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

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14 High-T

Superconductivity 767

perconductors contain four or more constituents

in their chemical composition and their crystallo-

graphic structures, although being rather similar for

all of them, exhibit some intricate details whose im-

portance is still debated. It is for this reason that,be-

fore presenting and discussing a selection of physical

properties of high-T

superconductors, a section on

materials aspects including chemical compositions

and crystal structures is inserted at the beginning of

this chapter. An additional justification for this sec-

tion is the fact that more recently,solids with similar

structural properties have attracted a lot of attention

in other areas of condensed matter research, involv-

ing spin charge and orbital ordering phenomena [8].

With respect to physical properties in general and

to features of the superconductingstate in particular,

we shall concentrate on some typical aspects rather

than list and present many details. For instance, the

entire field of vortex physics that has emerged and

has attracted a lot of attention in connection with

high-T

superconductors, is discussed in a special

chapter of this treatise.

It was recognized very early [9] that the cuprate

materials, which exhibit the highest critical temper-

atures for superconductivity at present, cannot sim-

ply be regarded as common metals, because even the

normal state of these materials exhibits anomalous

features that are difficult to understand. Therefore,

some attention is also given to properties of the nor-

mal state above T

14.2 Typical Structural Characteristics

Although, as pointed out above, no consensus about

the real causes for superconductivityat elevated tem-

peratures has yet been achieved, all relevant materi-

als to be discussed here, with the exception of the

fullerenes and MgB

,insomewayshareacommon

structural feature and this is the unit cell of the per-

ovskite structureshown in Fig.14.2.This structureis

adopted by ABO

compounds in which A is a fairly

large cation and B, a metal element, helps to form a

three-dimensional array of corner-sharing BO

octa-

hedra. The undistorted version is cubic,as indicated

in Fig. 14.2, and only very few compounds for which

the ionic radii of theA atoms are of sufficientsize,are

Fig. 14.2. Schematic representation of the crystallographic

unit cell of CaTiO

(perovskite)

known to adopt the truly cubic perovskite structure.

Most of the so called perovskite materials crystallize

in a distorted version, the most common being an

orthorhombic distortion.Most of the fullerenes also

crystallize in cubic structures (fcc) but the occupa-

tion per lattice site is given by a rather large basis,

formed by the C

Duringthe time,when investigationsof supercon-

ducting materials were focused on either chemical

elements or, at most binary compounds and alloys, it

was argued [10] that a high symmetry of the crystal

lattice was favorable for achieving high critical tem-

peratures. Superconductivity of the cubic A15 com-

pounds with critical temperatures between 15 and

20 K was taken as the show case for this conjecture.

The most recent and also rather surprising excep-

tion from this trend is,no doubt,MgB

which adopts

a structure with hexagonal symmetry [11]. Its criti-

cal temperature, of the order of 40 K, is by now no

longer a top value in general, but for simple binary

compounds, it most certainly is.

14.2.1 BaPb

1−x

,BaPb

1−x

,BaBi

1−x

The structure of these non cuprate materials of the

type BaPb

1−x

and Ba

1−x

BiO

varies with the

parameter x and different varieties of distorted per-

ovskitetypearrangementsoftheatomsareobserved.

The Pb/Bi alloy series exhibitsa number ofstructural

phase transitions,starting with an orthorhombic lat-

tice for metallic BaPbO

[12], changing to tetragonal

at x ∼ 0.1, back to orthorhombic for x ∼ 0.35 [13]

