Qiu X.G. (Ed.) High Temperature Superconductors

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BSCCO high-T

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In the case of 2201 thin ﬁlms, although J

(θ) is maximum in a parallel ﬁeld,

the 2D angular scaling is no longer valid, as there is a noticeable decrease of

(H ||) in increasing ﬁeld even at 4.2 K. This is related to the weaker anisotropy

of this phase.

Probing the anisotropy by columnar pinning centres

The value of anisotropy in cuprates has a strong inﬂuence on the vortex behaviour.

In a perpendicular magnetic ﬁeld, one has pancake vortices in 2D systems (Crisan

et al., 2005) while one has line vortices in 3D systems. This can be evidenced by

introducing linear pinning centres such as columnar defects (CD) created by heavy

ion irradiation (Gerhaüser et al., 1992; Hillmer et al.; 1999, Martel et al., 2000). So,

by measuring the angular dependence of the mixed state MR and of J

(θ) at given

ﬁeld and temperature, the vortex pinning behaviour by the same concentration of

CDs perpendicular to the CuO

planes has been compared in the different systems:

2201 and La-2201 thin ﬁlms (0 <La≤0.4), 2212 thin ﬁlms and (2212)

(2201)

ML.

A minimum of the MR or a maximum of J

(Fig. 5.9) occurs when the ﬁeld is

parallel to the direction of the CDs in pure 2201 ﬁlms or La-doped 2201 ﬁlms with

La < 0.2 (Pomar et al., 2001a; Raffy et al., 2004, 2006). There is no selective pinning

effect of the vortices in 2201 (La = 0.3–0.4) and 2212 ﬁlms, and in (2212)

(2201)

ML the 2D scaling laws are still valid. Therefore it was conﬁrmed that pure Bi-2201

ﬁlms are weakly anisotropic under magnetic ﬁeld while in La

/Sr

substituted

ﬁlms, the high anisotropy is recovered and they behave as 2212 thin ﬁlms (Raffy

et al., 2004, 2005, 2006). The reason for the increase of the anisotropy in La-2201

thin ﬁlms is attributed to a decrease of the amplitude of the structural modulation as

5.8 Field dependence of the critical current density of a (2212)

(2201)

multilayer (T

= 92 K) in a magnetic ﬁeld parallel to the layers and at

constant temperatures going from 4.2 K to 81 K.

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shown in an X-ray study (Li et al., 2005) and to the consecutive decrease of the

Josephson coupling between the CuO

planes.

A surprising result obtained in the study of the mixed state MR of irradiated

2212 thin ﬁlms and (2212)

(2201)

ML is the observation, in the liquid vortex

phase, of a re-entrant pinning effect of the pancake vortices by CDs, while the 2D

scaling remains valid. This was attributed to a conﬁnement of 2D pancake vortices

on the CDs, due to a balance between entropy, the energy gain obtained by vortex

localization on the CDs and vortex repulsion (Pomar et al., 2001).

5.2.5 Normal state properties of BSCCO ﬁlms

How to modify the doping level in BSCCO thin ﬁlms

It is well known that the electronic properties of BSCCO, like other cuprates, are

essentially a function of their doping level. Superconductivity emerges from a

Mott insulating state by introducing holes into the CuO

planes. This can be made

in several ways. One way is heterovalent cationic substitution which is realized

during the synthesis: for instance 2201 ﬁlms with electronic properties going from

superconducting to insulating states have been prepared by adjusting the Bi

/Sr

ratio (Inoue et al., 1995), or by La

/Sr

substitution (Zhang et al., 1998; Li et al.,

2005). A reversible way consists of modifying the oxygen content of a deposit,

either in situ or ex situ. In the in situ case, it has in general been consistent to ﬁnd

the best conditions to approach the highest T

of the compound. For instance, the

5.9 Directional pinning effect observed in the angular dependence

of the MR and I

of a Bi

0.9

.1CuO

thin ﬁlm with columnar

defects parallel to the c-axis (irradiation dose: n = 10

ions/m

= n

= 2 T) and measured in a ﬁeld H = 1 T (adapted from Raffy

et al., 2004)

