Buschow K.H.J. (Ed.) Concise Encyclopedia of Magnetic and Superconducting Materials

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A representative example of the morphology of a

c-axis YBa

7d

ﬁlm grown under conditions

yielding high T

(typically 88–90 K) and high

(typically 5 10

Acm

2

at 77 K) on a well-ori-

ented (100) perovskite substrate is shown in Fig. 7

(Schlom et al. 1992). The ﬁlm surface is seen to con-

tain many growth spirals (typically 10

–10

2

); a

close-up of a single growth spiral is shown in Fig. 8.

Each spiral emanates from the point at which a dis-

location with a screw component intersects the ﬁlm

surface. The resulting well-known spiral growth

mechanism (Frank 1949), in which dislocations with

a screw component provide energetically-favorable

attachment sites at the step edges that emerge from

them, occurs frequently in the growth of layered

materials.

A consequence of this growth mechanism is that

the ﬁlm surfaces are not atomically ﬂat over large

distances; instead, the (001) YBa

7d

surface

consists of mounds, each typically 300 nm in dia-

meter. The surface roughness depends on growth

conditions, but height variations of 5–10% of the ﬁlm

thickness (for ﬁlms 10–200 nm thick) from the top of

each mound to its intersection with the neighboring

mound are typical in ﬁlms made by gas phase

codeposition techniques on all of the common

substrates. Figure 9 shows the surface of a c-axis

Figure 7

STM image of a c-axis oriented, B120 nm thick

YBa

7d

ﬁlm sputtered on a (100)SrTiO

substrate.

Growth spirals emanating from dislocations with a

screw component indicate a density

(1.470.2) 10

2

of dislocations with a screw

component at the ﬁlm surface (after Schlom et al. 1994).

Figure 8

STM image of a c-axis oriented B150 nm thick

YBa

7d

ﬁlm sputtered on a SrTiO

substrate. The

image shows a growth spiral with a step height of one

unit cell (B1.2 nm). The small dark spots such as the one

pointed to by arrow A are either holes or isolated

insulating regions (e.g., Y

precipitates). Clumps of

material with irregular shape, for example at arrow B,

are present at the step edges. The in-plane /100S

directions are indicated (from Schlom et al. 1992).

Figure 9

AFM image of a c-axis oriented YBa

7d

ﬁlm

grown by off-axis PLD on a (100)MgO substrate. The

ﬁlm is characterized by growth spirals emanating from

dislocations with a screw component.

300

High-temperature Superconductors: Thin Films and Multilayers

YBa

7d

ﬁlm grown on (100)MgO; again the

growth mode is seen to be spiral growth. How the

plethora of dislocations with a screw component

are nucleated is not established, although several

mechanisms have been proposed (Schlom et al. 1992,

Burger et al. 1994, Schlom et al. 1994).

For c-axis YBa

7d

ﬁlms thinner than 10 to

20 nm (Burger et al. 1994, Schlom et al.1994),ﬁlms

grown on YBa

7d

substrates (Shimizu et al.

1994), or ﬁlms grown by PLD under conditions where

species reach the substrate with significant kinetic en-

ergies (Raistrick and Hawley 1994, Dam et al. 1998), a

layer-by-layer growth mode (also known as ‘‘birth and

spread’’) is possible. An example of this growth mode

is shown in Fig. 10. The observed morphology, which

has been described as ‘‘Tower of Hanoi’’ or ‘‘layer-

cake-like,’’ is indicative of a growth mode dominated

by two-dimensional nucleation coupled with an Eh-

rlich–Schwoebel step-edge barrier to the diffusion of

species from the higher terraces to the incomplete

lower terraces. As the surfaces of homoepitaxial

YBa

7d

ﬁlms are free of these high stacks of

incomplete terraces (Shimizu et al. 1994), the step-

edge barrier present in heteroepitaxial growth might

be induced by lattice mismatch with the substrate.