768 H.R.Ott

Fig. 14.3. Schematic representation of the crystallographic

unit cell of BaBiO

, as reported in [14]

and finally distorting to a monoclinic lattice struc-

ture at x ∼ 0.9 [14]. In the range of 0.1 < x < 0.3,

also the Pb/Sb alloys adopt a tetragonally distorted

perovskite-type structure. BaBiO

is electrically in-

sulating. Its crystallographic unit cell is shown in

Fig. 14.3, revealing the distorted perovskite-type ar-

rangement of the atoms by the quasi-octahedral co-

ordination of oxygen atoms around the Bi atoms on

inequivalent sites. On site B(1), one of the Bi-O dis-

tances is much shorter than on site B(2) and this

freezing of a breathing mode is thought to be the rea-

son for the insulating ground state. The substitution

of Ba with K atoms in BaBiO

to form Ba

1−x

BiO

eventually triggers a transition to a cubic crystal lat-

tice and a metallic ground state [15,16]. It is obvious

that for these oxides, structural and electronic prop-

erties are intimately coupled, a feature that is also

observed for the cuprate materials to be discussed

below.

14.2.2 Copper Oxide Superconductors

The crystal structures of all superconducting Cu ox-

ides are more or less evidently related to the per-

ovskite structure. These Cu compounds belong to a

large class of mixed-valency Cu oxides where the Cu

cations may adopt different ionic configurations (2+

or 3+). In some cases rather the concept of interme-

diate valence (between 2+ and 3+) seems appropri-

ate. The three-dimensional character of the original

perovskite structure,which may also be viewedas be-

ing built by a stacking of AO and BO

planes, is lost

because these planes are now stacked in different se-

quences,leading to a more or less sizeable anisotropy

between the directions parallel and perpendicular to

these planes. A fairly transparent case in this respect

is the parent compound of the material where su-

perconductivity of the cuprates was discovered by

Bednorz and M¨uller [1].

2−x

CuO

4+ı

(A = Sr, Ba)

An early study [17] of substances of this type with

A = Ca, Sr, Ba and Pb revealed the metallic conduc-

tivity for these materials in the form of a decreas-

ing electrical resistivity with decreasing temperature,

i.e.,∂/∂ T > 0. For unknown reasons,this study was

limited to temperatures above 200 K,but it contained

also important information concerning the crystal

structure of this series of compounds. Later a more

detailed investigation [18] confirmed and extended

these findings. As is already legend by now, it was

this type of materials where Bednorz and M¨uller [1]

found the first evidence for the onset of supercon-

ductivity between 30 and 40 K.

Ter nary La

CuO

, an insulating antiferromagnet,

crystallizes in a tetragonal K

NiF

-type structure

but at lower temperatures adopts an orthorhombi-

cally distorted version of this structure, induced by a

cooperative alternating tilting of the CuO

octahedra

about the [110] tetragonal axis, as shown in Fig. 14.4

[19, 20]. For x = 0 the tetragonal to orthorhombic

transition occurs at approximately 530 K. The on-

set temperature of the orthorhombic distortion T

can be reduced by partly replacing La by an alkaline

earth element A and above a critical concentration

of x ∼ 0.2, the tetragonal K

NiF

-type structure is

stable down to very low temperatures [21, 22]. The

tetragonal arrangement, also denoted as T-structure

and shown in Fig. 14.5,may be regarded as a stacking

of different planes that are also contained in the orig-

inal perovskite structure. Between two CuO

(BO

)

planes, two LaO (AO) planes instead of only one

are inserted,hence weakening the three-dimensional

14 High-T

Superconductivity 769

Fig. 14.5. Schematic representa-

tion of the tilting of the oxygen

octa-hedra in La

2−x

CuO

(see [36])

Fig. 14.4. Schematic representation of the tilting of the oxy-

gen octahedra in La

2−x

CuO

(see [36])

character of the structure.The essential subunitsare

clearly the CuO

planes, a major characteristics of

all known cuprate superconductors. For A = Ba, the

appearance of a low-temperature tetragonal phase

has been reported for x values around 0.125 [23].