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critical temperature, T

, of 2212 thin ﬁlms deposited on SrTiO

substrates by

high pressure sputtering (P

= 3.5 mbar, T

substrate

= 860 °C) was maximized

~ 90 K) either by optimizing the oxygen ﬂow during the deposition (Auge et

al., 1994) or by an in situ annealing stage during the cooling down process

(Wagner et al., 1992). The ex situ process consists of annealing treatments under

a controlled partial pressure of oxygen, at low temperatures (T ≤ 420 °C), for

which there is no modiﬁcation of the crystallographic structure. This procedure is

particularly easy in thin ﬁlms (large surface/volume ratio), giving the interesting

possibility of following the evolution of the electronic properties of a unique

sample throughout the complete phase diagram (see the following sub-section).

Other less conventional processes have been reported, able to modify the

oxygen content of cuprate deposits. One of them is heavy ion irradiation, used to

create amorphous columnar tracks in 2212 or 2201 thin ﬁlms. It appeared that it

also produces a self-oxygenation of the sample, the oxygen liberated in the

amorphous tracks diffusing into the CuO

planes (Pomar et al., 2000). As the

irradiation was generally made on optimally doped samples, the decrease of T

was attributed to disorder and this effect was ignored for a long time. It was well

evidenced by irradiating underdoped non superconducting thin ﬁlms, as they

turned superconducting after irradiation (Fig. 5.10). Subsequently, this effect was

also reported in irradiated 2212 single crystals (Li et al., 2002).

Also, the illumination of an underdoped cuprate can produce a photodoping

effect (Gilabert et al., 1999, 2000). One explanation is that under illumination

there is the creation of hole–electron pairs, and the electrons are pinned by oxygen

vacancies while holes are transferred to CuO

planes. This technique was

conveniently used for adjusting the doping level of grain boundary junctions.

5.10 (

◯

) R(T) of one underdoped semiconducting 2212 thin ﬁlm. After

1 GeV Pb ion irradiation along the c-axis (dose: n = 1.5 × 10

ions/m

or equivalent induction B

= n

= 3 T, if all the columns were occupied

by a vortex), a resistive transition is restored (

•

). In insert, a schematic

phase diagram indicates the increase of doping due to irradiation.

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Another technique, which potentially allows the changing of the carrier density

without affecting the chemical composition, thus avoiding introducing disorder, is

the electrostatic ﬁeld effect. An electric ﬁeld effect is applied across a gate

dielectric (generally the SrTiO

substrate) and the cuprate ﬁlm, changing the

density of carriers at the interface of the dielectric and of the oxide, and so the

electronic properties of the oxide channel. It has been successfully operated for

changing the critical temperature (T

modulation of 10 K, corresponding to

induced charge densities of 0.7 × 10

charges/cm

) of an underdoped NdBa

thin ﬁlm (3–4 unit cell thick) (Matthey et al., 2007) and is now routinely used for

changing the doping level of superconducting oxide interfaces (Caviglia et al.,

2008). However it has not been able to induce superconductivity in a nearly

insulating Bi

1.5

0.5

CaCu

8 +

thin ﬁlm on a SrTiO

substrate, although,

conversely, it has been able to produce a considerable carrier depletion (Oh et al.,

2004). The reason given by the authors is a localization of the induced carriers

conﬁned to the top single CuO

layer.

Finally, another possible doping technique would be chemical electrolysis,

which has been applied to YBaCuO thin ﬁlms. The difﬁculty is to ﬁnd an

electrolyte which does not attack BiSrCaCuO cuprates.

Evolution of the resistivity vs doping and phase diagram

The evolution of the T dependence of the resistivity of a same ﬁlm, 2212 or 2201,

has been reported as a function of its doping level, varied from very overdoped to

insulating states by removing a small quantity of oxygen in successive thermal

annealing treatments (Konstantinovic et al., 1999a, b, 2000a, b). It is interesting

to describe these results in parallel with the results of ARPES experiments

conducted on similar 2212 thin ﬁlms, which followed the evolution of normal

state electronic excitations with temperature and carrier concentration.

