Handbook of High-Temperature Superconductor Electronics doc

Handbook of
High-Temperature
Superconductor
Electronics
edited by

Neeraj Khare

National Physical Laboratory
New Delhi, India

MARCEL

B
MARCEL DEKKER, INC.

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APPLIED PHYSICS
A Series of Professional Reference Books
Series Editor
ALLEN M. HERMANN
University of Colorado at Boulder
Boulder, Colorado

1. Hydrogenated Amorphous Silicon Alloy Deposition Processes,
Werner Luft and Y. Simon Tsuo
2. Thallium-Based High-Temperature Superconductors, edited by Allen
M. Hermann and J. V. Yakhmi

3. Composite Superconductors, edited by Kozo Osamura
4. Organic Conductors Fundamentals and Applications, edited by JeanPierre Farges
5 Handbook of Semiconductor Electrodeposition, f?. K. Pandey, S. N.
Sahu, and S. Chandra
6. Bismuth-Based High-Temperature Superconductors, edited by Hiroshi
Maeda and Kazumasa Togano
7. Handbook of High-Temperature Superconductor Electronics, edited
by Neeraj Khare
Additional Volumes in Preparation

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.


Preface

The discovery of high-temperature superconductors (HTS) exhibiting superconductivity above liquid nitrogen temperature has led to rapid growth in the development of many special-purpose electronics devices that can be broadly grouped
under the umbrella term of “superconductor electronics.”
Superconductor electronics promises particular advantages over conventional electronics: higher speed, less noise, lower power consumption, and much
higher upper-frequency limit. Such characteristics are advantageous in communication technology, high-precision and high-frequency electronics, magnetic field
measurement, superfast computers, etc. The potential of several superconductor
electronics devices has already been established using low-Tc conventional superconductors. The discovery of cuprate superconductors with higher transition temperature and higher energy gap extends the capability of superconductor electronics considerably. Rapid advancement in the synthesis of HTS thin films and artificial
grain boundary HTS Josephson junctions has elicited considerable interest in the development of electronic devices found to be very promising for future applications,
such as superconducting quantum interference devices (SQUIDs) small microwave,
and digital devices. Some of the HTS devices are already on the market.
Advances in the physics and material aspects of HTS have been well documented in the form of books and monographs, serving as a starting block for general readers and beginners. However, the literature was scattered. Thus, this book
is vital, bringing together contributions from leaders in different areas of research
and development in HTS electronics.
The contents are organized to be self-explanatory, comprehensive, and useful to both general reader and specialist. In each chapter care has been taken to

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.

iv

Preface

introduce basic terminology so that the readers in other fields interested in hightemperature superconductor electronics will find no difficulty in reading it. Professionals will find it an easily available collection of valuable and relevant information. The chapters are sequentially organized for use as a text for the study of
high-Tc devices at the graduate and advanced undergraduate level.
Chapter 1 is an introduction to high-Tc superconductors, presenting the developments in the discovery of various HTS compounds, its structure, preparation,
various properties, and comparison to low-Tc superconductors. The developments
of various techniques for high-Tc thin-film fabrication are described in Chapter 2.
Readers interested in knowing the advancements in high-Tc film fabrication will
find it very interesting and informative.
Chapters 3 and 4 present fabrication details and characteristics of multilayer
edge junctions and step-edge junctions in high-Tc superconducting films.
It is not easy to prepare S/I/S Josephson junctions in high-Tc as it is usually done in low-Tc superconductors (LTS), due to the short coherence length of
HTS. Natural grain boundaries in high-Tc materials are found to behave as
Josephson junctions. Detailed studies of these grain boundaries have led to the
development of several techniques for realizing artificial grain boundaries and
junctions whose behavior is similar to that of Josephson junctions. Grain boundaries in HTS are of central importance in numerous applications, such as electronic circuits and sensors and SQUIDs. Also, for many experiments elucidating
the physics of high-Tc superconductivity, grain boundaries have been used with
outstanding success.
Chapter 5 discusses the progress in understanding the conduction noise in
high-Tc superconductors. Chapter 6 reviews noise mechanisms in HTS junctions,
experimental techniques, and quantitative data on the noise properties of a range
of junctions and devices.
Noise in electronic systems sets limits the sensitivity of devices. Superconducting devices offer levels of performance that are difficult or impossible to
achieve by conventional methods, but are also subject to limitations due to intrinsic noise. A full understanding of the noise mechanism remains one of the outstanding tasks in the way of successful high-Tc applications. Intrinsic noise is in
orders of magnitude greater than the limits imposed by quantum mechanics, and
it becomes important to understand the mechanism that causes the excess noise.

In recent years, progress in the development of the high-Tc SQUID has been
remarkable. It is among the first HTS devices to reach the market. The field sensitivity achieved in HTS SQUIDs is sufficiently high for several applications including biomagnetism measurement, nondestructive evaluation, and geophysical
measurement. Progress in high-Tc rf-SQUIDs and SQUID magnetometer are presented in Chapters 7 and 8.
Chapter 9 presents an overview of progress in HTS digital circuits. Chapter
10 reviews the progress in the development of several HTS microwave devices

