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The Evolution of HTS: T

-Experiment Perspectives 421

tivity could not be unambiguously resolved at the time because of the poten-

tial segregation of the magnetic dopant from the superconducting host. The

impasse was alleviated later when rare-earth (R) containing ternary com-

pounds were discovered, such as the rare-earth containing rhodium borides

series RRh

and Chevrel series RMo

. Superconducting, antiferromag-

netic and ferromagnetic orderings were found in these compounds, clearly

showing the coexistence of superconductivity with antiferromagnetism in

bulk form and with ferromagnetism in a real-space modulated state known

as the FFLO state. Antiferromagnetism was also shown to augment super-

conductivity as evidenced by the enhanced H

of some magnetic supercon-

ductors. While magnetism and superconductivity exist and interact in the

chemically ordered lattice of these compounds, they occur in two loosely

coupled sublattices, e.g. magnetism in the R-ion sublattice and supercon-

ductivity in the Mo

-cubes of RMo

In the 1970s, intermediate valence compounds, with an enhanced Som-

merfeld coeﬃcient γ = Ce/T of the electron speciﬁc heat C

and a quadratic

temperature dependent resistivity ρ = ρ

+ AT

at low temperature, had at-

tracted great attention. Since γ is proportional to the eﬀective electron mass

∗

, the enhanced value observed indicates that the electrons are strongly

correlated and heavily renormalized. Some of these compounds display a γ

that is orders of magnitude greater than that of the ordinary metallic com-

pounds. This was clearly demonstrated by experiments on CeAl

where

the conduction electrons near the Fermi surface are strongly renormalized

with a γ = 1.620 mJ/(mole.K

), an exact T

-term with A = 35 µΩ cm/K

and the development of coherence among the lowest lying virtual bound

states below 0.2 K. Heavy fermion systems were born, arising from the close

proximity of the 4f electrons to the Fermi energy.

The discovery of the heavy fermion superconductor CeCu

by Frank

Steglich et al.

of the Technical University of Darmstadt in 1979 demon-

strated for the ﬁrst time that highly renormalized electrons with heavy mass

can condense into an otherwise itinerant superconducting state. This repre-

sents a quantum advancement to unravel the intricate interplay of magnetism

with superconductivity, to uncover the nature of the superconducting state

and to reveal the fascinating normal state properties of rare-earth inter-

metallic compounds. It leads to the development of the exciting ﬁeld of

strongly correlated electron systems to which heavy fermion superconduc-

tors belong. In fact, the large γ associated with CeCu

also raised some

interest in the early days to search for superconductors with high T

in large

γ materials. The eﬀort was quickly abandoned, since the T

of heavy fermion

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

422 C. W. Chu

superconductors has never exceeded a few degrees, although ﬁnally reached

18.5 K years later in 2002.

I shall review the history of the discovery of the heavy fermion supercon-

ductors. Much of the exciting physics revealed by experiments over the last

three decades on this class of materials has been detailed elsewhere.

3.3.1. Ce-based heavy fermion superconductors: CeM

with M = Cu,

Pd, Rh or Ni and X = Si or Ge; Ce

MIn

3n+2

where M = Co or

Rh, Ir and n = 1 or 2; noncentrosymmetric superconductors

3.3.1.1. CeM

with M = Cu, Pd, Rh or Ni and X = Si or Ge

In the process of exploring how superconductivity or magnetism interacts

with a “third kind” of collective phenomenon, i.e. the Kondo or intermediate-

valence phenomenon, Frank Steglich et al. of the Technical University of

Darmstadt discovered

the ﬁrst heavy fermion superconductor, CeCu

characterized by the typical signatures of a bulk superconductor, i.e. a zero

resistivity below T

∼ 0.5 K, a Meissner eﬀect below ∼0.6 K and a large

speciﬁc heat jump ∆C at T

(Fig. 17). What seems most unusual of all are

its large γ = 1 J/mole-K

, its large Pauli susceptibility and its ∆C/γT

∼ 1.4

close to the BCS value. The ﬁrst two show that the conduction electrons

near the Fermi level in the normal state of CeCu

are highly renormalized

heavy electrons due to their hybridization with the 4f magnetic electrons

and the last demonstrates that the same heavy electrons participate in the

superconducting process. The observations show that magnetism plays a

crucial role in both the normal and superconducting states of CeCu

In contrast to previous magnetic superconductors, CeCu

embodies

superconductivity and magnetism in the same electron system. The excit-

ing results changed and broadened Kondo physics research. They were pub-

lished in the December 17, 1979, issue of Physical Review Letters in an article

entitled “Superconductivity in the Presence of Strong Pauli Paramagnetism:

CeCu

” (Fig. 17).

