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The Evolution of HTS: T

-Experiment Perspectives 431

(ii) In 1978, Brandt et al.

claimed to observe superconductivity up to

170 K in CuCl under pressures based on the large resistive and magnetic

anomalies detected, and attributed the observation to electron pairing

via the exchange of excitons. It may be interesting to note that ac

susceptibility and resistivity anomalies above 90 K over a temperature

range of 10–20 K in the thermally non-equilibrium state during rapid

warming were also detected, corresponding to a possible paramagnetic-

diamagnetic-paramagnetic transition. No deﬁnitive conﬁrmation or

refutation has been reported to date. It has been suggested that a more

complex material than CuCl, due to its disproportionation in rapid cool-

ing under pressure, may be responsible for the observation. Given the

role of Cu in HTS and certain similarities appearing in HTS and CuCl

under pressure and rapid cooling, another visit may be warranted.

(iii) Since the discovery of YBCO, there have been numerous claims of T

in cuprates close to 300 K.

None satisﬁed the four criteria I set for

a genuine superconductor: i.e. zero resistivity, large diamagnetic shift

decisively showing the Meissner eﬀect, high stability long enough for

a deﬁnitive diagnosis and good reproducibility from sample to sample

and from lab to lab. These reports may at best be called Unidentiﬁed

Superconducting Objects (USOs). Some of the USOs have been shown

to arise from experimental artifacts or from misinterpretation of the

data. However, the high frequency of sighting USOs in the similar high

temperature range (∼240–300 K) and in some reputable labs makes

these USOs too tantalizing to ignore. In view of the extremely unstable

chemical nature of the cuprates, and the small coherence length for

HTS with very high T

, the ﬂeeting nature of USOs reported may not

be totally unexpected.

4.3. Examples of visionary predictions

Many visionary predictions have been made to reach the RTS-wonderland.

A few examples proposed in 1960s and 1970s that may still provide valuable

inspiration are given below:

• In 1964, Little

examined the question originally posed by London —

whether superconductivity occurs in organic macromolecules within the

framework of the BCS theory — and concluded that superconductivity

above room temperature is not only possible but also expected in or-

ganic macromolecules of a special design. The proposed model macro-

molecule consists of a long spine and a series of side chains. By choosing

September 14, 2010 9:46 World Scientiﬁc Review Volume - 9.75in x 6.5in ch16

432 C. W. Chu

the molecules in the side chains with proper oscillation of charges, the

electrons in the spine can be polarized to form pairs via the exchange of

excitons with the side chain molecules. According to Little’s estimation,

a superconductivity transition should occur at temperatures well above

room temperature. One challenge in realizing Little’s vision is in synthe-

sizing and characterizing the macromolecules with the proposed design.

With the great advancement in material syntheses and diagnostic tech-

niques for nanomaterials made in recent years, an attempt to produce and

characterize macromolecules including the model macromolecule proposed

by Little may be worthwhile and timely.

• In 1964, Ginzburg

noticed the possible drawbacks of the one-dimensional

organic macromolecule superconductor proposed by Little, such as ﬂuctu-

ations, instabilities and lack of Coulomb screening, and therefore focused

instead on two-dimensional materials. He proposed a novel mechanism to

enhance T

within the weak limit of BCS, i.e. to increase T

to as high as

105 K by taking advantage of the high characteristic temperature Θ

the electron-electron interaction via the exchange of excitons. In order to

facilitate the so-called exciton mechanism, he conjectured that one should

consider the following material systems: metallic thin ﬁlms, metal surfaces

covered by dielectrics, metal sandwiches with dielectrics in between and

two-dimensional layer compounds. Many experiments were done in the

ensuing years but did not yield clear conﬁrmation. It may not be surpris-

ing to ﬁnd a connection between the layered materials Ginzburg proposed

and the layer cuprate and Fe-pnictide HTSs. New understanding and

synthesis-knowledge of layer HTS materials in the last two decades will

provide new means to test the proposal.

• In 1973, Allender, Bray and Bardeen

carried out a more rigorous analysis

on a simple model system to explore the existence of the exciton mech-

anism and its impact on T

, if it exists.