As is well known, enhancing x eventually leads to

a metallic behavior and superconductivity. Optimal

conditions for superconductivity are reached for ma-

terials exhibiting the orthorhombiccrystal structure

at T ∼ 4T

. Structural effects are particularly pro-

nounced in La

CuO

4+ı

, containing excess oxygen on

interstitial sites.Also oxygen rich material undergoes

a transition from a tetragonal high-temperature to

an orthorhombic low-temperature phase [24]. The

transition temperature T

is only weakly reduced

upon increasing ı. For low oxygen surplus, a macro-

scopic phase separation phenomenon is observed be-

low room temperature. The material separates into

an oxygen-rich metallic phase and an oxygen-poor

insulating phase with an antiferromagnetically or-

dered ground state [24].

2−x

CuO

4−ı

(Ln = Pr, Nd, Sm)

Cu-oxides with a 214-type composition as men-

tioned above also form if La is replaced by rare-earth

or lanthanide (Ln) elements.These compounds,how-

ever, adopt a somewhat different crystal structure

[25], the so called T’ structure and they keep the

tetragonal structure down to low temperatures. It is

depicted in Fig. 14.5. Here, the oxygen environment

of each Cu atom in the form of a planar square is

distinctly different from that of an octahedron in the

T structure. As will be discussed later, the ternary

compounds are again insulating antiferromagnets.

Both the Cu spins and the localized Ln moments are

involved in magnetic-orderingphenomena,at differ-

ent temperatures, however.Metallic behavior and su-

perconductivity is obtained by a partial replacement

of the trivalent Ln element by tetravalent Ce and, in

addition, a slight reduction of the oxygen content.

770 H.R.Ott

Fig. 14.6. Schematic representation of the unit

cells of the crystal structure of YBa

CuO

7−ı

for

(a) ı =0,and(b) ı =1

2−x−y

CuO

4−ı

Yet another type of Cu-O coordination is obtained

in this type of compounds where part of the Ln sites

areoccupied by Ce and Sr [26].The resulting unitcell

of the structure is shown in Fig. 14.5. A remarkable

featureof this T*-structureisthe lack of an inversion

center, obviously implying polarity but, nevertheless,

with the proper values of x,y, and ı, superconductiv-

ity may still be achieved.The Srcontent mustbe large

enough in order to allow for a sequential ordering

(Sr,Ce) and (Nd,Ce) planes as indicated in Fig. 14.5.

MBa

7−ı

,MBa

Structurally,these two types of compounds, where M

may be Yttrium or any element of the rare-earth se-

ries except Ce and Tb, are related but chemically,

the second type of materials is much more stable

than the first. Again the structures may be viewed

as stackings of different layers with different chemi-

cal compositions. For YBa

7−ı

(YBCO-123),the

stacking sequence in the crystallographic unit cell is

Y-CuO

-BaO-CuO

-Y, reminiscent of the

perovskite structure [27]. The resulting orthorhom-

bic unit cell is shown in Fig. 14.6a for the ideal case

where ı = 0, i.e., x = 1. We note two inequivalent

Cu sites which can most easily be distinguished by

their different oxygen environments. In detail the M

atoms separate two identical blocks which contain

two CuO

planes with the Cu(2) sites,two BaO planes

and a plane formed by Cu-O chains along the b di-

rection of the orthorhombic structure involving the

Cu(1) sites. As may be seen from Fig. 14.6a, the oxy-

gen coordination of the two Cu sites is pyramidally

for the Cu(2) sites and linear for the Cu(1) sites. It is

the missing oxygen between the chains which gives

rise to the orthorhombic distortion of the lattice.

This low temperature orthorhombic structure devel-

ops out of a tetragonal high temperature structure

at about 750

◦

C by a rearrangement of atoms within

the oxygen sublattice. This rearrangement can be re-

versed at low temperatures by reducing the oxygen

content of the material. For ı =0.6, the structure

is again tetragonal also at low temperatures. Upon

depletion, oxygen vacancies are formed within the

Cu-O chains and they redistribute in a fashion such

that on the average, oxygen atoms occupy sites along

the a and b directions with equal probability [28].For

ı = 1, i.e., x = 0, the former Cu-O chains are fully

depleted of oxygen. The resulting structure is shown

in Fig. 14.6b. This variation of the oxygen content

not only inﬂuences the structure of the crystal lattice

but also many other properties of different ground

states, as we shall see below. A particular aspect of

14 High-T

Superconductivity 771

Fig. 14.7. Schematic representation of the unit cell of the

crystal structure of YBa

(see [36])

the crystal structure in this YBCO-123 series is the

formation of superstructures in different regions of

oxygen content, leading to inhomogeneities and dif-

ferent orthorhombic phases at different values of ı.