CeCu

crystallizes in the tetragonal ThCr

-type layer structure of

the I4/mmm space group similar to AFe

, the A122 Fe-pnictide super-

conductors. Under pressure, the T

rises from 0.5 K rapidly up to 2.25 K

at 2.5 GPa

and decreases at higher pressures. Despite the signiﬁcance of

the discovery of CeCu

, the material complexity encountered and the ini-

tial skepticism associated hampered studies of the compound for many years.

For example, a slight deviation from stoichiometry, e.g. a few % Cu-deﬁcient,

drastically changes its ground state from superconducting to antiferromag-

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

The Evolution of HTS: T

-Experiment Perspectives 423

Fig. 17. ρ(T ) of CeCu

shows a T

∼ 0.6 K in 1979 by Steglich et al. [F. Steglich

et al., Phys. Rev. Lett. 43, 1892 (1979)].

netic. The isostructural series CeM

with M = Cu, Pd, Rh or Ni and X

= Si or Ge were successful synthesized only after 1993. They were found to

be heavy fermion compounds and become superconducting under pressures

with a T

below 1 K, except in the case of CeNi

, which is superconduct-

ing below 0.64 K at ambient. The ensuing extensive investigation on pure

and mixed compounds of the CeM

series shows that they are strongly

correlated electron systems and that the superconductivity in CeCu

not conventional of the BCS-type but arises from electron-electron interac-

tion that is magnetic in nature. Clearly, the CeM

compounds sit on the

border between magnetism and superconductivity, exhibiting competition

and/or enforcement between the two interactions and also display instabil-

ities associated with the ambivalent nature of Ce. The CeM

supercon-

ductors and cuprate HTSs bear many resemblances, although with a huge

gap between their T

3.3.1.2. Ce

MIn

3m+2

where M = Co or Rh, Ir and m = 1, 2, . . . , ∞

MIn

3m+2

crystallize in the tetragonal layer structure of space group of

P4/mmm, which consists of layers of CeIn

interleaved by MIn

-layers. They

also sit close to the border between antiferromagntism and superconductiv-

ity. While CeCoIn

and CeIrIn

are superconducting at ambient at the

edge of an antiferromagnetic quantum critical point, CeIn

, CeRhIn

and

RhIn

are antiferromagnetic at ambient but become superconducting

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

424 C. W. Chu

under pressures. Aside from detailed and some subtle diﬀerences, they

exhibit the complex phase diagrams that are similar to CeM

and bear

some resemblance to cuprate HTSs. For instance, CeIn

, which can be con-

sidered the parent compound of the series, i.e. for m = ∞, orders anti-

ferromagnetically at a T

= 10.2 K and becomes superconducting at a

= 0.18 K when T

is suppressed to < 0.18 K by a pressure of 2.6 GPa.

Its P (T ) phase diagram is similar to that for the cuprate HTSs and its su-

perconductivity has been shown to be magnetically mediated. It should be

noted that CeCoIn

has the highest T

among the Ce-based heavy fermion

superconductors, but only at 2.3 K.

3.3.1.3. The noncentrosymmetric heavy fermion superconductors:

CePt

Si, CeIrSi

, CeRhSi

, CeCoGe

The study of the eﬀect of crystal symmetry on T

has a long history in

superconductivity research, reaching back to Matthias’ days. For instance,

it was thought that cubic compounds favored high T

. The absence of cen-

trosymmetry in thin-ﬁlm and amorphous superconductors has long been rec-

ognized but without detailed research. The relationship between the spatial

symmetry and the electron-pairing symmetry of a superconductor is of great

academic and device interest but was not actively pursued until the discov-

eries of heavy fermion superconductors and HTSs. The strong spin ﬂuctua-

tions in strongly correlated electron systems have been shown to suppress the

conventional s-wave superconductivity but to allow the spin-triplet pairing,

provided that time reversal symmetry and inversion symmetry are preserved.

In other words, spin-triplet pairing cannot exist in a heavy fermion supercon-

ductor without centrosymmetry. The recent discovery of noncentrosymmet-

ric heavy fermion superconductors CePt

Si, CeIrSi

, CeRhSi

and CeCoGe

was surprising.