It should be remarked that the oxygen content cannot be measured in a thin

ﬁlm, due to its small mass. The doping state can be characterized by a parameter

which varies monotonically with the doping level, such as the conductivity at

300 K or the Hall number, or even the c-axis lattice parameter. It is also possible

to calculate the value of the doping level from the universal phenomenological

relation: T

cmax

= 1-82.6 (p-0.16)

, T

cmax

being the maximum value of T

obtained for p = 0.16, where p is the number of holes per Cu in a CuO

plane.

However this relation may fail in the case of the underdoped 2201 phase

(Konstantinovic et al., 2003).

In a large temperature interval from room temperature to the onset of

superconducting ﬂuctuations, the in-plane resistivity,

(T), can be described by

an empirical law of the form:

(T) =

+ bT

. The value of

allows one to

conveniently locate the doping level. In the overdoped region, the exponent

decreases linearly from 1.3 to 1 with decreasing doping p (Konstantinovic et al.,

2000a). In the most overdoped state (

= 1.3), one can reach a pure metallic state

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only in the 2201 phase. The value

= 1 corresponds to the doping state for which

there is the largest T interval where there is a linear variation of R(T) and is

obtained for a doping level (p = 0.19) close to optimal doping (p = 0.16), but in

the overdoped side (Oh et al., 2005). For p < 0.19 and in the underdoped side, the

value of

of the law:

(T) =

+ bT

becomes less than one.

Let us analyse more precisely the evolution of the resistivity through the phase

diagram (T, p). In the overdoped side, it appeared that one can determine a

temperature T** above which

(T) is linear and below which R(T) becomes

superlinear (positive curvature). Conjugated transport and ARPES experiments

on similar 2212 thin ﬁlms at various doping states have shown that this crossover

temperature T**, which increases with increasing doping, separates a coherent

region, below T**, where a bilayer splitting is observed in the ARPES spectra,

from an incoherent one above T**, without bilayer splitting (Kaminski et al.,

2003, and ﬁg. 5 of this reference).

In the underdoped side, a

(T) curve comprises a high T linear part above a

temperature T* while below T* the decrease of

(T) becomes more rapid and

sublinear (negative curvature), the signature of a rapid reduction of the inelastic

scattering rate of the electrons. The temperature, T*, higher for lower doping levels,

is considered as the temperature below which the pseudogap opens (Ito

et al., 1993). In this region, ARPES spectroscopy shows a partial destruction of the

Fermi surface near the nodal regions (Norman et al., 1998). Low energy-excitations

occupy disconnected segments called Fermi arcs. By ARPES studies on underdoped

2212, it was reported that the Fermi arc length decreases linearly vs T/T*(p), where

p is the hole content, and extrapolates to zero as T goes to zero, suggesting that the

state at T = 0 is a nodal liquid (Kanigel et al., 2006). When the superconducting

transition occurs, there is an abrupt collapse from a ﬁnite arc length which lies on

the scaling line to a point node below T

, (Kanigel et al., 2007, see Fig. 5.4). The

collapse of the Fermi arc has the same width as the resistive transition. Considering

the resistive transition at various doping, a scaling law of the temperature dependent

part of the resistivity, (

(T) −

)/b as function of T/T* has also been reported

(Fig. 5.11 and Konstantinovic et al., 2000a). This demonstrates that the important

energy scale in this region is T*, while in the superconducting ﬂuctuative region,

close to T

, the corresponding decrease of the resistivivity scales with T/T

. However,

important pending questions concern the origin of the pseudogap and the nature of

the temperature T*: is it a crossover or a transition temperature? By the use of

circularly polarized photons and 2212 thin ﬁlms in different doping states,

underdoped and overdoped, it was shown by ARPES that, below T*, left-circularly

polarized photons give a different photocurrent than right circularly polarized ones

(Kaminski et al., 2002). This observation, which demonstrates that time reversal

symmetry is spontaneously broken below T*, appears to indicate a phase transition

at T*. This result has been highly discussed since 2002. The variation with doping

of the characteristic temperatures T

, T*, T** allows us to establish the phase

diagram (T, doping) (Fig. 5.12). Except for the region to the right below the T**line,

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where properties are getting close to that of a Fermi liquid for strong doping, the

electronic properties of cuprates are anormal. The two lines representing T* and

T** vs doping delimit a wedge region called strange metal where the temperature

dependence of the resistivity is linear. The region below T* is the pseudogap region

which is not yet understood.