Their model material consists

of a metal thin ﬁlm of Fermi energy E

on a semiconductor of a narrow

gap of E

. They concluded that T

can indeed be enhanced by adding the

exciton mechanism to the phonon mechanism when the material condi-

tions are optimized and that the exciton mechanism is a promising vehicle

for higher T

. They also pointed out the diﬃculty in creating the model

material system with the proper metal/semiconductor interfaces that sat-

isfy the stringent requirements. Several experimental attempts had been

made before the late 80s but with no success reported. With the recent

advancement in multi-thin-ﬁlm synthesis, one should be able to artiﬁcially

prepare samples satisfying the stringent criteria speciﬁed for the exciton

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The Evolution of HTS: T

-Experiment Perspectives 433

mechanism. Naturally occurring metal/semiconductor layered compounds

may be a good alternative if the E

is adjusted to be located in the middle

of E

4.4. Common features of superconductivity with high T

At the moment, we do not yet know enough about a RTS other than that

it has a T

> 300 K, as we have chosen, to ask intelligent questions with

answers that will lead us to the promised land of RTS. It is also not unlikely

that a RTS to be discovered may turn out to be a very diﬀerent material from

the HTSs to which we are accustomed. However, being a superconductor,

VHTS and/or RTS has to have the basic superconducting characteristics

and very likely has to share at least some features with the HTSs we have.

A summary of these features is considered most helpful and can serve as a

launching pad for our attempt to look for VHTS and/or RTS.

4.4.1. Electron-pairing and phase-coherence

According to the BCS theory, electron-pairing and phase-coherence are the

very basic features of a superconducting state that exhibits zero resistivity

(ρ = 0) and perfect diamagnetism (magnetic induction B = 0). It has

long been accepted that electron-pairing and phase-coherence occur at the

same temperature, T

, for LTSs. However, suggestions have been made that

electron-pairing may precede phase-coherence at a temperature higher than

in the cuprate HTSs. If true, the feature provides a new degree of freedom

in the search for VHTSs.

4.4.2. Strongly correlated electron systems with multi-interactions

The current HTSs belong to the class of materials of transition metal oxides

and pnictides where strongly correlated electrons exist. Strongly correlated

electron systems are rich in electronically induced phase transitions over a

wide temperature range and therefore may provide various avenues to HTS.

Figure 20 shows schematically the linkages between magnetism and super-

conductivity and between magnetism and ferroelectricity in strongly corre-

lated electron systems. In contrast to the original thinking, we now ﬁnd that,

under the proper conditions, magnetism and superconductivity can enforce

each other; similarly, magnetism and ferroelectricity can help each other. I

believe that if the missing link between ferroelectricity and superconductiv-

ity is found, higher T

can be achieved. Optimization of multi-interactions

will be the key.

September 14, 2010 9:46 World Scientiﬁc Review Volume - 9.75in x 6.5in ch16

434 C. W. Chu

Fig. 20. The interplay between the superconducting-magnetic and ferroelectric-

magnetic interactions in strongly correlated electron systems, where P is pressure,

H is magnetic ﬁeld and E is electric ﬁeld.

4.4.3. Instabilities and ﬂuctuations

In the strongly correlated electron systems to which HTSs belong, there

exist various electronic, phononic and electric charge instabilities, e.g.

superconducting, structural, antiferromagnetic, ferromagnetic, ferroelectric,

antiferroelectric, metal-insulator, charge-density-waves, spin-density-waves,

charge-order, orbital-order, etc., some of which can induce transitions at

very high temperatures. The associated ﬂuctuations may become a source

of electron pairing for superconductivity. The eﬀect becomes most eﬀective

at temperatures near the phase transition, which is tunable by both physical

and chemical means.

4.4.4. Layered structure with multi-substructures

Reduced dimensionality has been shown to facilitate high T

, generally due

to the relatively large density of states and the stronger electron-electron

interaction associated with a 2D electron system. Compounds with two

distinct substructures have an extra advantage: the active block for su-

perconductivity to take place and the charge reservoir block to provide

charge carriers for inducement of superconductivity and suppression of un-

wanted ordering through doping and/or physical means, while keeping the

integrity of the layers and minimizing defects in the layer substructure for

superconductivity.

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The Evolution of HTS: T

-Experiment Perspectives 435

4.4.5. Covalency, mixed valence and low carrier density

Both cuprate and Fe-pnictide HTSs appear to originate from a magnetic

insulating parent state through doping or pressure by changing the carrier

density. Mixed valence states appear to be indispensable for the parent

compounds to evolve into a conducting state with strong covalency to achieve

high T

. Conducting compounds of this kind will have low carrier density.

