Rep. Prog. Phys. 60 (1997) 1673–1721. Printed in the UK
PII: S0034-4885(97)55215-8
Superlattices of high-temperature superconductors:
synthetically modulated structures, critical temperatures
and vortex dynamics
Jean-Marc Triscone and Øystein Fischer
DPMC, University of Geneva, 24 Quai E.-Ansermet, 1211 Geneva 4, Switzerland
Received 26 April 1996, in final form 4 August 1997
Abstract
We present in this paper an overview of the work that has been performed on hightemperature superconductor superlattices, with a special emphasis on the superconducting
The critical temperature and
properties of YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers.
superconductivity in ultra-thin films, the vortex dynamics, and the field-temperature vortex
phase diagram in YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers are studied and compared to bulk
behaviour. In particular, the roles of the individual layer thicknesses and the conductivity
of the spacer material are studied, as well as the coupling between superconducting layers
and the effect of finite multilayer thickness. Comparisons with other systems are made, and
an interpretation is proposed for the understanding of superconductivity in ultra-thin oxide
films. The field-temperature vortex phase diagram is determined in coupled multilayers
and compared to single crystal results. Finally, we discuss the development of novel oxide
systems and heterostructures, and the possibilities brought out by new material combinations.
c 1997 IOP Publishing Ltd
0034-4885/97/121673+49$59.50 1673
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J-M Triscone and Ø Fischer
Contents
Page
1. Introduction
1675
2. Materials
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2.1. Systems investigated
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2.2. Deposition techniques
1678
2.3. Characterization
1680
3. Using multilayers as model systems for probing fundamental properties of high1684
Tc superconductors
1684
3.1. High-Tc and low dimensionality
3.2. The critical temperature of ultra-thin high-temperature superconducting
layers
1687
3.3. Vortex dynamics and vortex state phase diagrams of multilayers
1698
4. Exploratory systems: new systems and new materials
1712
4.1. Layer-by-layer growth of oxide materials
1712
4.2. Infinite layer based superlattices
1714
4.3. New material combinations
1715
5. Conclusions
1717
Acknowledgments
1718
References
1718
Superlattices of high-temperature superconductors
1675
1. Introduction
Since the discovery of superconductivity in LaBaCuO in 1986 (Bednorz and Müller 1986),
research in the field of high-temperature (high-Tc ) copper oxide superconductivity has grown
extremely rapidly. From the very beginning, a significant effort has been put into the
realization of epitaxial films of these oxide materials, motivated largely by the potential
applications of thin films and by the possibility of using epitaxial films to study the
anisotropic physical properties of these layered materials. Developments and improvements
in thin film technology now allow one not only to grow very high-quality thin films, but
also to achieve the growth of epitaxial oxide superlattices. The fabrication, characterization
and properties of these synthetically modulated structures, the important issues which can
be addressed using these multilayers, and the promising future of this field are the subject
of this review.
There are several main motivations behind the effort put into the growth and the study
of high-Tc multilayer structures. First, there is a technological need for heterostructures
containing superconductors and insulating (or metallic) layers, for instance in the fabrication
of Josephson and proximity effect junctions. Second, multilayers have in the past been
demonstrated to be very powerful tools for studying the basic physics of semiconductors
(see for instance, Esaki (1985)) and metals (see, for instance, Falco and Schuller (1985) or
Ruggiero and Beasley (1985)). We will see throughout this paper that oxide multilayers can
also be used to probe specific properties of high-Tc superconductors. These structures take
advantage of the naturally layered structure of the superconducting oxides and allow one
to study superconductivity at the unit cell level, as well as to understand how systematic
changes of certain material parameters influence characteristic physical properties. There are
also quite fundamental differences between high-Tc superlattices and low-Tc superconducting
superlattices. In the latter, interesting new physics has often be been generated by the fact
that the experimentally accessible multilayer wavelength 3 (the multilayer period) is easily
of the order of the superconducting coherence length ξ . Dimensional crossover (Chun
et al 1984) and interesting related features such as the Takahashi–Tachiki effect (Karkut
et al 1988), a new anomaly in the behaviour of Hc2 (T ), have been observed. In highTc materials, the coherence lengths are much shorter (ξc , the c-axis coherence length, is
about 3 Å in YBa2 Cu3 O7 (see, for instance, Salomon (1989))), rendering the observation
of similar crossover behaviour extremely difficult. Another difference is that in metallic
multilayers, many interesting studies have been made on non-epitaxial layers (see, for
instance, Falco and Schuller (1985) or Ruggiero and Beasley (1985)), while epitaxial growth
is a requisite condition for being able to grow multilayers of high-Tc materials. Finally, an
important advantage of epitaxial oxide structures is the possibility of incorporating, along
with superconductors, insulating materials, which allows one to probe the properties of
ultra-thin layers, as described in detail in section 3.