5.11 (a) Temperature dependence of the resistivity of a 2212 thin ﬁlm,

examined at decreasing oxygen content, going from overdoped (lower

resistances) to underdoped insulating states. The arrows indicate the

temperature T* below which the resistivity decreases more rapidly

than linear. (b) Scaling of the temperature dependent part of the

resistivity normalized by its value at T*, as a function of T/T* (at T > T*,

T). The temperatures T* and T

, indicated by arrows in the

main ﬁgure, correspond to the temperature where the derivative

–1

dT starts to increase from 1 (T*) and is maximum (T

), respectively

(adapted from Konstantinovic et al., 2000).

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By comparing the evolution of R(T) curves of 2212 and 2201 thin ﬁlms vs doping,

it was found that T* has comparable values in both phases despite a factor four

difference in their optimal critical temperature, suggesting that superconductivity

and pseudogap are independent phenomena (Konstantinovic et al., 2000a). This

result on T* was conﬁrmed later on by Yurgens et al. (2003) by a tunnelling

experiment on La-2201 single crystals.

By further decreasing the oxygen content, the superconducting-insulating

transition (SIT) is approached. So adjusting the oxygen content offers a convenient

way to drive the SIT in cuprates. This has been studied both in 2212 and 2201 thin

ﬁlms (Konstantinovic et al., 2000a, 2001; Oh et al., 2006; Matei et al., 2009). In

all cuprates, near the SIT, R(T) exhibits a high T metallic behaviour, a minimum

at a temperature T

min

followed by a non metallic behaviour (dR/dT< 0) and a

maximum at T

caused by the onset of the superconducting transition at T

. This

re-entrant metallic behaviour was attributed to a phase segregation in the sample

due to strong electronic correlations and/or inhomogeneous oxygen distribution

(Oh et al., 2006; Matei et al., 2009). Here again, a scaling of the resistance divided

by its value at T

vs the reduced temperature T/T

is observed both for 2212 and

5.12 Experimental phase diagram and characteristic temperatures

, T*, T** obtained by studying the evolution of the temperature

dependence of the resistivity of 2212 ﬁlms as a function of their carrier

concentration varied by progressively decreasing their oxygen content

(adapted from Konstantinovic et al., 2000a).

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2201 ﬁlms (Fig. 5.13). By further deoxidation, superconductivity disappears and

an insulating behaviour is only shown with successively logarithmic, activated

and variable range hopping behaviours of R(T), with increasing deoxidation. Oh

et al. (2006) claimed that the SIT transition occurs without an intermediate

metallic state. Recently, ARPES experiments on underdoped non-superconducting

5.13 Superconducting–insulating transition of a La-2201 (La = 0.6)

thin ﬁlm monitored by oxygen doping: (a) resistance per square as a

function of log T for decreasing oxygen contents for the states going

from 1 to 28 (not all the curves are represented for clarity); (b) scaling

for the states 1 to 18 of the low T part of R renormalized by its value R

vs T/T

, where R

and T

are the coordinates of the maximum of R(T)

(adapted from Matei et al., 2009).

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superconducting ﬁlms 199

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ﬁlms have shown the existence of a d-wave-like gap that persists through the

insulator to superconductor transition (ﬁg. 2d in Chatterjee et al., 2010). This led

the authors to conclude that the nodal liquid appears as a phase-incoherent version

of the d-wave superconductor (Chatterjee et al., 2010). How superconductivity

emerges from the Mott insulating state is a fundamental question to be solved in

the route towards the comprehension of cuprate properties.

Interestingly, it was thought possible to follow the evolution of the resistivity

along the c-axis,

(T), as a function of the oxygen content of a Bi-2212 ﬁlm

deposited on a vicinal substrate. The resistivity curves,

(T), along the c-axis,

metallic at high T, exhibit a minimum at T

min

followed by an insulating low

T increase. A remarkable scaling was observed on the resistivity normalized by

its value at T

min

(T)/

min

), vs T/T

min

. Here, T

min

was considered as the

temperature of the opening of the pseudogap, easier to detect on

(T) (Raffy

et al., 2007).