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Preface

v

such as filters, delay lines, low loss resonators, and antennas etc. Chapter 11 describes the principles and characteristics of high-Tc IR detectors.
HTS digital circuits are more suitable for use in single-flux quantum (SFQ)
circuits than in LTS ones, because HTS Josephson junctions are naturally overdamped, which means that their I-V curves do not show hysteresis, and the junctions in SFQ circuits must be overdamped junctions. The IcRn product of HTS
junctions can also be expected to be larger than that of LTS junctions because it
intrinsically depends on the gap voltage of the superconductor.
For a widespread application of HTS electronics, a package of high-Tc components in closed-cycle cryocoolers is required. Chapter 12 presents advances in the
area of cryocoolers and high-Tc devices. In order to make this chapter more comprehensive for beginners, the principles and details of various closed-cycle methods
such as the Joule-Thomson, Brayton, Claude, Stirling, Gifford-McMahon, and
pulse tube cryocoolers along with their relative merits, are discussed. Finally, the
last Chapter 13 presents a summary of the status and future of HTS electronics.
This book would have never been possible without the support of all the
contributors. I am grateful to all of them for their contributions. In spite of their
own busy schedules and commitments, they spared the time to prepare an exhaustive and critical review. The idea of preparing a book on HTS electronics
came after a thought-provoking discussion with Prof. Allen M. Hermann. I am
grateful to him for the enthusiasm he created and for his support during the entire
course of preparation of the book. I am thankful to the publisher, Marcel Dekker,
Inc., for inviting me to edit this book, which indeed proved to be a very interesting and rewarding experience. I am also thankful to my production editor, Brian

Black, for his editorial support.
I have greatly benefited from the experienced advice of Prof. S. Chandra on
several occasions and I am grateful to him for all the encouragement and support.
Encouragement and guidance received from Prof. S. K. Joshi, Dr. K. Lal, Dr.
Praveen Chaudhari, Prof. G. B. Donaldson, Prof. O. N. Srivastava, Prof. E. S. Rajagopal, Prof. A. K. Raychaudhuri, and Dr. A. K. Gupta are gratefully acknowledged. I am thankful to Dr. N. D. Kataria and Dr. Vijay Kumar for their help and
cooperation.
Concern and words of appreciation of Prof. O. P. Malviya have been a great
source of encouragement for me. Emotional support from my well-wishers particularly came from Priyadarshan Malviya, Pankaj Khare, and Alka Wadhwa. I
wish to express my gratitude to my wife, Sangeeta, for her untiring help, cooperation, and patience, without which it would not have been possible to complete
this book. The smiling face and shining eyes of my little son, Siddharth have been
a great source of stress relief for me and always inspired me to devote more time
to completing the book.
Neeraj Khare

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.


Contents

Preface
1

Introduction to High-Temperature Superconductors
Neeraj Khare

2

Epitaxial Growth of Superconducting Cuprate Thin Films
David P. Norton

3

High-Temperature Superconducting Multilayer
Ramp-Edge Junctions
Q. X. Jia

4

Step-Edge Josephson Junctions
F. Lombardi and A. Ya. Tzalenchuk

5

Conductance Noise in High-Temperature Superconductors
László Béla Kish

6

Noise in High-Temperature Superconductor Josephson Junctions
J.C. Macfarlane, L. Hao, and C.M. Pegrum

7

High-Temperature RF SQUIDS
V. I. Shnyrkov

8

High-Temperature SQUID Magnetometer
Neeraj Khare

9

High-Temperature Superconducting Digital Circuits
Mutsuo Hidaka

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viii

10

High-Temperature Superconductor Microwave Devices
Neeraj Khare

11

High-Temperature Superconducting IR Detectors
John C. Brasunas

12

Cryocoolers and High-Tc Devices
Ray Radebaugh

13

High-Temperature Superconductor Electronics:
Status and Perspectives

Shoji Tanaka

Copyright © 2003 by Marcel Dekker, Inc. All Rights Reserved.


Contributors

John C. Brasunas
Maryland, U.S.A.

NASA’s Goddard Space Flight Center, Greenbelt,

L. Hao* Department of Physics and Applied Physics, University of Strathclyde,
Glasgow, Scotland
Mutsuo Hidaka NEC Corporation, Ibaraki, Japan
Q. X. Jia Superconductivity Technology Center, Los Alamos National
Laboratory, Los Alamos, New Mexico, U.S.A.
Neeraj Khare National Physical Laboratory, New Delhi, India
László Béla Kish Texas A&M University, College Station, Texas, U.S.A.
F. Lombardi Chalmers Institute of Technology and Göteborg University,
Göteborg, Sweden
J. C. Macfarlane Department of Physics and Applied Physics, University of
Strathclyde, Glasgow, Scotland
David P. Norton University of Florida, Gainesville, Florida, U.S.A.
C. M. Pegrum Department of Physics and Applied Physics, University of
Strathclyde, Glasgow, Scotland

*Current affiliation: Centre for Basic Metrology, National Physical Laboratory,
Teddington, England

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x

Ray Radebaugh
Colorado, U.S.A.

Contributors

National Institute of Standards and Technology, Boulder,

V. I. Shnyrkov Institute for Low Temperature Physics and Engineering,
Academy of Sciences, Kharkov, Ukraine
Shoji Tanaka Superconductivity Research Laboratory, ISTEC, Tokyo, Japan
A. Ya. Tzalenchuk National Physical Laboratory, Middlesex, England

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1
Introduction to High-Temperature
Superconductors
Neeraj Khare
National Physical Laboratory, New Delhi, India

1.1 INTRODUCTION
The discovery of superconductivity in copper oxide perovskite (1) has opened a
new era of research in superconducting materials. This class of materials not only
show high-temperature superconductivity but also show properties that are different from classical superconductors. This offers a great challenge to understanding

the basic phenomenon that causes superconductivity in these materials and to developing the appropriate preparation methods so that these can be exploited for a
wide range of applications. During the last one and half decades after the discovery of high-Tc materials, several high-Tc superconductors have been discovered
which show superconductivity at temperatures higher than liquid-nitrogen temperature (77 K). There has also been great progress in understanding the properties of these materials, developing different methods of preparation, and realizing
superconducting devices which use these superconductors.
This chapter will give a brief description of the historical developments in
raising the transition temperature (Tc) of the superconductors, preparation, and
structure of the material. Different properties of the high-Tc materials such as critical magnetic field, penetration depth, coherence length, critical current density,
weak link, and so forth are also discussed.