Since a detailed discussion of these aspects is beyond

the scope of this review, we refer to relevant work in

the literature [29]. The unit cell of the MBa

(YBCO-124) compounds[30,31] is shown in Fig.14.7.

As mentionedabove this type of compoundis chemi-

cally less fragile than theYBCO-123 variety and crys-

tals may be grown without twin boundaries, a ma-

jor problem in the growth of YBCO-123 compounds.

The insertion of a second Cu-O chain element,form-

ing Cu-O ribbons rather than chains, enhances the

anisotropy, especially within the planes perpendicu-

lar to the c axis. In this Y–Ba–Cu–O quaternary sys-

tem,an additional stable compound with yet another

although related structure and composition, namely

14+ı

,in short YBCO-123.5,has been iden-

tified [32,33].The corresponding unit cell is obtained

by stacking theunitcellsof YBCO-123andYBCO-124

on top of each other.Concerning the Cu-O structural

elements, the unit cell of the atomic arrangement

thus contains, apart from the notoriousCu-O planes,

both Cu-O ribbons and Cu-O chains.

n−1

3n+m+1

A fairly large number of high-T

cuprate supercon-

ductors may be classified according to the schematic

chemical composition given in the subtitle.Thistype

of compounds form with A = Hg, Tl or Bi, M = Sr

or Ba and R = Ca or a heavy rare earth. These ma-

terials are of particular importance because some of

them exhibit the highest critical temperatures that

have been achieved until today. For A = Hg, m may

be 1, for Bi only 2 and for Tl 1 or 2. Although Bi-

Fig. 14.8. Schematic represen-

tation of the crystal structure

of some Bi-based Cooper ox-

ide superconductors: Bi-2201,

Bi-2212 and Bi-2223 (see [36])

772 H.R.Ott

Fig. 14.9. Schematic representation of the crys-

tallographic unit cells of Hg-12(n-1)n copper

oxides

Fig. 14.10. Schematic representation of the crystallographic

unit cell of HgBa

8+ı

based cuprates have been synthesized with the 1222-

type structure, all of them turned out to be non su-

perconducting above 1.5 K [34]. In most cases the

parameter n varies from 1 to 4 but may also adopt

higher values.The parameter n indicates the number

of CuO

planes within one unit cell, separated from

each other by n-1 Ca layers, and as such it is related

with some physical properties to be discussed below.

Thestructuresofthesecompoundsmaybeviewedas

sequential stackings of elements of the perovskite as

well as the NaCl structure [35].Very often, crystallo-

graphic shears,i.e., shifts between adjacent layers are

introduced in the stacking sequences. A nice com-

pilation of possible atomic arrangements in the Tl-

based and Bi-based compounds is given, e.g., in [36]

and therefore we present only three examples of the

physically most important Bi compounds in Fig. 14.8

(on page 771). It is also possible to partially replace

some of the above mentioned constituents by other

elements. One such example is Pb substituting for

Bi, which in some cases provides a way to stabilize

a favorable phase, such as the Bi-2223 phase [37].

The latest progress in raising T

has been made in

the series HgBa

n−1

3n+2

[38] and it also has

been possible to synthesize thin layers of material

where n ≥4 [39]. A schematic representation of the

stacking with increasing n is shown in Fig. 14.9 and

a somewhat more detailed drawing of the unit cell of

HgBa

8+ı

,the material for which the highest

values of T

have as yet been observed, is presented

in Fig. 14.10.