They all undergo an antiferromagnetic transition at diﬀer-

ent T

s < 21 K and enter a superconducting state under pressures at lower

temperatures. Strong spin-orbit coupling has been proposed to alleviate

the impasse in these noncentrosymmetric heavy fermion superconductors.

Extensive experiments were carried out and indeed found spin-orbit cou-

pling in these compounds although of diﬀerent strength and isotropy.

3.3.2. U-based heavy fermion superconductors: UBe

, UPt

, URu

UPd

, UNi

UGe

, URhGe, UCoGe

In 1975, Bucher et al. of Bell Labs investigated the magnetic and crystal-ﬁeld

properties of the easily formed MBe

series with M being a rare earth, Th

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

The Evolution of HTS: T

-Experiment Perspectives 425

or U, in their search for better compounds for nuclear cooling and nuclear

ordering. In contrast to expectation, they did not detect the temperature-

independent Van Vleck susceptibility or any magnetic ordering down to

0.65 K in UB

. Instead, they observed a sharp superconducting transition

at 0.97 K with a very high critical ﬁeld and a speciﬁc heat that increases upon

cooling below 4 K giving an estimated γ ∼ 1 J/mole-K

at ∼1 K. At the

time, a very high critical ﬁeld was known to occur only in superconductors in

ﬁlamentary form. The observed superconductivity in UBe

was therefore at-

tributed to possible ﬁlamentary U impurity. The discovery of heavy fermion

superconductivity was unfortunately missed. Eight years later in 1983, Hans

Ott and colleagues at ETH Zurich and LANL believed that UBe

might be

the U-version of the CeCu

heavy fermion superconductor and decided to

revisit it. They did systematic measurements on the magnetic and thermal

properties of both the poly- and single-crystalline UBe

and demonstrated

unambiguously that UBe

is a bulk superconductor as evidenced by the zero

resistivity at 0.85 K accompanied by a speciﬁc heat jump (Fig. 18). Similar

to Bucher et al., they observed a large γ = 1.1 J/mole-K

, a large Pauli

magnetic susceptibility and a high critical ﬁeld and concluded that UBe

indeed a heavy fermion superconductor. The discovery of the second heavy

fermion superconductor and the ﬁrst containing the 5f -electrons of actinides

was published in the May 16, 1983, issue of Physical Review Letters in an

article entitled “UBe

: An Unconventional Actinide Superconductor.”

UBe

crystallizes in the cubic NaZn

-type structure with the Fm3c

space group. It is the only compound formed congruently in the U-Be sys-

tem. Quality UBe

samples can thus be obtained readily once the Be-

toxicity and the U-supply issues are resolved. The unambiguous UBe

results in comparison with CeCu

in its early stage accelerated the

research on heavy fermion superconductivity. The T

of UBe

was found

to decrease with pressure while the normal state resistivity returns more

to the conventional coherent Kondo-lattice-like. The Th-doped samples

1−x

exhibit a complex phase diagram with two superconducting

phases for 2% < x < 4%. Many studies on UBe

in the ensuing years

have seemed to show that it is rather diﬀerent from other heavy fermion

superconductors and still leave some questions about its magnetic and su-

perconducting properties unanswered.

Soon after the discovery of UBe

, UPt

was discovered

as the

third heavy fermion superconductor with a T

∼ 0.54 K and a large

γ ∼ 1 J/mole-K

in 1984. It is perhaps the most extensively studied heavy

fermion superconductor with an unambiguously established unconventional

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

426 C. W. Chu

Fig. 18. χ(T ) and C

(T ) of UBe

shows a T

∼ 0.85 K in 1983 by Ott et al.

[H. R. Ott et al., Phys. Rev. Lett. 50, 1595 (1983)].

superconducting state with a spin-triplet f -wave pairing. Later speciﬁc heat

measurements showed a second superconducting transition at 0.48 K at zero

ﬁeld. In the presence of a magnetic ﬁeld, H

(T )s for the ﬁrst and second

superconducting phases cross at 0.44 K and 0.6 T and evolve into a third

superconducting phase above 0.6 T between the two H

(T )s. An unusual

tetracritical point therefore forms. Seven more U-based heavy fermion su-

perconductors were discovered after 1984. Some (UPt

, URu

, UPd

UNi

) order antiferromagnetically before entering their superconducting

state on cooling, while others (UGe

, URhGe, UCoGe) become ferromagnetic

before undergoing a superconducting transition (for UGe

, under pressure,

but for URhGe and UCoGe, at ambient). Similar to the Ce-based heavy

fermion superconductors, their superconducting states take place deep in

the magnetically ordered states, be it ferromagnetic or antiferromagnetic.