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Khare

1.2 RAISING THE TRANSITION TEMPERATURE
Superconductivity is the phenomenon in which a material loses its resistance on
cooling below the transition temperature (Tc). Superconductivity was first discovered in mercury by Onnes (2) in 1911. The temperature at which mercury becomes
superconducting was found to be close to the boiling point of liquid helium (4.2
K). Subsequently, many metals, alloys, and intermetallic compounds were found
to exhibit superconductivity. The highest Tc known was limited to 23.2 K (3) in
the Nb3Ge alloy; however, in September 1986, Bednorz and Muller (1) discovered
superconductivity at 30 K in La–Ba–Cu–O. The phase responsible for superconductivity was identified to have nominal composition of La2Ϫx Ba x CuO4Ϫy (x ϭ
0.2). The discovery of high-temperature superconductivity in ceramic cuprate oxides by Bednorz and Muller led to unprecedented effort to explore new superconducting oxide material with higher transition temperatures. The value of Tc in
La2Ϫx Ba xCuO4 was found to increase up to 57 K with the application of pressure
(4). This observation in La2Ϫx Ba xCuO4 material raised the hope of attaining even
higher transition temperatures in cuprate oxides. This, indeed, turned out to be true
when Chu and co-workers (5) reported a remarkably high superconductivity transition temperature (Tc) of 92 K on replacing La by Y in nominal composition
Y1.2Ba0.8CuO4Ϫy. Later, different groups identified (6–8) that the superconducting phase responsible for 90 K has the composition YBa2Cu3O7Ϫy.

The discovery of superconductivity above the boiling point of liquid nitrogen led to extensive search for new superconducting materials. Superconductivity
at transition temperatures of 105 K in the multiphase sample of the
Bi–Sr–Ca–Cu–O compound was reported by Maeda et al. (9) in 1988. The highest Tc of 110 K was obtained in the Bi–Sr–Ca–Cu–O compound having a composition Bi2Sr2Ca2Cu3O10 (10,11). Sheng and Hermann (12) substituted the nonmagnetic trivalent Tl for R in R-123, where R is a rare-earth element. By reducing
the reaction time to a few minutes for overcoming the high-volatility problem associated with Tl2O3, they detected superconductivity above 90 K in TlBa2Cu3Ox
samples in November 1987. By partially substituting Ca for Ba, they (13) discovered a Tc ϳ 120 K in the multiphase sample of Tl–Ba–Ca–Cu–O in February
1988. In September 1992, Putillin et al. (14) found that the HgBa2CuOx (Hg-1201)
compound with only one CuO2 layer showed a Tc of up to 94 K. It was, therefore,
rather natural to speculate that Tc can increase if more CuO2 layers are added in
the per unit formula to the compound. In April 1993, Schilling et al. (15) reported
the detection of superconductivity at temperatures up to 133 K in HgBa2
Ca2Cu3Ox. The transition temperature of HgBa2Ca2Cu3Ox was found to increase
to 153 K with the application of pressure (16).
Figure 1.1 depicts the evolution in the transition temperature of superconductors starting from the discovery of superconductivity in mercury. The slow but
steady progress to search for new superconductors with higher transition temper-

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Introduction to High-Temperature Superconductors

3

FIGURE 1.1 The evolution of the transition temperature (Tc) subsequent to
the discovery of superconductivity.

atures continued for decades until superconductivity at 30 K in La–Ba–Cu–O oxide was discovered in 1986. Soon after this, other cuprate oxides such as
Y–Ba–Cu–O, Bi–Sr–Ca–Cu–O, Tl–Ba–Ca–Cu–O with superconductivity above
the liquid-nitrogen temperature were discovered.
Table 1.1 gives a list of some of high-Tc superconductors with their respective transition temperature, crystal structure, number of Cu–O layers present in
unit cell, and lattice constants. Transition temperature has been found to increase

as the number of Cu–O layer increases to three in Bi–Sr–Ca–Cu–O,
Tl–Ba–Ca–Cu–O, and Hg–Ba–Ca–Cu–O compounds. In all of the cuprate superconductors described so far, the superconductivity is due to hole-charge carriers,
except for Nd2Ϫx Cex CuO4 (Tc ϳ 20 K), which is an n-type superconductor (17).
The superconductor Ba0.6K0.4BiO3, which does not include Cu, was reported by
Cava et al. (18) in 1988 exhibiting Tc ϳ 30 K. A homologous series of compounds
(Cu,Cr)Sr2CanϪ1CunOy [Cr12(nϪ1)n] has been synthesized under high pressure.

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Khare

TABLE 1.1 Transition Temperature (Tc), Crystal Structure and Lattice Constants of
Some High-Tc Superconductors
High-Tc superconductors
Formula

Notation

Tc
(K)

na

Crystal
structure

La1.6Ba0.4CuO4

La2Ϫx Srx CuO4
YBa2Cu3O7

214
214
123

30
38
92

1
1
2

Tetragonal
Tetragonal
Orthorhombic

YBa2Cu4O8

124

80

2

Orthorhombic

Y2Ba4Cu7O14

247

40

2

Orthorhombic

Bi2Sr2CuO6
Bi2Sr2CaCu2O8
Bi2Sr2Ca2Cu3O10
TlBa2CuO5
TlBa2CaCu2O7
TlBa2Ca2Cu3O9
TlBa2Ca3Cu4O11
Tl2Ba2CuO6
Tl2Ba2CaCu2O8
Tl2Ba2Ca2Cu3O10
HgBa2CuO4
HgBa2CaCu2O6
HgBa2Ca2Cu3O8
(Nd2ϪxCex) CuO4
(Nd, CeSr) CuO4