Temperature dependence of the Hall effect at various doping

Another anormal property of the normal state of cuprates is the fact that the Hall

effect is T dependent. It has been measured on 2212 and La-2201 (La = 0.4) thin

ﬁlms at various doping levels (Konstantinovic et al., 2000b). All the R

(T) curves

exhibit a broad maximum (around 130 K in the underdoped region). A quantity

studied theoretically (Anderson, 1991), the cotangent of the Hall angle,

deﬁned as

H, displays a simpler behaviour which can be described by a

phenomenological expression of the form b + cT

above a temperature T

. The

exponent

is equal to two only in the strongly underdoped region and decreases

with increasing doping to the value 1.65 in the overdoped region. No evidence

of the opening of a pseudogap is seen in the T variation of cot

. The behaviour

of the two phases (2212 and La-2201 with La = 0.4) is very similar. Interestingly

the Hall number n

measured at 300 K appears to be proportional to the

number of holes per Cu. Also it varies linearly as a function of the conductivity at

300 K,

300 K

The T dependence of the Hall effect has been revisited in a pure 2201 ﬁlm with

a maximum T

of 10 K. The pure 2201 phase is more disordered due to the larger

amplitude of the incommensurate modulation (Li et al., 2005). The T dependence

of the Hall effect has been found weakly dependent on doping (Fruchter et al.,

2007). It is proposed that the maximum in R

(T) arises from a combination of a

large T-independent scattering rate and an anisotropic T dependent one in this

compound.

5.3 Concluding remarks and future trends

The synthesis of epitaxial BSCCO thin ﬁlms and multilayers, described in the

ﬁrst part of the chapter, has stimulated a lot of work leading to improvements and

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advances in the techniques of thin ﬁlm synthesis. Techniques previously used for

semiconductor preparation, like MBE, have been adapted to grow oxides. A new

technique, PLD, has known an impressive development and is now the most

frequently used technique to grow various kinds of oxide thin ﬁlms. Sputtering

appears to be well suited to grow BSCCO thin ﬁlms and it allows one to reach

very high doping levels with an oxygen-rich plasma.

In the second part, the description of physical properties was focused on a

few important aspects of BSCCO properties, as obtained from the study of

BSCCO thin ﬁlms. Although there is a consensus on the d-wave character of the

order parameter, there is still no answer concerning the mechanism of HTC

superconductivity which remains an open question. The research on BSCCO ML

with ultrathin layers has shown that HTC superconductivity exists in CuO

bilayers, provided they are in proximity with metallic layers. Such a result, which

is inverse of usual proximity effect, is an important fact to take into account in the

search for the mechanism of superconductivity. The works on cuprate multilayers

have been pioneering, leading to a wider range of study of oxide heterostructures.

This is now a ﬁeld in active development.

In the mixed state, strong anisotropy (n = 2 phase and (2212)

(2201)

ML)

leads to interesting scaling laws of the MR and J

, as a function both of angle and

temperature. However the n = 1 phase, which has a much lower T

than other

cuprates, also has a lower anisotropy under magnetic ﬁeld, probably related to

the presence of a structural modulation leading to an increase of the interlayer

coupling. Interestingly, the temperature T* of the pseudogap opening, the puzzling

phenomenon of the normal state, is unchanged in contrast to T

. The study of

the normal state (temperature, doping) phase diagram of BSCCO thin ﬁlms

with various doping has been performed using resistivity and spectroscopic

experiments. In the underdoped region, various scaling laws have been shown to

be a function of T/T*, pointing out the fact that, in this region, the important

energy scale is T*. Such experiments will no doubt contribute to resolving the

mystery of HTC.

Although only fundamental aspects were considered in this chapter, some

properties are of interest for applied research. One of them is the possibility to

easily tune the doping in BSCCO thin ﬁlms, and modulate it spatially by

appropriate masking during oxygenation or deoxidation, to produce insulating

zones in contact with SC areas. Finally, an interesting property of BSCCO is the

fact that its structure realizes a natural nanometric, 1D, Josephson lattice. Studies

are being carried out, mainly on single crystals, to see if such a system may be

used to produce or detect signals in the THz range. If this turns out to be the case,

BSCCO thin ﬁlms and multilayers could know a new development.

5.4 Acknowledgements

I am indebted to my colleague C. Pasquier for critical reading of this chapter.

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