1−x

CuO

The structure of this type of compound is of interest

here, because it may be viewed as the result of en-

hancing the number n of CuO

layers per unit cell

in the compounds discussed in the previous section

towards infinity. Taking into account the n −1Ca

interlayers, for large values of n,thestoichiometry

will approach that of CaCuO

. With respect to the

perovskite structure, the (Ca/Sr) layers may be re-

garded as AO layers from which all the oxygen atoms

have been removed. CaCuO

, a hypothetical tetrago-

14 High-T

Superconductivity 773

Fig. 14.11. Schematic representation of the crystal structure

of Ca

1−x

CuO

(see [40])

nal compound does not form but it has been found

that small amounts of Sr on Ca sites can stabilize

the structure, which is shown in Fig. 14.11, and sin-

gle crystals may be grown [40]. Subsequently it has

been found that a high pressure synthesis helps to

extend the compositional range of stability consid-

erably [41].

General Remarks

This brief overview of some crystal structures of rel-

evant cuprate materials demonstrates quite clearly

that one ingredient, namely the CuO

planes, are

a common building element for all the structures

presented in the previous subsections. Even before

discussing the physical properties of these materials

we note that the electronic features are, to a large

extent, dominated by these CuO

planes. They are

separated from each other by additional building

blocks that serve both to stabilize the structure and

as charge reservoirs, which control the number of

itinerant charge carriers in the planes containing Cu

atoms.In this sense, the structures of the compounds

mentioned in the first three subsections contain one

CuO

plane per unit cell. Two CuO

planes per unit

cell are the hallmark of the compounds mentioned

in the fourth subsection. Structurally the most sim-

ple member of this type of double-layer compounds,

but not mentioned in detail here,is La

2−x

CaCu

[42]. The compounds with the possibility of accom-

modating more than two CuO

planes per unit cell

are mentioned in Sect.14.5.Another important com-

pound,with all the features of the m =2andn =2Tl-

based or Bi-based compounds,except foran inserted

oxygen depleted Cu layer, is Pb

YCu

[43].

14.2.3 Fullerites, Fullerides

Fullerites are solids composed by a regular arrange-

ment of C

molecules, which belong to a large class

of fullerenes,i.e.,stable molecules formed by a closed

carbon network (C

540

,etc.)[44].Forourpur-

poses, only C

molecules are of interest, because up

to now, bulk superconductivity has only been ob-

served in solids formed by them. A pure C

solid

is, under normal circumstances, an electrical insula-

tor [45]. It adopts an fcc structure which, with de-

creasing temperature, transforms to a simple cubic

structure, at 260 K, accompanied by an orientational

order of the individual C

molecules [46]. Metal-

lic C

-based compounds, the fullerides, may be ob-

tained by doping [47] and the most relevant ma-

terials in our context are A

,whereAisK,Rb,

Cs or some combination of these three alkali ele-

ments and Na

,where A may again be one of the

other alkali elements or a combination of them [45].

The structure of these materials is of fcc type with

Fig. 14.12. Schematic representation of the unit cell of

fcc C

774 H.R.Ott

varying space groupsymmetries,however.Non cubic

structures of superconducting fullerides have been

reported for the cases of Cs

and NH

under pressure. The compounds with chemical com-

position of the type A

usually adopt a bct cubic

structure and are insulators. A schematic drawing

of the cubic structure of the A

type materials is

shown in Fig.14.12.Moreon structuralaspects of C

material may be found in [48].

14.2.4 MgB

Although this compound has been known for a long

time, it obviously had never been tested for super-

conductivity until late in 2000. The discovery of its

unexpectedly high critical temperature of the order

of 40 K by Akimitsu and co-workers [11] came as

a real surprise. MgB

crystallizes in the hexagonal

AlB

-type structure, shown in Fig. 14.13, which ex-

hibits clear 2D-type features. The B atoms form lay-

ers that are equivalent to the layered structure of

graphite. It has been suggested [49] that this appar-

ent two-dimensionality might be the key to the high

value of T

of this material, reminiscent of the case

of the cuprates.