If the substrate is misoriented sufﬁciently (typically

a few degrees from the low-index plane on which

spiral growth occurs), the growth mode of c-axis

YBa

7d

changes from spiral growth to step-

ﬂow growth (Schlom et al. 1992). Step-ﬂow growth

occurs by the collective propagation of the terraces

across the substrate surface. The terraces on vicinal

substrate surfaces accommodate the tilt of the subst-

rate and are energetically-favorable incorporation

sites. This cross-over in growth mode can be seen in

Figs. 11 and 12. In Fig. 11 the misorientation of the

substrate is such that both spiral growth and step-ﬂow

growth modes are operative. At larger misorientation

or higher substrate temperature, as shown in Fig. 12,

the growth mode has become purely step-ﬂow.

The impurity phases that occur in YBa

7d

ﬁlms and have been conclusively identiﬁed by TEM,

have characteristic morphologies that can be distin-

guished by AFM (Catana et al. 1993). An example is

shown in Fig. 13 in which the most common impurity

phases found in YBa

7d

ﬁlms with good trans-

port properties i.e., CuO, Y

, and YCuO

, are seen.

A powerful in situ analysis tool used during the

growth of high-T

ﬁlms is RHEED. The sensitivity of

RHEED to surface structure is ideal for monitoring

the growth process, and RHEED, in particular, has

been key to the atomic-layer engineering of oxide su-

perconductors. RHEED patterns themselves reveal

the formation of impurity phases, the in-plane orien-

tation relationship between ﬁlm and substrate or be-

tween the many layers in a multilayer, and allow the

relaxation of in-plane lattice constants to be followed

in real-time. Growth conditions may be adjusted

during growth in response to the RHEED pattern.

Figure 11

STM image of a c-axis oriented B130 nm thick

YBa

7d

ﬁlm sputtered on a vicinal SrTiO

substrate (misoriented by B31 from (100)) at a substrate

temperature of B750 1C. The surface morphology of the

ﬁlm is characterized by growth steps originating from

the substrate tilt and from dislocations with a screw

component. This image shows the cross-over from spiral

growth to step ﬂow (after Mannhart et al. 1994).

Figure 10

STM image of a c-axis oriented B150 nm thick

YBa

7d

ﬁlm grown on (100)SrTiO

by PLD. The

growth mounds referred to as ‘‘wedding cake’’ towers or

‘‘Tower of Hanoi’’ structures are free of spirals and

indicate that the growth mode involves two-dimensional

nucleation of unit-cell-high layers and their lateral

outgrowth.

301

High-temperature Superconductors: Thin Films and Multilayers

Oscillations in the intensity of the RHEED pattern

allow the thickness of the growing ﬁlm to be precisely

monitored. In deposition techniques where the spe-

cies are codeposited, the intensity of the RHEED

pattern oscillates as shown in Fig. 14. The period of

these RHEED oscillations corresponds to a deposited

thickness of an electrically neutral formula unit of

each compound (Terashima et al. 1990).

For the growth of c-axis oriented high-T

super-

conductor ﬁlms, this amounts to one c-axis unit cell

thickness for YBa

7d

and other high-T

mate-

rials (e.g., (Ba,K)BiO

and TlBa

n

2n þ3

)

whose unit cells contain one formula unit, and one

half the c-axis unit cell thickness for doped La

CuO

and other high-T

materials (e.g., Bi

n1

2n þ4

and Tl

n1

2n þ4

) whose unit

cells contain two formula units. This minimum

growth unit determined by RHEED oscillations is

consistent with the step heights that have been

observed by STM observations on the surfaces of

high-T

superconductor ﬁlms and single crystals.

RHEED has traditionally been limited to high-

vacuum deposition techniques like molecular beam

epitaxy (MBE) and ion-beam sputtering, however,

using differential pumping this technique has been

extended to PLD (see Superconducting Thin Films:

Materials, Preparation, and Properties, Superconduct-

ing Thin Films: Multilayers, Karl and Stritzker 1992,

Frey et al. 1994, Rijnders et al. 1997). The rate of

recovery of the RHEED intensity when growth is

interrupted (between the stop and start marks in Fig.