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

The Evolution of HTS: T

-Experiment Perspectives 427

Fig. 19. T

–T

∗

where T

∗

measures the strength of spin-ﬂuctuations [C. Pﬂeiderer,

Rev. Mod. Phys. 81, 1551 (2009); plot from N. Curro et al., Nature 434, 622 (2005)

as shown in J. L. Sarrao and J. D. Thompson, J. Phys. Soc. Jpn. 76, 051013

(2007)].

3.3.3. Actinide-based heavy fermion superconductors: PuCoGa

PuRhGa

, NpPd

The actinide-based PuCoGa

, PuRhGa

and NpPd

are all unconven-

tional superconductors at ambient with the highest T

among all heavy

fermion superconductors at 18.5 K, 8.7 K and 4.9 K, respectively.

The

high T

s have been attributed to the 5f -electrons, which have been shown

to sit at the border between itinerancy and localization, signaling some kind

of instabilities, and to have a wider band-width and stronger spin-orbit cou-

pling compared with the 4f -electrons. These unusual characteristics place

this group of compounds between the 3d-HTSs and the 4f-heavy fermion

superconductors and become the bridge between the two, as clearly demon-

strated by the T

–T

∗

relation where T

∗

is the characteristic temperature

of the spin-ﬂuctuations in the compounds (Fig. 19). Such a T

–T

∗

seems

to suggest that the study of heavy fermion superconductors may provide

insight into the underlying working mechanism of HTS and may even lead

to higher T

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

428 C. W. Chu

4. The VHTS (or RTS)-Period: 2009

The designation of the very high temperature superconductivity (VHTS)

or, more aggressively, room temperature superconductivity (RTS) period

after 2009 is rather subjective and speculative in terms of materials and

commencing time. It reﬂects in part the hope and vision of the practitioners

in the ﬁeld and the public in general. The year 2009 also coincides with the

year when the U.S. Department of Defense and other federal funding agencies

started making a conscientious push for the search for novel superconductors

with higher T

to harness the fruits of the accumulative knowledge on HTS

over the last 23 years. During this period, it is anticipated that the focus

will be on existing as well as the yet-to-be discovered materials to achieve

VHTS with a T

higher than the current record, preferably RTS, and at the

same time, to obtain new insight into HTS and to uncover new physics.

In the last 20 years, many theoretical models have been advanced to

account for numerous unusual observations in HTSs and many HTS proto-

type devices constructed and demonstrated successfully with superior per-

formance to their non-superconducting counterparts. To take advantage

of the full prowess of superconductivity for our daily lives, RTSs will be

the ultimate goal, although lofty. VHTSs will reduce the burden of cool-

ing and RTSs will eliminate completely the inconvenience of cooling. Even

before the discovery of superconductivity, people were already fascinated by

the concept of perpetual motion machines in our lives and RTS is consid-

ered the closest thing to such a machine. Therefore, RTS found its way

into popular culture from science-ﬁction to cinema before it became serious

science. The most recent example is the “Unobtainium” in the highest gross-

ing movie Avatar. RTS, if achieved, could profoundly change the world

scientiﬁcally and technologically.

4.1. A practical room temperature superconductor

As a graduate student in 1967, I asked my thesis advisor, the late Professor

Bernd T. Matthias, whether there existed a RTS and if yes, where. His

answer was succinct and direct: “Yes, just go to the edge of the universe.”

At the time, he had just discovered a T

∼ 21 K in a pseudoternary inter-

metallic compound, Nb

(Al,Ge) and the ambient temperature at the edge

of the universe is 3 K, residue of the Big Bang. A 21 K superconductor is

thus a RTS at the edge of the universe. However, the edge of the universe

is more than 13 billion light years away from us, an astronomical distance

that indeed can be reached by us only in our dreams. Therefore, strictly

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The Evolution of HTS: T

-Experiment Perspectives 429

speaking, RTS is a relative term, depending on its operating environment

temperature. In principle, one can achieve RTS either by raising the T

a superconductor or by lowering the ambient temperature of the operating

environment so that the two temperatures can cross. In this discussion, our

goal is to raise the T

Over the years, diﬀerent target-T

s have been set at diﬀerent times,

e.g. 77 K (liquid nitrogen boiling point before YBCO), 100 K (inside the

cargo bay of the Space Shuttle or on the moon’s surface opposite the sun

before TBCCO), 120 K (liquid natural gas boiling point before HBCCO),

148 K (liquid Freon boiling point before HBCCO under pressure), 198 K

(dry ice temperature) and 300 K (temperature of our living environment).