Bi-2201
Bi-2212
Bi-2223
Tl-1201
Tl-1212

Tl-1223
Tl-1234
Tl-2201
Tl-2212
Tl-2223
Hg-1201
Hg-1212
Hg-1223
T
T*

20
85
110
25
90
110
122
80
108
125
94
128
134
30
30

1
2
3

1
2
3
4
1
2
3
1
2
3
1
1

Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal
Tetragonal

Lattice constants (Å)

a ϭ 3.79, c ϭ 13.21
a ϭ 3.78, c ϭ 13.23
a ϭ 3.82, b ϭ 3.89,
c ϭ 11.68
a ϭ 3.84, b ϭ 3.87,
c ϭ 27.23
a ϭ 3.85, b ϭ 3.87,
c ϭ 50.2
a ϭ 5.39, c ϭ 24.6
a ϭ 5.39, c ϭ 30.6
a ϭ 5.39, c ϭ 37.1
a ϭ 3.74, c ϭ 9.00
a ϭ 3.85, c ϭ 12.74
a ϭ 3.85, c ϭ 15.87
a ϭ 3.86, c ϭ 19.01
a ϭ 3.86, c ϭ 23.22
a ϭ 3.86, c ϭ 29.39
a ϭ 3.85, c ϭ 35.9
a ϭ 3.87, c ϭ 9.51
a ϭ 3.85, c ϭ 12.66
a ϭ 3.85, c ϭ 15.78
a ϭ 3.94, c ϭ 12.07
a ϭ 3.85, c ϭ 12.48

a

n represents the number of Cu-O planes in the unit cell.

In the Cr series, the value of n can be changed from 1 to 9, with a maximum Tc of
107 K at n ϭ 3. The Pr(Ca)Ba2Cu3Oy compound has also been synthesized under

high pressure, showing a transition temperature of 97 K (19).
1.3 CRYSTAL STRUCTURE OF HIGH-Tc
SUPERCONDUCTORS
The structure of a high-Tc superconductor is closely related to perovskite structure. The unit cell of perovskite consists of two metal (A, B) atoms and three oxygen atoms, with the general formula given as ABO3. The ideal perovskite structure is shown in Fig. 1.2a. Atom A, sitting at the body-centered site, is coordinated
by 12 oxygen atoms. Atom B occupies the corner site and the oxygen atom occupies the edge-centered position.

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Introduction to High-Temperature Superconductors

5

Figure 1.2b shows the unit cell of La2Ϫx Bax CuO4, which has a tetragonal
symmetry and consists of perovskite layers separated by rock-salt-like layers made
of La (or Ba) and O atoms. This compound is often termed 214 because it has two
La, one Cu, and four O atoms. The 214 compound has only one CuO2 plane. Looking at the exact center of Fig. 1.2b, the CuO2 plane appears as one copper atoms surrounded by four oxygen atoms, with one LaO plane above the CuO2 plane and one
below it. The entire structure is layered. The LaO planes are said to be intercalated.
The CuO2 plane is termed the conduction plane, which is responsible for superconductivity. The intercalated LaO planes are called “charge-reservoir layers.” When
the intercalated plane contains mixed valence atoms, electrons are drawn away from
the copper oxide planes, leaving holes to form pairs needed for superconductivity.
The structure of YBa2Cu3O7 is shown in Fig. 1.2c. The unit cell of
YBa2Cu3O7 consists of three pseudocubic elementary perovskite unit cells (8).
Each perovskite unit cell contains a Y or Ba atom at the center: Ba in the bottom
unit cell, Y in the middle one, and Ba in the top unit cell. Thus, Y and Ba are
stacked in the sequence [Ba–Y–Ba] along the c-axis. All corner sites of the unit
cell are occupied by Cu, which has two different coordinations, Cu(1) and Cu(2),
with respect to oxygen. There are four possible crystallographic sites for oxygen:
O(1), O(2), O(3), and O(4). The coordination polyhedra of Y and Ba with respect
to oxygen are different. The tripling of the perovskite unit cell (ABO3) leads to

nine oxygen atoms, whereas YBa2Cu3O7 has seven oxygen atoms accommodat-

FIGURE 1.2 Structure of (a) perovskite ABO3, (b) (La,Ba)2CuO4, and (c)
YBa2Cu3O7.

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6

Khare

ing the deficiency of two oxygen atoms. Thus, the structure of the 90 K phase deviates from the ideal perovskite structure and, therefore, is referred to as an oxygen-deficient perovskite structure. Oxygen atoms are missing from the Y plane
(i.e., z ϭ 1/2 site); thus, Y is surrounded by 8 oxygen atoms instead of the 12 if it
had been in ideal perovskite structure. Oxygen atoms at the top and bottom planes
of the YBa2Cu3O7 unit cell are missing in the [100] direction, thus giving (Cu–O)
chains in the [010] direction. The Ba atom has a coordination number of 10 oxygen atoms instead of 12 because of the absence of oxygen at the (1/2 0 z) site. The
structure has a stacking of different layers: (CuO)(BaO)(CuO2)(Y)(CuO2)(BaO)
(CuO). One of the key feature of the unit cell of YBa2Cu3O7Ϫ␦ (YBCO) is the
presence of two layers of CuO2. The role of the Y plane is to serve as a spacer between two CuO2 planes. In YBCO, the Cu–O chains are known to play an important role for superconductivity. Tc maximizes near 92 K when ␦ Ϸ 0.15 and the
structure is orthorhombic. Superconductivity disappears at ␦ Ϸ 0.6, where the
structural transformation of YBCO occurs from orthorhombic to tetragonal.
The crystal structure of Bi-, Tl-, and Hg-based high-Tc superconductors are
very similar to each other. Like YBCO, the perovskite-type feature and the presence of CuO2 layers also exist in these superconductors. However, unlike YBCO,
Cu–O chains are not present in these superconductors. The YBCO superconductor has an orthorhombic structure, whereas the other high-Tc superconductors
have a tetragonal structure (see Table 1.1).
The Bi–Sr–Ca–Cu–O system has three superconducting phases forming a
homologous series as Bi2Sr2CanϪ1CunO4ϩ2nϩy (n ϭ 1, 2, and 3). These three
phases are Bi-2201, Bi-2212, and Bi-2223, having transition temperatures of 20,
85, and 110 K, respectively (10,11). The structure of Bi-2201 together with Bi2212 and Bi-2223 is shown in Fig. 1.3. All three phases have a tetragonal structure which consists of two sheared crystallographic unit cells. The unit cell of