14) provides information on surface diffusion and has

been studied as a function of substrate temperature,

oxidant pressure, and monolayer coverage. These

observations have led to major improvements in PLD

by interrupting and resuming deposition depending

Figure 13

AFM image of the (001) surface of a B100 nm thick

sputtered YBa

7d

ﬁlm showing densely

distributed outgrowths of three different types: (I)

a-oriented Y

), (II) YCuO

and (110)-oriented Y

(III) agglomerates of CuO, Y

, and a-oriented

YBa

7d

) (reproduced by permission of the

American Institute of Physics from Appl. Phys. Lett. 63,

553–5).

Figure 14

Time dependence of the specular RHEED beam

intensity during deposition of a YBa

7d

ﬁlm on

(100)SrTiO

with a PrBa

7d

buffer grown by

growth-interrupted PLD. The growth rate was changed

after the ﬁrst three layers (reproduced by permission of

the American Institute of Physics from Phys. Rev. B,

1994, 49, 3483–91).

Figure 12

STM image of a c-axis oriented, B130 nm thick

YBa

7d

ﬁlm sputtered on a vicinal (100)SrTiO

substrate (misoriented by 2.31 from (100)) at a substrate

temperature of B780 1C. The surface morphology is

dominated by steps between (001)YBa

7d

terraces

which accommodate the substrate tilt. The

YBa

7d

is growing by step ﬂow. The in-plane

/100S directions are indicated (after Schlom et al.

1992).

302

High-temperature Superconductors: Thin Films and Multilayers

on the RHEED intensity, in order to optimize the

smoothness of the ﬁlms grown (Frey et al. 1994,

Koster et al. 1999).

2.2 Transport Properties

For most studies or applications epitaxial ﬁlms are

required, rather than polycrystalline ones that con-

tain large-angle grain boundaries. This is due to the

fact that generally grain boundaries reduce the J

high-T

superconductors and increase their surface

resistance (Hilgenkamp and Mannhart 2000). A plot

showing the J

reduction that occurs in YBa

7d

ﬁlms due to grain boundaries of different angles and

different types is shown in Fig. 15. Grain boundaries

have also been correlated with an increase in the

surface resistance of epitaxial YBa

7d

ﬁlms

(Laderman et al . 1991, Lauder et al. 1998); this

correlation is illustrated in Fig. 16.

The challenges associated with the growth of epit-

axial superconducting cuprate ﬁlms have resulted in

such drastic improvements in the deposition technol-

ogy for multicomponent oxide ﬁlms, that a large

number of groups now routinely grow high-T

ﬁlms

with superb properties. Of particular significance for

basic studies and applications are the J

and R

of the

ﬁlms, discussed below. It is important to note that the

electrical transport properties, including T

, J

, and

, depend in different ways on the microstructure

and composition of the ﬁlms. For example, the high-

est J

values are obtained in ﬁlms with a huge density

of dislocations, which pin vortices strongly and thus

support more current before the resistive losses

caused by the movement of vortices set in. These

pinning sites, however, reduce T

. This illustrates that

it is not possible to optimize all transport properties

with one type of ﬁlm.

As the density of dislocations and other defects

in epitaxial YBa

7d

ﬁlms is always large

compared to that of single crystals, single crystals

outperform ﬁlms in those aspects for which a min-

imum defect density is key, such as mean free path or

. On the other hand, due to their defect structure,

ﬁlms have much higher critical current densities than

single crystals. J

for single crystals are typically in

the low 10

Acm

2

range at 77 K and in the low

Acm

2

range at 4 K (Worthington et al. 1987).

These J

values can be increased significantly through

the introduction of defects into single crystals, e.g.,

via irradiation with heavy ions (Civale et al. 1991).