With the superconductors we have, many of these target temperatures have

been reached. Unfortunately, they are still not practical for the ubiqui-

tous applications of superconducting devices in our daily life. For instance,

HgBa

with the current record T

of 164 K under high pressure

can be considered a RTS in a liquid Freon environment, achievable by an

air conditioner. However, the high pressure required renders it impractical

not to mention the undesirable eﬀect of Freon on the protective ozone layer

in our upper atmosphere. As a result, the practical and desirable RTS that

we want today is one that has a T

of 300 K, high enough so that its su-

perconducting state can be achieved in our living environment without any

cryogenic cooling. On the other hand, in order to take advantage of 90% of

the maximum current-carrying capacity of a superconductor, the operating

temperature usually should be kept at ∼70% of its T

or lower. For an op-

erating temperature of 300 K of our living environment, the T

required will

therefore be ∼430 K. However, we shall be very happy to settle for a T

300 K. The discovery of such a superconductor will have an all-encompassing

impact on our lives and a new industrial revolution will follow. According

to our current theoretical understanding and experimental evidence, there

exists no reason why RTS should be impossible.

4.2. Examples of interesting claims

The long and tortuous path in the search for superconductors with higher T

has been dotted with triumphs of success and agonies of failure, including

extravagant claims. Being an optimist who believes that whatever is not

prohibited by the basic laws of physics will happen, I do not dismiss claims

outright until they are proven false by reasoning or by testing them experi-

mentally to the best of my ability. Consequently, I have been contacted by

many such claimers. Unfortunately, so far, to ﬁnd them not superconducting

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430 C. W. Chu

is the norm, let alone superconducting at room temperature. Examples are

abundant, but let me just cite just a few for amusement. A few years ago,

the head of a California based company contacted me and asked me to test

samples of an alleged RTS polymer material developed in the former Soviet

Union with published references. I did but found them to be insulating. In

another example, the anchor lady of a reputable TV program asked me to

test a piece of material that was allegedly left by an extraterrestrial vehicle

in an Arizona desert and determined by a few reputable labs to be supercon-

ducting at room temperature in the presence of a strong microwave. I found

it to be a rather ordinary metal, containing elements such as Fe, Mn, In,

etc., and not superconducting. Yet another example was a call several years

ago from a Croatian physicist who asked me to sign a disclosure agreement

before faxing me information about the RTS he discovered. After seeing his

faxed message, I had some doubts but still repeated what was described in

the message. When told of our negative results, he attributed them to our

alleged poor sample quality. Still giving him the beneﬁt of doubt, I asked for

a piece of his sample to test, but he wanted me to purchase it after he mass-

produced it and put it on the market before Easter that year. Unfortunately,

I have yet to hear from him since that Easter.

While many of the claims can be ignored outright due to experimen-

tal artifacts or dismissed after cursory examinations, others are interesting

and may be worth further examination. Revisiting these may lead to new

understanding of HTS and new mechanisms for HTS, in addition to possible

higher T

. I shall brieﬂy describe three such examples below:

(i) In 1946, Ogg reported

a large drop in resistance and the presence of

persistent current in their sodium-ammonia solution at temperatures

as high as 180 K upon rapid cooling but not on slow cooling. He at-

tributed the observations to superconductivity arising from possible

Bose–Einstein condensation of electron-pairs. Conﬂicting experimen-

tal reports followed immediately and interest died oﬀ rapidly. Interest

in this material system was renewed in the early 1970s, mostly in the

former Soviet Union, but waned in the late 1970s. However, the topic

has been picked up by some recently in the West. As the study of HTS

progresses, similarities between cuprates and the Na-ammonia can be

found, such as phase-separation, possible occurrence of phase coherence

and pairing at diﬀerent temperatures, etc. It may be time to bring the

vast knowledge and sophisticated diagnostic tools developed for HTS in

the last 23 years to bear on unraveling the mystery of this interesting

system.