Another motivation behind the work put into the realization of high-Tc multilayers is
the very challenging and promising way of growing high-Tc materials in an atomic layerby-layer fashion. This multilayer approach takes advantage of the fact that the high-Tc
structure is based on stacked two-dimensional (2D) CuO2 planes separated by layers that
act as charge reservoirs. Pioneering work in this direction is discussed in section 4.
The paper is organized as follows: section 2 describes the different materials systems
which have been explored, the deposition techniques used to prepare oxide multilayers,
and the characterization of the materials; section 3 addresses the physical properties of
the superlattices, as well as some model experiments; and section 4 describes the atomic
layer-by-layer construction of oxide superconductors as well as exploratory systems.
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J-M Triscone and Ø Fischer
2. Materials
2.1. Systems investigated
The most commonly studied mulitlayer system is based on the ‘123’ compound (materials
with the YBa2 Cu3 O7 structure), with several groups having reported the growth of 123
heterostructures (Triscone et al 1989, 1990b, Li Q et al 1990, Lowndes et al 1990,
Terashima et al 1991, Jakob et al 1992, Chan et al 1993, Eom et al 1991, Obara et al 1991,
Ariosa et al 1994b). This large effort on the 123 system is partly due to the early report of caxis YBa2 Cu3 O7 /Dy(Pr)Ba2 Cu3 O7 superlattice growth (Triscone et al 1989, 1990b), and to
the availability of isostructural insulating (PrBa2 Cu3 O7 ), conducting ((Y1−x Prx )Ba2 Cu3 O7 ),
and superconducting (REBa2 Cu3 O7 , RE = Y, Dy, Eu, Er. . . ) materials. This large
choice of compounds, which have essentially the same lattice parameters (see, for instance,
Hulliger and Ott (1987)) and nearly identical growth parameters, but very different electronic
properties, makes the ‘123’ materials ideal superlattice constituents. This idyllic picture is
unfortunately tarnished by the somewhat complicated growth of the ‘123’ compound, which
can result, depending on the deposition technique and conditions, as well as on the film
thickness, in undesirable spiral growth (Gerber et al 1991, Hawley et al 1991).
Figure 1 is a schematic diagram of the ideal structure of a c-axis (001)
YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayer (in the figures YBCO and PrBCO are often used for
YBa2 Cu3 O7 and PrBa2 Cu3 O7 ). In this multilayer structure one unit cell of YBa2 Cu3 O7
alternates with one unit cell of PrBa2 Cu3 O7 . The important point to notice is that
the multilayer structure is obtained by periodically replacing yttrium by praseodymium,
while the remainder of the structure is the same. In these c-axis multilayers, the groups
of CuO2 planes sandwich either yttrium or praseodymium, rendering the planes either
superconducting or insulating. A-axis (100) (Eom et al 1991) and (103) (Eom et al 1996)
superlattices of the 123 compounds have also been successfully grown. In these multilayers,
the planes are either perpendicular or at 45◦ to the substrate surface. While these geometries
appear to be more susceptible to interdiffusion since yttrium and praseodymium atoms share
the same planes, it does not in fact seem to be a major problem, and high-quality superlattices
have been realized without significant traces of interdiffusion (Eom et al 1991). In addition,
new physics is expected in this orientation since there should be a channel-like behaviour
in each group of planes (Eom et al 1991, Triscone et al 1992).
Similar efforts have been pursued to explore the growth and properties of
Bi2 Sr2 Can−1 Cun O2n+2 (Matsushima et al 1990, Kanai et al 1990, Bozovic et al 1992,
Eckstein et al 1992a, b, Li Z Z et al 1994) and (La1−x Srx )2 CuO4 (Tabata et al 1991,
1993, Locquet et al 1996, Cretton et al 1994, Williams et al 1994) heterostructures. As
with the 123 multilayers, the advantage of these systems is that one can remain within
one family of materials, alleviating the problems of strain and interfacial defects. For the
Bi2 Sr2 Can−1 Cun O2n+2 materials, changing n changes the critical temperature from 10 K for
n = 1 to 110 K for n = 3. Insulating BiSrCaCuO can also be obtained by substituting Dy,
for example, for Ca (Eckstein et al 1992b). In the (La2−x Srx )CuO4 system, changing the
Sr doping allows one to go from an insulating state for x = 0 to a superconducting state
with a maximum Tc of about 30 K for x = 0.15. Above x = 0.30, the material exhibits
paramagnetic metallic behaviour (see, for instance, Ong (1990)).