The critical current density routinely achieved with

c-axis oriented epitaxial YBa

7d

ﬁlms is an im-

pressive 5 10

Acm

2

at 4.2 K and 5 10

Acm

2

77 K, as shown in Fig. 17. The critical current density

is limited by the onset of ﬂux ﬂow, rather than

by Josephson decoupling or depairing. As the

YBa

7d

ﬁlms are usually highly twinned, this

behavior demonstrates that twin boundaries do not

act as Josephson junctions. At ﬁrst current densities

above 10

Acm

2

(77 K) could only be achieved by

ﬁlms grown on single crystalline SrTiO

or other per-

ovskite substrates, but now such J

values are readily

obtained in ﬁlms grown on a large variety of other

substrate materials, including sapphire, silicon, silicon-

on-sapphire, GaAs, and ﬂexible tapes of stainless steel

or nickel, covered by buffer layers such as yttria-sta-

bilized cubic zirconia (Y

–ZrO

), MgO, or CeO

Such high current densities have been obtained in

scalable processes on long, ﬂexible tapes (Foltyn et al.

1999, Park et al. 1999), or on 8 inch wafers, where a J

Figure 15

The intergrain J

in YBa

7d

ﬁlms as a function of

grain boundary misorientation angle y for three

different types of grain boundaries: [001] symmetric tilt

boundaries ( ~), [100] symmetric tilt boundaries ( ), and

[100] twist boundaries (m) (after Goetz et al. 2000).

Figure 16

Surface resistance at 77 K and 10 GHz for YBa

7d

ﬁlms as a function of the intensity of the 006 and 200

X-ray reﬂections. The 006/200 ratio increases as the

amount of a-axis grains decreases in the c-axis oriented

ﬁlms and is therefore indicative of the number of grain

boundaries (reproduced by permission of VCH

Verlagsgesellschaft from Adv. Mater., 1998, 10,

1249–54).

303

High-temperature Superconductors: Thin Films and Multilayers

of 3 10

Acm

2

at 77 K varying by only 75% over

the whole wafer area has been achieved (W. Prusseit,

personal communication, 2000).

The high critical current densities of YBa

7d

ﬁlms in the (001) plane are caused by strong pinning

of vortices at dislocation cores and weaker pinning at

other defects, such as oxygen vacancies and the de-

fects that surround inclusions (Mannhart et al. 1992,

Douwes et al. 1993, Dam et al. 1999). This is dem-

onstrated by Figs. 18 and 19. In Fig. 18 the critical

current density of a YBa

7d

ﬁlm is plotted for

various temperatures as a function of applied mag-

netic ﬁeld. Clearly, as a function of applied ﬁeld, J

stays almost constant up to a characteristic ﬁeld B*,

above which J

starts to drop rapidly. As shown in

Fig. 19, B* depends almost linearly on the dislocation

density in the ﬁlm, providing evidence that below B*

the ﬂux lines are pinned at the dislocations. At ﬁeld

strengths exceeding B*, the excessive ﬂux lines are

only weakly pinned and J

is reduced.

For microwave applications, YBa

7d

ﬁlms

have to be grown c -axis oriented on substrates with

low dielectric losses such as MgO, LaAlO

, or CeO

buffered sapphire. Since grain boundaries cause sub-

stantial microwave losses (see for example Habib

et al. 1998), the ﬁlms have to be as devoid of grain

boundaries as possible. The microwave surface re-

sistance R

for such ﬁlms is shown in Fig. 20. In this

ﬁgure, R

is plotted as a function of frequency f in

comparison to the surface resistance of copper, nio-

bium, Nb

Sn, and polycrystalline YBa

7d

.As

can be seen in the ﬁgure, at 77 K the surface resist-

ance of YBa

7d

is smaller than R

of copper for

frequencies below 200 GHz, though still larger than

the surface resistance of the conventional supercon-

ductors that are measured at much lower tempera-

tures. Good ﬁlms reach values around 200–300 mO at

10 GHz and 77 K. YBa

7d

ﬁlms have been fab-

ricated in which these values are nearly independent

Figure 19

The characteristic magnetic ﬂux density B* as a function

of the dislocation density n

disl

for YBa

7d

ﬁlms

grown by sputtering and by PLD (reproduced by

permission of Macmillan Magazines Ltd. from Nature,

1999, 399, 439–42).