Fig. 14.13. Schematic representation of the crystallographic

unit cell of MgB

14.3 Occurrence of Superconductivity

For all thematerials thatin this review are considered

in relation with high-T

superconductivity, a super-

conducting ground state is achieved only in limited

regions of chemical composition. In this section, we

brieﬂy discuss the relation between chemical compo-

sition and the observation of superconductivity, in-

cluding the established critical temperatures T

, for

a few instructive cases.

14.3.1 BaPb

1−x

,Ba

1−x

BiO

Superconductivity in the Pb/Bi compound series [50]

is restricted to values of x that are close to 0.25 where

a maximum critical temperature of approximately 12

K isobserved [51,52].Thisvalueof T

is unexpectedly

high and remarkable becauseof the absence of any el-

ement of the d-transition range in the chemical com-

position. Figure 14.14 demonstrates that, although

partial superconductingtransitions, measured mag-

netically and resistively, have been observed around

x=0.1 and x = 0.3, narrow and complete transi-

tions are monitored only for x = 0.25 [52].It is there-

fore quite obvious that the optimal conditions for

superconductivity are reached for BaPb

0.75

0.25

and any deviation from this composition leads to a

rapid deterioration of the superconducting proper-

ties and, in addition, favors inhomogeneities in the

chemical composition. It is conceivable that the oc-

currence of superconductivity is extremely depen-

dent on the doping level and that compositional in-

homogeneities lead to the spread in T

displayed in

Fig. 14.14.

Replacing Bi with Sb leads to a less favorable sit-

uation for superconductivity [53].Maximum critical

temperatures are again reached for x ∼0.25 but they

barely exceed 3 K. It is not quite clear why T

is so

low in this case.

More successful in this respect were experiments

with material that was prepared by partly replacing

the divalent Ba by the monovalent alkaline metal K in

BaBiO

. This type of substitution and the concomi-

tant reduction of the electron concentration induces

the already mentioned structural phase transition

and the symmetry of the crystal lattice changes from

monoclinic to cubic. Likewise, the chemical substi-

tution leads from an insulating to a metallic state.

K-doped BaBiO

is electronically very similar to Bi-

doped BaPbO

. Optimal conditions are reached at

the composition Ba

0.6

0.4

BiO

for which T

is ap-

proximately 30 K [54,55].

14 High-T

Superconductivity 775

Fig. 14.14. Onset and widths of the superconducting tran-

sition of BaPb

1−x

(see [52])

14.3.2 Copper Oxides

Very shortly after the discovery of superconductivity

inCuoxidesitwasrealized thatinthesematerials,the

occurrence of superconductivity is intimately related

with the number of itinerant charge carriers which,

in most cases, can be varied rather easily by simply

altering the chemical compositions of the materials

in specific ways. For some types of compounds, the

result of this procedure in the form of a transition

from an insulating to a metallic behavior and super-

conductivity, or vice versa, may be illustrated very

well, for others it proves to be less obvious. In what

follows, four rather instructive cases, representative

for the cuprate superconductors, are presented.

2−x

CuO

4+ı

The ternary compound La

CuO

has long been

known to be an electrical insulator. Early measure-

ments revealed peak features in the temperature

dependence of the magnetic susceptibilitywhich in-

dicatedsometypeofmagneticorderbelowapprox-

imately 200 K [56]. It was only after the discovery

of superconductivity in exactly this class of cuprates,

when the physical properties of these materials were

studied in great detail. The results of these investi-

gations are being reviewed in some of the follow-

ing sections but we summarize part of them in the

form of low temperature phase diagrams, display-

ing the variation of the physical behavior as a func-

tion of the concentration of itinerant charge carriers.

The charge carrier doping may be accomplished in

two ways, either by enhancing the oxygen content

to above four atoms per formula unit or by replac-

ing part of the trivalent La ions by divalent ions of

the alkaline earth elements Sr and Ba. No successful

attempts to replace La by Ca have been reported.