these phases has double Bi–O planes which are stacked with a shift of (1/2 1/2 z)
with respect to the origin. The stacking is such that the Bi atom of one plane sits
below the oxygen atom of the next consecutive plane. The Ca atom forms a layer
within the interior of the CuO2 layers in both Bi-2212 and Bi-2223; there is no Ca
layer in the Bi-2201 phase. The three phases differ with each other in the number
of CuO2 planes; Bi-2201, Bi-2212, and Bi-2223 phases have one, two, and three
CuO2 planes, respectively. The c axis of these phases increases with the number
of CuO2 planes. The lengths of the c axis are 24.6 Å, 30.6 Å, and 37.1 Å respectively for the Bi-2201, Bi-2212, and Bi-2223 phases. The coordination of the Cu
atom is different in the three phases. The Cu atom forms an octahedral coordination with respect to oxygen atoms in the 2201 phase, whereas in 2212, the Cu atom
is surrounded by five oxygen atoms in a pyramidal arrangement. In the 2223 structure, Cu has two coordinations with respect to oxygen: one Cu atom is bonded
with four oxygen atoms in square planar configuration and another Cu atom is coordinated with five oxygen atoms in a pyramidal arrangement.

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Introduction to High-Temperature Superconductors

7

FIGURE 1.3 Unit cells of the Bi2Sr2CanϪ1 CunOx compound with n ϭ 1, 2, and
3. (Adapted from Ref. 11.)

Figure 1.4 shows the unit cells of two series of the Tl–Ba–Ca–Cu–O superconductor (20). The first series of the Tl-based superconductor containing one
Tl–O layer has the general formula TlBa2CanϪ1CunO2nϩ3, whereas the second series containing two Tl–O layers has a formula of Tl2Ba2CanϪ1CunO2nϩ4 with n ϭ
1, 2, and 3. In the structure of Tl2Ba2CuO6, there is one CuO2 layer with the stacking sequence (Tl–O) (Tl–O) (Ba–O) (Cu–O) (Ba–O) (Tl–O) (Tl–O). In
Tl2Ba2CaCu2O8, there are two Cu–O layers with a Ca layer in between. Similar to
the Tl2Ba2CuO6 structure, Tl–O layers are present outside the Ba–O layers. In
Tl2Ba2Ca2Cu3O10, there are three CuO2 layers enclosing Ca layers between each
of these. In Tl-based superconductors, Tc is found to increase with the increase in
CuO2 layers. However, the value of Tc decreases after four CuO2 layers in

TlBa2CanϪ1CunO2nϩ3, and in the Tl2Ba2CanϪ1CunO2nϩ4 compound, it decreases
after three CuO2 layers.
The crystal structure of HgBa2CuO4 (Hg-1201), HgBa2CaCu2O6 (Hg1212), and HgBa2Ca2Cu3O8 (Hg-1223) is similar to that of Tl-1201, Tl-1212, and
Tl-1223 (Fig. 1.4) with Hg in place of Tl (21). It is noteworthy that the Tc of the
Hg compound (Hg-1201) containing one CuO2 layer is much larger as compared
to the one-CuO2-layer compound of thallium (Tl-1201). In the Hg-based superconductor, Tc is also found to increase as the CuO2 layer increases. For Hg-1201,
Hg-1212, and Hg-1223, the values of Tc are 94, 128, and 134 K respectively, as
shown in Table 1.1. The observation that the Tc of Hg-1223 increases to 153 K under high pressure (16) indicates that the Tc of this compound is very sensitive to
the structure of the compound.

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FIGURE 1.4 Unit cells of the Tl1Ba2CanϪ1 CunO2nϩ3 compound containing one
Tl–O layer and the Tl2Ba2CanϪ1 CunO2nϩ4 compound containing two Tl–O layers for n ϭ 1, 2, and 3. (Adapted from Ref. 20.)