Figure 18

Superconducting critical current density of a c-axis

oriented YBa

7d

ﬁlm grown by PLD with a

dislocation density n

disl

¼6 10

2

at various

temperatures as a function of magnetic ﬂux density B

applied along the c-direction. The critical current density

was measured magnetically using a torque

magnetometer. The arrows indicate the ﬁeld strength of

the characteristic ﬁeld B* (reproduced by permission

of Macmillan Magazines Ltd. from Nature, 1999, 399,

439–42).

Figure 17

Temperature dependence of the critical current density

ﬂowing in the a,b-plane of a B150 nm thick, c-axis

oriented YBa

7d

ﬁlm. Also shown are the critical

current densities across a symmetric 241 [001] tilt grain

boundary in a YBa

7d

ﬁlm and in a

0.7

0.3

7d

/YBa

7d

0.7

0.3

7d

trilayer.

304

High-temperature Superconductors: Thin Films and Multilayers

of the applied microwave power for rf magnetic ﬁeld

strengths of up to 17 mT at 77 K (Zaitsev et al. 1998).

increases with frequency, characteristically var-

ying as f

. At low temperatures the surface resistance

of YBa

7d

ﬁlms saturates at values of about

20 mO at 10 GHz, which is much larger than the

achievable losses for niobium or Nb

Sn (Chaloupka

and Mu

ller 1991, Hensen et al. 1997, Hein 1999).

It has been shown that the microwave losses are

consistent with the d-wave pairing symmetry of

YBa

7d

(Hensen et al. 1997).

An excellent discussion of the microwave properties

of YBa

7d

ﬁlms as well as Tl

CaCu

8 þx

ﬁlms (which are also frequently used for microwave

applications) is given in (Hein 1999).

3. Multilayers and Superlattices

High-T

ﬁlms, which themselves have a layered

perovskite structure, naturally suggest interspersing

other layers to form a multilayer. Such multilayers

can be divided into three types:

(i) the combination of relatively thick layers of

different compounds, as is done in the integration of

a high-T

layer with an insulating layer to make a

pick-up coil of a SQUID (see SQUIDs: The Instru-

ment);

(ii) the integration of thinner layers of known

compounds as is done in artiﬁcial superlattices or in

the fabrication of sandwich-type SIS or SNS Joseph-

son junctions in which two relatively thick high-T

layers are separated by a thin barrier layer of an in-

sulator or conductor; and

(iii) the extreme case in which the high-T

struc-

tures are altered on the atomic-layer level and the

multilayers produced can be regarded as new high-T

phases.

Examples of multilayers consisting of relatively

thick layers of different compounds are PrBa

7d

/YBa

7d

bilayers (Poppe et al. 1989) and

ﬁeld-effect devices in which high-T

ﬁlms are layered

with highly insulating SrTiO

ﬁlms (Mannhart et al.

1991). By cutting diffusion paths by means of arti-

ﬁcial interfaces in YBa

7d

/Ba

1x

TiO

YBa

7d

samples, interlayer resistivities as high

as 3 10

O cm have been achieved (Frey et al.

1996). As multilayer technology is an essential

advantage for many applications, multilayers have

been grown for a variety of studies and applications,

e.g., for superconducting quantum interference

devices (SQUIDs) (Koelle et al. 1999) or for tunable

microwave components (Boikov et al. 1995). In many

cases it has turned out to be difﬁcult to fabricate

operating multilayers with a high yield; some of the

associated problems are discussed by Wellstood et al.

(1994).