4.5. A holistic, multidisciplinary, enlightened empirical

approach

In philosophy, scholars have long debated “Empiricism versus Rationalism.”

The diﬀerence between the two lies mainly in the diﬀerent relationships

between reason and knowledge and between experience and knowledge: em-

piricists consider experience to be the source of knowledge and independent

of reason, while rationalists claim reason to be the source of knowledge and

independent of experience. In the long search for superconductors of higher

, Matthias and Mueller reminded us at diﬀerent times of the eﬀectiveness

of the empirical approach.

The study of HTS in the past shows that HTS and future RTS are both

all-encompassingly complex in terms of materials, physics and chemistry.

It appears that a holistic, multidisciplinary, enlightened empirical approach

that embodies both experience and reason and engages researchers, experi-

mental and theoretical, from diﬀerent disciplines with complementary exper-

tise appears to be most eﬀective to lead us to achieve VHTSs and/or RTSs.

The historical review given above can guide us enlightened-empirically to the

most fruitful future path to VHTSs and/or RTSs. It includes also some of

the interesting claims that may warrant further tests, some visionary predic-

tions that may be pursued and the common features of superconductors with

high T

that may form the general basis for the search for novel supercon-

ductors. The worldwide extensive studies on HTS cuprates, Fe-pnictides and

heavy fermion superconductors over the decades have given us unusual physi-

cal insight into materials, powerful computational capabilities for materials,

sensitive material characterization techniques and new materials synthesis

tools. The time is ripe to bring all these skills to bear in the search for novel

superconductors with higher T

, preferably at room temperature. If history

is any guide, I strongly believe that, in the process, in addition to higher T

new physics will be discovered and novel materials found with both scientiﬁc

and technological signiﬁcance.

September 14, 2010 9:46 World Scientiﬁc Review Volume - 9.75in x 6.5in ch16

436 C. W. Chu

5. Conclusion

High-temperature superconductivity never ceases to excite scientists, engi-

neers and the general public because of the continuing challenges it poses to

scientists and the promises it holds for technologists. The search for HTS

commenced immediately after the discovery of superconductivity by Kamer-

lingh Onnes in 1911. As described in Sec. 1, HTS is a relative term because

varies with time and the whole period of superconductivity is divided into

three periods for the convenience of presentation in this paper, namely, LTS,

HTS and VHTS and/or RTS. Brief recounts of the discoveries of the major

HTS material systems were given.

The era of modern HTS was heralded by the discovery of cuprate

superconductors in 1986 and the tumbling down of the 77 K liquid-nitrogen

temperature barrier in 1987. In the ensuing years, impressive progress has

been made in HTS following the extensive world-wide eﬀort: T

has risen

continuously to the current record of 134 K at ambient and 164 K at 30 GPa,

many new compounds discovered, new physics uncovered, numerous theo-

retical models proposed, various theoretical and experimental techniques

developed, and many prototypes constructed and demonstrated. However,

the record-T

has stagnated since 1993, a commonly accepted microscopic

theory has yet to be found and the full technological prowess of HTS is yet

to be developed.

Although HTS reduces the burden of cryogenic cooling and a VHTS

will further reduce the burden, making superconductivity applications more

practical, RTS will eliminate completely the need for cooling and applications

will become ubiquitous. Unprecedented scientiﬁc excitement and challenges

associated with VHTS and RTS are expected. There exists no theoretical

or experimental reason why VHTS or RTS is impossible. In addition, I

believe that whatever physics laws do not say cannot happen will happen

eventually. It appears that a holistic comprehensive enlightened empirical

approach may be most eﬀective in the search for VHTS and/or RTS and

some speciﬁc steps have been proposed by optimizing the multi-interactions,

controlling the instabilities, and eﬀectively introducing charge carriers to

materials with characteristics as described in Sec. 4.4.

Acknowledgments

I would like to thank my colleagues Yuyi Xue and Bernd Lorenz for dis-

cussions and in the preparation of ﬁgures. Partial support for the work in

September 14, 2010 9:46 World Scientiﬁc Review Volume - 9.75in x 6.5in ch16

The Evolution of HTS: T

-Experiment Perspectives 437

Houston by the U.S. Air Force Oﬃce of Scientiﬁc Research, the U.S. Depart-

ment of Energy through Oak Ridge National Laboratory, the T.L.L. Temple

Foundation, the John J. and Rebecca Moores Endowment, and the State

of Texas through the Texas Center for Superconductivity at the University

of Houston; and at Lawrence Berkeley Laboratory by the Director, Oﬃce of

Science, Oﬃce of Basic Energy Sciences, Division of Materials Sciences and

Engineering of the U.S. Department of Energy is greatly appreciated.