1.4 PREPARATION OF HIGH-Tc SUPERCONDUCTORS
High-Tc superconductors are prepared in the form of bulk, thick films, thin films,
single crystals, wires, and tapes. Fabrication in the form of wires and tapes are required for high-current applications. On the other hand, thick and thin films are
needed for electronic application. Strict control of the stoichiometry of the composition is very much required for preparing high-Tc superconductors with desirable characteristics. Even a small change in oxygen content or a small change in
cation doping level can transform the material from a superconductor to a low-carrier-density metal or even to an insulator. The following paragraphs give a brief

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Introduction to High-Temperature Superconductors

9

description of high-Tc superconductors in the form of bulk and thick films. The
preparation of high-Tc thin films is given in more detail in the other chapters of
this book.
The simplest method for preparing high-Tc superconductors is a solid-state
thermochemical reaction involving mixing, calcination, and sintering. The appropriate amounts of precursor powders, usually oxides and carbonates, are mixed
thoroughly using a ball mill. Solution chemistry processes such as coprecipitation,
freeze-drying, and sol–gel methods are alternative ways for preparing a homogenous mixture. These powders are calcined in the temperature range from 800°C to
950°C for several hours. The powders are cooled, reground, and calcined again.
This process is repeated several times to get homogenous material. The powders
are subsequently compacted to pellets and sintered. The sintering environment
such as temperature, annealing time, atmosphere, and cooling rate play a very
important role in getting good high-Tc superconducting materials. The
(La1Ϫx Bax )2CuO4Ϫ␦ high-Tc superconductor is prepared by heating a mixture of
La2O3, BaCO3, and CuO in a reduced oxygen atmosphere at 900°C. After regrinding and reheating the mixtures, the pellet is prepared and sintered at 925°C
for 24 h. The YBa2Cu3O7Ϫ␦ compound is prepared by calcination and sintering of
a homogenous mixture of Y2O3, BaCO3, and CuO in the appropriate atomic ratio.
Calcination is done at 900–950°C, whereas sintering is done at 950°C in an oxygen atmosphere. The oxygen stoichiometry in this material is very crucial for obtaining a superconducting YBa2Cu3O7Ϫ␦ compound. At the time of sintering, the
semiconducting tetragonal YBa2Cu3O6 compound is formed, which, on slow
cooling in oxygen atmosphere, turns into superconducting YBa2Cu3O7Ϫ␦. The uptake and loss of oxygen are reversible in YBa2Cu3O7Ϫ␦. A fully oxidized orthorhombic YBa2Cu3O7Ϫ␦ sample can be transformed into tetragonal YBa2Cu3O6
by heating in a vacuum at temperature above 700°C.
The preparation of Bi-, Tl-, and Hg-based high-Tc superconductors is
difficult compared to YBCO. Problems in these superconductors arise because
of the existence of three or more phases having a similar layered structure. Thus,
syntactic intergrowth and defects such as stacking faults occur during synthesis
and it becomes difficult to isolate a single superconducting phase. For
Bi–Sr–Ca–Cu–O, it is relatively simple to prepare the Bi-2212 (Tc ϳ 85 K) phase,
whereas it is very difficult to prepare a single phase of Bi-2223 (Tc ϳ 110 K). The

Bi-2212 phase appears only after few hours of sintering at 860–870°C, but the
larger fraction of the Bi-2223 phase is formed after a long reaction time of more
than a week at 870°C (11). Although the substitution of Pb in the Bi–Sr–Ca–Cu–O
compound has been found to promote the growth of the high-Tc phase (22), a long
sintering time is still required.
Toxicity and low vapor pressure of Hg–O and Tl–O make fabrication of Hgand Tl-based high-Tc superconductors much more difficult and one has to follow
special precautions and stringent control on the preparation atmosphere. The Tlbased superconductor is prepared by thorough mixing of Tl2O3, BaO, CaO, and

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Khare

CuO in appropriate proportions and pressing the powders into a pellet. The pellet
is wrapped in a gold foil and fired at 880°C for 3h in a sealed quartz tube containing 1 atm oxygen to reach superconductivity (20).
For the preparation of a Hg-based high-Tc superconductor (15), first a precursor material with the nominal composition Ba2CaCu2O5 is obtained from a homogenous mixture of the respective metal nitrates by sintering at 900°C in oxygen. Dry boxes are used for grinding and mixing of the powders. After regrinding
and mixing with HgO powder, the pressed pellet is sealed in an evacuated quartz
tube. This tube is placed horizontally in a tight steel container and sintered at
800°C for a few hours.
Several techniques such as screen printing (23–27), spin-coating (28) and
spray pyrolysis (29–33) are used in preparing high-Tc thick films. For the screen
printing or spin-coating method, the first step is to prepare homogenous powders
of high-Tc materials; this is accomplished by solid-state reaction or by a chemical
route involving mixing, calcination, and sintering of appropriate powders in the
form of oxides or carbonates. After sintering the powders are sieved through a
screen woven from stainless steel or nylon wire. The diameter of the screen wire
and the size of the opening can vary depending on the process requirement. The
opening size is usually given in terms of a standard mesh number that varies from

100 to 400. The fine sieved powders are converted into thick paste by mixing with
an organic solvent such as propylene glycol, octyl alcohol, heptyl alcohol, triethanolamine, or cyclohexagonal. In the screen-printing technique, thick paste is
used for printing the substrate through the mesh screen and dried at an appropriate temperature. In the spin-coating method, one drop of the paste is put on the
substrate and the substrate is spun to get a uniform coating of the material. The resultant films are fired at a suitable annealing temperature. In general, single-crystal and polycrystalline substrates of magnesium oxide (MgO), strontium titnate
(SrTiO3), lanthanum aluminate (LaAlO3), yattria-stabilized zirconia (YSZ), and
aluminum oxide (Al2O3) are used for the high-Tc thick-film preparation.
For YBCO thick films, the sintering temperature is kept between 940°C and
970°C followed by slow cooling in an oxygen atmosphere (23). In order to achieve
YBCO films with a larger grain size and higher current density, the firing temperature is increased to 1000°C (24). Bi-2212 high-Tc films are prepared by firing the
films at 880–885°C. It has been found that partial melting and quenching of the Bi2212 films from 885°C to room temperature leads to a Tc as high as 96 K (25). For
high-Tc films with a Bi-2223 phase, the films are fired at ϳ880°C for a few minutes and then annealed at 864°C for a duration of 70–80 h (26). The preparation of
Tl–Ba–Ca–Cu–O thick films requires a two-step process (27). In the first step, a
film of Ba–Ca–Cu–O is prepared, and in the second step, this precursor film is
heated in Tl2O3 vapor followed by slow cooling to room temperature.
Spray pyrolysis is another simple and inexpensive technique for preparing
high-Tc films (30–33). For YBCO film, an aqueous solution for the spray is pre-

