention. Humans

however, after the discovery of the superconducting state, try to derive a good

dealofbeneﬁt from use of its peculiar properties.

Nevertheless, the superconducting state is a state of matter,evenifitisan

instability, and in this book we shall discuss its characteristic properties. As

any state of matter, superconductivity is not a property of isolated atoms, but

is a collective effect determined by the structure of the whole sample.

The superconducting state is a quantum state occurring on a macroscopic

scale. In a sense, the superconducting state is a “bridge” between the mi-

croworld and the macroworld. This “bridge” allows us to study the physics

of the microworld directly. This is one of the reasons why superconductiv-

ity, driven only by a 10

−4

fraction of “abnormal” electrons, has attracted the

attention of so many scientists since its discovery in 1911 (thus, more than

90 years of intensive research!). Between 1911 and 1957, many best minds

tried to unravel the mystery of this state caused only by 0.01 % of conduction

electrons.

How do normal electrons in a superconductor become “abnormal”? At the

Big Bang, Nature has created two types of elementary particles: bosons and

fermions. Bosons have an integral spin, while fermions a half-integral spin. As

a consequence, bosons and fermions conform to different statistics. Electrons

are fermions with a spin of 1/2 and obey the Fermi-Dirac statistics. In a super-

conductor, two electrons can form a pair which is already a boson with zero

spin (or a spin equal to 1). These electron pairs conform to the Bose-Einstein

statistics and, being in a phase, can move in a crystal without friction. This

is how, in a classical superconductor, a tiny fraction 0.01 % of all conduction

electrons becomes “abnormal.” Simple, is it not?

2. A brief historical introduction

The history of superconductivity as a phenomenon is very rich, consist-

ing of many events and discoveries. Therefore, it is not possible to describe

all of them in one section. There are a few books devoted to the history of

superconductivity—the reader who is interested to know more on this issue, is

referred to these books (see, for example, [1]). The goal of this introductory

section is primarily to give some historical perspective to the evolution of the

subject.

In most textbooks on superconductivity, the subject is presented chronolog-

ically. The presentation in this book does not follow this tradition: in this sec-

tion we consider the most important events and discoveries, and in the subse-

Introduction 3

quent chapters, we discuss the physics of the superconducting state in different

compounds without emphasizing the historical order.

2.1 Phenomenon of superconductivity: its discovery and

evolution

The phenomenon of superconductivity was discovered in 1911 by the Dutch

physicist H. Kamerlingh Onnes and his assistant Gilles Holst in Leiden. They

found that dc resistivity of mercury suddenly drops to zero below 4.2 K, as

shown in Fig. 1.1. Gilles Holst actually made this measurement [1]. However,

his name has become lost in the recesses of history, as is often the case with

junior researchers working under a famous scientist. A year later, Kamerlingh

Onnes and Holst discovered that a sufﬁciently strong magnetic ﬁeld restores

the resistivity in the sample as does a sufﬁciently strong electric current.

4.00

4.10

4.20

4.30

4.40

0.15

0.00

0.025

0.05

0.075

0.10

0.125

-5

Ω

(

Ω

)

(K)

Figure 1.1. Experimental data obtained in mercury by Gilles Holst and H. Kamerlingh Onnes

in 1911, showing for the ﬁrst time the transition from the resistive state to the superconducting

state.

In two years after the discovery of superconductivity in mercury, lead was

found to superconduct at 7.2 K. In 1930, superconductivity was discovered in

niobium, occurring at 9.2 K. This is the highest transition temperature among

all elemental metals.

In 1933, W. Meissner and R. Ochsenfeld discovered in Berlin one of the

most fundamental properties of superconductors: perfect diamagnetism. They