Superlattices were ﬁrst deposited by Triscone and

coworkers, who grew c–axis oriented YBa

7d

DYBa

7d

structures with periods as small as

2.4 nm by sputtering (Triscone et al. 1989). Soon

thereafter, a-axis oriented superlattices consisting of

YBa

7d

/PrBa

7d

layers were deposited

(Eom et al. 1991). Superlattices involving high-T

su-

perconductors have been applied to many studies of

the physics of high-T

superconductors, especially

studies of the dimensionality of high-T

supercon-

ductivity (Triscone et al. 1990, Lowndes et al. 1990,

Kanai et al. 1990), experiments concerning the phys-

ics of Abrikosov vortices (Suzuki et al. 1994) or of

phonons in high-T

superconductors (Storozhuk

et al. 1995). In 1999, doping superlattices consisting

of YBa

7d

1x

7d

were deposit-

ed to successfully enhance the grain boundary critical

current density in YBa

7d

ﬁlms as shown in

Fig. 17 (Hammerl et al. 2000). Superlattices contain-

ing other functional materials, such as the CMR-

manganates, have also been grown (Jakob et al.

1995).

A very advanced example of multilayers are those

that are engineered on literally the atomic level. MBE

has been particularly successful in creating such mul-

tilayers. This has been used to make device struc-

tures with selectively doped barriers, barriers of new

Figure 20

Frequency dependence of the surface resistance R

77 K of high-quality YBa

7d

epitaxial ﬁlms

fabricated by various laboratories compared to

polycrystalline YBa

7d

samples and copper. Also

shown are the data of Nb

Sn at 9 K. Note that the data

for the Nb

Sn samples have been taken at a reduced

temperature T/T

E0.5, whereas the YBa

7d

samples have been measured at T/T

E0.85 (reproduced

by permission of Springer-Verlag from ‘‘High-

Temperature-Superconductor Thin Films at Microwave

Frequencies (Springer Tracts in Modern Physics 155),’’

1999.)

305

High-temperature Superconductors: Thin Films and Multilayers

materials, as well as new high-T

materials (see Super-

conducting Thin Films: Materials, Preparation, and

Properties, Superconducting Thin Films: Multilayers,

Eckstein and Bozovic 1995, Schlom and Harris 1995).

An example is shown in Fig. 21 in which a single

formula-unit-thick layer of Bi

(2278)

has been grown between thick layers of the super-

conductor Bi

CaCu

(2212).

4. Summary and Outlook

As we have described in this article, ﬁlms and mul-

tilayers containing a great number of high-T

com-

pounds are grown routinely and have exceptional

properties—well beyond all expectations when high-

superconductivity was discovered in 1986. Multi-

layers have progressed from combining known

materials to literally engineering new materials at

the atomic-layer level.

The progress achieved and the knowledge acquired

will be applied in the future to the growth of ﬁlms and

heterostructures of other oxide or nitride compounds,

into which high-T

superconducting ﬁlms will be em-

bedded. As in semiconductors, through doping and

material selection, the functionality of individual lay-

ers can be tailored in heterostructures. It is expected

that the challenges and the potential beneﬁts of such

heterostructures will provoke further improvements

in the control of ﬁlm growth.

5. Acknowledgments

We gratefully acknowledge our many collaborators

with whom, beginning in early 1987, we have worked

on the properties of high-T

superconducting thin

ﬁlms and multilayers, especially D. Anselmetti, J.G.

Bednorz, I. Bozovic, A. Catana, P. Chaudhari, Ch.

Gerber, J. N. Eckstein, T. Frey, J. S. Harris, Jr., E. S.

Hellman, H. Hilgenkamp, K. A. Mu

ller, and C. C.

Tsuei. We also thank D. H. A. Blank, B. Dam, O.

Eibl, D. Face, S. Foltyn, B. Go

tz, G. Hammerl, M.

Hein, K. E. Myers, W. Prusseit, C. W. Schneider, J.-

M. Triscone, M. Yoshimoto, and H. Zandbergen for

providing us with original ﬁgures or data of their

work for use in this article, and to K. Wiedenmann

and M. A. Zurbuchen for their skillful assistance.