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Introduction to High-Temperature Superconductors

11

pared by dissolving Y(NO3)и6H2O, Ba(NO3), and Cu(NO3)и3H2O in triple-distilled water in a 1 : 2 : 3 stoichiometric ratio (29). The solution is sprayed on a single-crystal YSZ or SrTiO3 substrate through a glass nozzle using oxygen for few
minutes and then slowly cooled to room temperature. The starting solution for depositing Bi-2212 film is prepared by mixing aqueous solution of Bi2O3, SrCO3,
CaCO3, and CuO in dilute nitric acid (30). A two-step process is used for preparing Tl- and Hg-based high-Tc films by the spray pyrolysis technique (31–33). The
first step involves preparation of Ba–Ca–Cu–O precursor films by spraying an
aqueous solution of Ba, Ca, and Cu nitrates on a single-crystal substrate. In the
second step, Tl or Hg is incorporated in the precursor films by annealing the film

in a controlled Tl–O or Hg–O vapor atmosphere.
Different techniques such as sputtering, evaporation, molecular beam epitaxy, laser ablation, chemical vapor deposition, and so forth have been used successfully to prepare thin films of high-Tc superconductors. A detailed account of
these techniques is given in Chapter 2. Most of these techniques work in a vacuum
environment and the oxygen partial pressure near the substrate is controlled to obtain a superconducting film. This can be done during the film deposition (in situ
process) or by postdeposition oxygen annealing. The substrate temperature during
the deposition is a crucial parameter that determines microstructural details such
as texture and the degree of epitaxy of the film. Substrate–film interaction such as
interdiffusion can affect the quality of the films. Thus, it is desirable to develop
processes that allow a low substrate temperature.
1.5 PROPERTIES OF HIGH-TEMPERATURE
SUPERCONDUCTORS
A superconducting state is defined by the transition temperature (Tc) at which material exhibits zero resistance on cooling. Apart from the transition temperature,
other properties characterizing the high-Tc superconductors are critical magnetic
field, penetration depth, coherence length, critical current density and weak link,
energy gap, and so forth. A brief description of these is presented here.
1.5.1 Anisotropy
As described in Section 1.3, the crystal structure of high-Tc superconductors is
highly anisotropic. This feature has important implications for both physical and
mechanical properties. In high-Tc superconductors, electrical currents are carried
by holes induced in the oxygen sites of the CuO2 sheets. The electrical conduction
is highly anisotropic, with a much higher conductivity parallel to the CuO2 plane
than in the perpendicular direction. Other superconductivity properties such as coherence length (␰), penetration depth (␭), and energy gap (⌬) are also anisotropic.
The mechanical properties of high-Tc materials are also very anisotropic. For ex-

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Khare

ample, in YBCO, upon cooling, the lattice contracts far more along a-b planes
than along c axis. Torque magnetometry measurements have been made for several high-Tc superconductors for studying anisotropy (34,35). For Tl-2212, an
anisotropy of ϳ105 is found for the ratio of the mass along the c axis to that of ab plane. A similar large ratio is obtained for the Bi-2212 compound. In Y-123, the
value of this ratio is found to be ϳ25, which is much smaller compared to Bi and
Tl compounds. The anisotropy factor of a high-Tc superconductor at the optimally
doped composition is related to the interlayer spacing between CuO2 layers in the
unit cell. It has been also noted that increasing carrier doping or substituting ions
on the blocking layer for certain other ions such as Pb in Bi-2212 reduces
anisotropy without changing the interlayer spacing significantly.
1.5.2 Critical Magnetic Field
The abrupt transition from the normal to superconducting state occurs at a boundary defined not only by the transition temperature (Tc) but also by the magnetic
field strength. There is a critical value of magnetic field, Hc, above which the superconductivity is destroyed. If a paramagnetic material is placed in a magnetic
field, then the magnetic lines of force penetrate through the material. However,
when the same material is made superconducting by cooling to a low temperature
below Tc, then the magnetic lines of force are completely expelled from the interior of the material. This effect is called the Meissner effect. Based on the Meissner effect, the superconducting materials are classified as type I and type II superconductors. If there is a sharp transition from the superconducting state to the
normal state, then this type of material is called a type I superconductor. This kind
of behavior is shown, in general, by pure metals. In type II superconductors, there
are two values of the critical field: the lower critical field, Hc1, and the upper critical field, Hc2. For H Ͻ Hc1, the field is completely expelled from the superconductor. However, for H Ͼ Hc1, the magnetic field penetrates the material slowly
and continues up to Hc2, beyond which the material transforms completely from
the superconducting state to the normal state. The state between Hc1 and Hc2 is
called the vortex or mixed state. Figure 1.5a shows the H–T phase diagram for
conventional low-Tc superconductors. At low fields, there is Meissner state, and
at high fields, vortices enter the material and form a vortex lattice. Superconductivity is completely destroyed at Hc2, for which the density of vortices is such that
the normal cores fill the entire material. For low-Tc superconductors, this behavior is exhibited, in general, by alloys and compounds. On the other hand, all highTc superconductors behave as type II superconductors. For high-Tc superconductors, the value of Hc1(0) is low (ϳ100 Oe), whereas the value of Hc2(0) is quite
high (about few hundred tesla). The value of the critical field is anisotropic
for these materials. For a YBCO single crystal, values of Hc1(0) in the direction
parallel to the c axis and in the a-b plane are estimated as 850 and 250 Oe,