Figure 14.15 captures the low temperature phases

that are identified if La is replaced by Sr [57].The di-

agram is somewhat more complicated if Ba is chosen

as the substitute. In the region of x ∼ 0.12 where a

slight indentation in T

(x) is apparent for the Sr dop-

ing (see Fig.14.15),T

is suppressed completely if the

dopant is Ba (see also below). As mentioned above,

the ternary compound La

CuO

is an insulator with

an antiferromagnetically ordered ground state.Upon

doping with Sr

,theN´eel temperature T

of 325 K

for x = 0 is efficiently reduced, giving way to a spin-

glass type ground state for 0.02 < x < 0.05. Once

Fig. 14.15. Low temperature phase diagram of

2−x

CuO

(see [57])

776 H.R.Ott

the Sr concentration exceeds 5%, superconductivity

sets in at low temperatures. The optimal doping, i.e.,

the highest transition temperature T

of about 40 K

is reached at x ∼ 0.15. Further increasing x reduces

and superconductivity is lost for x > 0.25. Since,

as mentioned above, the structural transition from

a tetragonal to an orthorhombic structure has been

reported to disappear at x ∼ 0.21, bulk supercon-

ductivity seems to persist into the tetragonal struc-

ture regime. This observation is important in view

of discussing relations between the crystal structure

symmetry and the occurrence of superconductiv-

ity, as illustrated in the following case. A tiny dip in

the T

(x)curveatx ∼ 0.125, displayed in Fig. 14.15,

signals an effect that is much more pronounced in

1−x

CuO

. Again around a concentration of

x ∼ 0.125, T

oftheBa-dopedseriesissuppressed

to zero and static magnetic order is observed in-

stead [58,59]. Detailed studies have traced this back

to the occurrence of a low temperature tetragonal

structure [23,59,60].

As already mentioned in a previous section en-

hancing the oxygen content leads to phase separation

phenomena in La

CuO

4+ı

. The oxygen rich metallic

Fig. 14.16. Low temperature phase diagram of

2−x

CuO

4−ı

-type compounds (see [63])

phase is superconducting at low temperatures and

again, T

values exceeding 30 K are achieved. An in-

structive discussion of the ground state properties of

CuO

4+ı

is offered in [57].

2−x

CuO

4−ı

(Ln = Pr, Nd, Sm)

This variety of compounds is, with respect to elec-

tronic properties, distinctly different from all the

other Cu-oxide compounds. Here, the doping is not

withholesbutwithelectrons[61].Thisdifference

is also reﬂected in the phase diagram capturing the

occurrence ofsuperconductivity [62,63].Theantifer-

romagnetic phase is again rapidly suppressed upon

doping and gives way to a superconducting ground

state rather abruptly, as may be seen in Fig. 14.16.

The maximum value of T

is found next to the phase

boundary and a further enhancement of doping

leads to a reduction of the critical temperature and,

again, to a rather abrupt disappearance of supercon-

ductivity. The range of doping where superconduc-

tivity has been observed is much more narrow than

in the hole doped cuprates.The discovery of electron

doped superconductors was initiated by the preced-

ing observation of a superconductingground statein

the chemically similar but somewhat more compli-

cated series adopting the T

∗

structure [64] (see also

Sect. 14.2.2).

YBa

6+ı

In this series of compounds, tetragonal YBa

represents the electrically insulating and antiferro-

magnetically ordering parent compound [65]. The

doping of this material is accomplishedby enhancing

the oxygen content. Superconductivity sets in at oxy-

gen concentrations close to those where the struc-

tural instability leads to an orthorhombic crystal lat-

tice,i.e.,ı ∼ 0.45.The critical temperature increases

roughly in two steps, with two plateaus at approxi-

mately 60 and 90 K [66]. Optimal values for T

,ofthe

order91to92Kareobtainedforı between 0.9 and

0.95. Further enhancing the oxygen content leads to

aslightdecreaseofT

,by1or2K.Theschematic

(x) variation is displayed in Fig. 14.17.