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27. See, for example C. W. Chu and B. Lorenz, Physica C 469, 326 (2009) and

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August 30, 2010 11:44 World Scientiﬁc Review Volume - 9.75in x 6.5in ch17

THE EVOLUTION OF HIGH-TEMPERATURE

SUPERCONDUCTIVITY: THEORY PERSPECTIVE

Elihu Abrahams

Center for Materials Theory, Serin Physics Laboratory,

Rutgers University, Piscataway, NJ 08854, USA

and

∗

Department of Physics and Astronomy,

University of California, Los Angeles,

405 Hilgard Avenue, Los Angeles, CA 90095, USA

Theoretical developments concerning the high transition temperature

cuprate superconductors are reviewed.

1. Historical Remarks: Strongly-correlated Electrons

It is often pointed out that the discovery in 1986, by J. G. Bednorz and

K. A. M¨uller, of superconductivity at 30 K in lanthanum barium copper ox-

ide

generated a historically unprecedented volume of research papers. They

ranged from materials preparation to reﬁned experimental technique to novel

theoretical proposals and tools. In the domain of theory, no paper has been

more inﬂuential than that of P. W. Anderson on the resonating valence bond

(“RVB”) state and superconductivity

in 1987. This paper, although con-

centrating on RVB as a consequence of strong electron–electron correlations,

did set a particular framework for addressing the physics of the cuprates,

as well as emphasizing the problem of the physics of situations in which the

largest energy scale is determined by electron–electron interactions, rather

than by the kinetic energy (in contrast to the circumstances of the familiar

Landau Fermi-liquid approach

Such situations are the domain of the modern many-body problem in

condensed matter physics. The theoretical challenge is to ﬁnd methods

to treat systems in which strong interactions dominate the physics: when

perturbative methods fail and/or when ﬂuctuations are so strong that

∗

Current address

439

August 30, 2010 11:44 World Scientiﬁc Review Volume - 9.75in x 6.5in ch17

440 E. Abrahams

mean-ﬁeld treatments are inadequate. The explosion of activity in this ﬁeld

of strongly-correlated electrons is due in part to the aforementioned seminal

article of Anderson.

Of course, high-temperature superconductivity is not the ﬁrst case of

strongly-correlated electron physics in condensed matter. Other examples,

which attracted much attention earlier and are still important problems

include the Kondo problem, the so-called heavy-fermion metals, quantum

antiferromagnetism and other magnetic states, metal-insulator transitions,

non-Fermi liquid normal metallic states, quasi-one-dimensional systems . . .

Nevertheless, it is the case that much of the intense activity in recent years

to construct frameworks beyond the Fermi liquid that are suitable for the

strong-correlation situation has been generated by the mysteries of high-

temperature superconductivity.

The Bardeen-Cooper-Schrieﬀer (BCS) theory of superconductivity,

which this volume commemorates, and its strong-coupling extensions,

bril-

liantly accounted for “conventional” superconductivity. It is also a beautiful

exemplar of the fundamentals of the practice of theoretical condensed matter

physics. Starting from the complicated many-body Hamiltonian for a solid,

containing the dynamics and interactions of electrons and ions, one needs

to systematically remove the irrelevant degrees of freedom. In general, this

results in a reduced Hamiltonian that contains everything necessary to cap-

ture the low-energy physics of the system. Thus, in the BCS case, even the

electron–phonon interaction on which the theory is based is not explicitly

treated. Instead, the reduced Hamiltonian contains only the kinetic energy

of the Fermi liquid quasiparticles of the normal state and a short-range

attractive interaction between them. Remarkably, this is suﬃcient to

account for all the essential physics of most conventional “low-temperature”

superconductors.

2. Phase Diagram and Eﬀective Hamiltonians

In contrast to conventional superconductors, the cuprates are complex

materials with many unique properties determined by strong repulsion be-

tween the mobile carriers. It is worthwhile to illustrate the complexity of

the physics of the cuprates by showing a sketch of a typical phase diagram,

Fig. 1. In this phase diagram we can see a number of themes that dominate

current research on strongly-correlated materials, in particular competing

phases and quantum critical points. For the cuprates, three of these phases

have received the most attention. The mystery of the superconducting phase