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Introduction to High-Temperature Superconductors

13

FIGURE 1.5 H–T phase diagram of (a) low-Tc type II superconductors and (b)
high-Tc superconductor.

respectively (36), whereas the value of Hc2(0) is estimated to be 670 T and 120 T
in the a-b plane and along the c axis, respectively (37).
Cuprate high-Tc superconductors display a complex H–T phase diagram
(Fig. 1.5b) due to their high-Tc, short coherence length, layered structure and
anisotropy (38). Apart from Hc1 and Hc2, there are irreversibility (Hi ) and melting
(Hm) lines. The melting line separates a vortex lattice and a vortex liquid state. The
irreversibility line occurs in the vicinity of the melting line. This line provides a
boundary between the reversible and irreversible magnetic behavior of a superconductor.
The structure of the vortex line in high-Tc superconductors is different from
the conventional type II superconductors. The individual two-dimensional “pancake” vortices on neighboring layers couple to form three-dimensional vortex

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14

Khare

lines. A weakness of attractive interaction between the “pancakes” from different
layers results in a strong reduction of the shear modulus of the vortex lattice along
the layers as well as a strong influence from thermal fluctuations. The phase diagram of such flexible vortices in the presence of thermal fluctuations and pinning

is a topic of intense study. A better understanding of the dynamics of the vortices
will help to increase the transport critical current density in the material and also
to control the flux noise for electronic applications.
1.5.3 Penetration Depth
Below Hc1, the external magnetic field is excluded from the bulk of a superconducting material by a persistent supercurrent in the surface region, which induces
a field that exactly matches the applied field. The depth of this surface is called the
penetration depth (␭) and the external field penetrates the superconductor in an
exponentially decreasing manner. To be more precise, penetration depth is the distance over which an applied magnetic field decays to 1/e of its value at the surface. For an isotropic superconductor, the lower critical field (Hc1) is related to the
penetration depth by
⌽0
Hc1 Ϸ ᎏᎏ
␭2

(1)

where ⌽0 is the flux quantum. The value of the penetration depth can be obtained
from magnetization of the thin superconducting crystal, muon spin rotation, kinetic inductance, or microwave measurements. Anisotropy in ␭ can be estimated
from flux decoration and magnetic torque experiments. For high-Tc superconductors, the penetration depth along the c axis is different than that along the a-b
plane. For the YBCO single crystal, the value of ␭ab(T → 0) is obtained as 1400
Å (39). There has been much interest in studying the temperature dependence of
␭ because it is expected to provide information about the symmetry of the order
parameter of high-Tc superconductors. The two-fluid model describes the temperature dependence as
4 Ϫ1/2

΄ ΂ ΃΅

T
␭(T) ϭ ␭(0) 1 Ϫ ᎏᎏ
Tc

(2)

For a weak coupling BCS superconductor, the ⌬␭ [ϭ␭(T) Ϫ ␭(0)] varies exponentially with temperature (40). If there are nodes in the energy gap, then ␭(T)
varies linearly with T (41). The results of the temperature dependence of ␭ for
high-Tc superconductors are discussed in Section 1.5.8.
1.5.4 Coherence Length
One of the important parameters determining the performance of a superconductor is the coherence length (␰). It is a measure of the correlation distance of the su-

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Introduction to High-Temperature Superconductors

15

perconducting charge carriers. Coherence length represents the size of the Cooper
pair. In terms of the Fermi velocity (vF) and transition temperature Tc, coherence
length is given as
hvF
␰ ϭ ᎏᎏ
2␲2kBTc

(3)

where kB is the Boltzman constant and h is Planck’s constant. The higher value of
Tc in copper oxide superconductors is expected to lead to a low value for the coherence length. Direct measurement of the coherence length is difficult. However,
the value of the coherence length can be extracted from fluctuation contributions
to the specific heat, susceptibility, or conductivity. The value of the coherence
length can also be obtained via measurement of Hc2 using
⌽0

Hc2 Ϸ ᎏᎏ
2␲␰2

(4)

The value of the coherence length is found to be highly anisotropic for high-Tc materials. The coherence length parallel to the c axis is typically 2–5 Å, and in the ab plane, the value is typically 10–30 Å. Thus, perpendicular to the a-b plane, the
superconducting wave function is essentially confined to the few adjacent unit
cells. In conventional low-Tc, type I superconductors, the coherence length is
1000 Å, which is several orders of magnitude larger than that in high-Tc superconductors. The low value of the coherence length in high-Tc superconductors
means that the coherence volume contains only a few Cooper pairs, implying that
the fluctuations may be much larger in the high-Tc superconductors than in the
conventional superconductors. The low values of the coherence length make these
materials very sensitive to the presence of local defects such as oxygen vacancies,
dislocations, and deviation from the stoichiometry.
1.5.5 Flux Quantization
In the classical low-Tc superconductors, magnetic flux (⌽) trapped in a closed superconducting ring is always an integral multiple of a flux quantum, ⌽0:
⌽ ϭ n⌽0

(5)
Ϫ7

where n is an integer, ⌽0 ϭ h/2e ϭ 2 ϫ 10 G/cm , h is Planck’s constant, and
e is the electronic charge; the factor 2 in the denominator shows that the superconducting ground state is composed of paired electrons.
Soon after the discovery of light-Tc superconductors, various experiments
were performed to find out if the superconducting state in high-Tc superconductors consisted of paired electrons or of something else. One way to find out is by
measuring a trapped flux in the high-Tc superconducting ring. Gough and coworkers (42) performed an experiment to measure the flux through a sintered

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2