DGS acknowledges the support of DOE through

grant DE-FG02-97ER45638 and a research fellow-

ship from the Alexander von Humboldt Foundation

during the preparation of this article during his sab-

batical stay at Augsburg University. JM acknowl-

edges the support of the BMBF (project 13N6918/1).

See also: Films and Multilayers: Conventional

Superconducting; High-temperature Superconduc-

tors: Thin Films and Multilayers; Superconducting

Materials, Types of; Thin Films Multilayers and

Devices, Superconducting

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D. G. Schlom and J. Mannhart

Universita

t Augsburg, Germany

High-temperature Superconductors:

Transport Phenome na

The discovery of high-temperature superconductors

in 1986 by Bednorz and Mu

ller (1988) started a

worldwide explosive growth of research and develop-

ment in the ﬁeld of superconductivity. The discovered

new class of superconductors shows a critical tem-

perature T

for the appearance of superconductivity

much higher than for the superconductors known be-

fore. The value of T

even exceeds the boiling point

(77.3 K) of liquid nitrogen, a result highly important

for the technical applications of superconductors. The

discovered new class of superconductors are cuprate

perovskites with electronic properties which depend

sensitively on the admixture of specific doping ele-

ments. Up to now the highest critical temperature T

was observed for the cuprate HgBa

8 þd

with T

¼133 K at room pressure (Tinkham 1996,

Waldram 1996).

The common structural element of the copper per-

ovskites are the copper oxide planes in which the su-

perconducting properties are believed to originate.

The crystallographic unit cell contains varying num-

bers of CuO

planes, depending on the particular

oxide compound. Because of the different possible

chemical composition there are ﬁve main families of

high-temperature superconductors, the ‘‘parent com-

pounds’’ of which are listed in Table 1.

In addition to the high values of the critical tem-

perature T

and the strong anisotropy due to the

prominent role of the CuO

planes, the third novel

feature of the cuprate superconductors is the small

value of the superconducting coherence length x. The

length x indicates the size of the wave function rep-

resenting a Cooper pair, i.e., the elementary constit-

uent of superconductivity. The coherence length

reaches values as small as only 1–2 nm. Hence, the

upper critical magnetic ﬁeld B

attains values as

high as B

¼j

/2px

¼100–200 T. Here, j

¼h/2e ¼

2.07 10

15

Vs is the magnetic ﬂux quantum

(h Planck’s constant, e elementary charge). The small

values of the coherence length in the cuprate super-

conductors have other important consequences: The

number of overlapping Cooper pairs within a ‘‘co-

herence volume’’

is about 20, whereas in the

classical superconductors it is about 1 10

times

larger (since x is up to 100 times larger than in the

cuprates). Furthermore, the small values of x result

in a high sensitivity of the superconducting properties

of the cuprates to atomic size defects such as, for

example, oxygen vacancies (Poole et al. 1995).

1. Normal-state Transport Properties

The undoped cuprate perovskites are antiferromag-

netic electric insulators, the antiferromagnetism re-

sulting from the arrangement of localized spins on the

Cu atoms of the CuO

planes. Superconductivity only

appears after doping, and there exists an optimum

doping concentration for each cuprate, where a max-

imum value of T

is obtained. Most high-temperature

superconductors require hole doping. However, a few

electron-doped oxide superconductors have also been

found. In many cases doping is accomplished by the

variation of the oxygen stoichiometry. Hence, during

the preparation of the high-temperature supercon-

ductors the oxygen concentration must be carefully

controlled (Levin et al. 1991, Pickett 1989).

The normal-state electric resistivity of the optimal-

ly doped high-temperature superconductors is several

orders of magnitude larger than in a typical metal.

Furthermore, it is highly anisotropic. The electric

conduction occurs mainly within the CuO

planes

(oriented parallel to the crystallographic ab planes),

whereas in the perpendicular direction (along the

Table 1

Parent compounds of the ﬁve main families of the

cuprate superconductors.

(K)

2x

CuO

YBa

7d

CaCu

8 þx

10 þx

125

HgBa

8 þd

133

309

High-temperature Superconductors: Transport Phenomena