Compared to the multilayer systems described above, whose constituents are
isostructural, less work has been done on the growth of multilayers consisting of materials
with different crystalline structures, although heteroepitaxy in this large family of oxides is
often possible. One of the problems with choosing two different materials is the possible
Superlattices of high-temperature superconductors
1677
Figure 1. The ideal structure of a YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayer where one unit cell of
YBa2 Cu3 O7 (about 12 Å) alternates with one unit cell of PrBa2 Cu3 O7 . One can see that in this
type of structure, the period is obtained by substituting Pr for Y in between the CuO2 planes,
while the rest of the structure remains unchanged. (From Triscone and Fischer 1993.)
difference in the deposition conditions of the constituents. Another is the occurrence of strain
and/or dislocations at the interfaces due to lattice mismatch, which is more likely to affect
the physical properties of these structures than in well matched isostructural systems. This a
priori less ideal choice of constituents might generate, however, some new physics precisely
because of a modified crystal structure related to interfacial strain and dislocation fields. For
instance, an enhanced critical current has been observed in YBa2 Cu3 O7 /(Nd2−x Cex )CuO4
multilayers (Gupta et al 1990), which was attributed to these interfacial modifications.
Investigations performed on conventional superconducting metallic superlattices, including
the Mo/V system that we investigated in detail (Karkut et al 1985, Triscone et al 1987,
Ariosa et al 1987a, b), give an idea of how the balance between elastic energy and dislocation
energy can affect superconductivity.
Other multilayer structures have been reported, such as (La2−x Srx )CuO4 /YBa2 Cu3 O7
(Horiuchi et al 1991, Eom 1991), SrCuO2 /CaCuO2 (Adachi et al 1995, Gupta et al 1995,
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J-M Triscone and Ø Fischer
Fàbrega et al 1996a), SrRuO3 /YBa2 Cu3 O7 (Antognazza et al 1993, Dömel et al 1995,
Miéville et al 1996b), and SrRuO3 /SrCuO2 (Satoh et al 1994). Recently, epitaxial films of
ferroelectric perovskites such as BaTiO3 and Pb(Zr1−x Tix )O3 have been successfully grown
(Boikov et al 1992, Lee J et al 1993, Tiwari et al 1993, Braun et al 1993, Ramesh et al
1993, Eom et al 1993, Triscone et al 1996) using the deposition techniques developed at
first specifically for high-Tc superconductors. These techniques turn out to be of general use
for the growth of oxide materials, and several groups have started to grow and study not
only epitaxial ferroelectrics, but also giant magnetoresistance materials (see, for instance,
the Proceedings of the MRS Fall meeting (1995)). Heteroepitaxy between these different
materials is also feasible, and epitaxial oxide ferroelectric-superconductor heterostructures
have been prepared recently (Boikov et al 1992, Lee J et al 1993, Tiwari et al 1993,
Braun et al 1993, Ramesh et al 1993, Eom et al 1993, Triscone et al 1996), offering new
possibilities for devices and numerous potential applications. One of these possibilities is
to use the surface electric field produced by a ferroelectric material to artificially modify the
number of carriers at an interface. This approach is described in recent papers investigating
Pb(Zr1−x Tix )O3 /SrCuO2 and Pb(Zr1−x Tix )O3 /SrRuO3 heterostructures (Ahn et al 1995,
1997a) and will be discussed in section 4.
Finally, one of the most challenging ideas is to use multilayer capabilities to produce
new structures grown in an atomic layer-by-layer fashion, as has been demonstrated by
molecular beam epitaxy in the BiSrCaCuO family, where Bi2 Sr2 Can−1 Cun O2n+2 with
various n have been produced (Bozovic et al 1992, Eckstein et al 1992a, b, Lagües et al
1993). Another recent and exciting result is the report of superconductivity in multilayers
of BaCuO2 /CaCuO2 (Li X et al 1994) and BaCuO2 /SrCuO2 (Norton et al 1994), materials
for which neither of the constituents are superconducting. These exploratory systems will
also be described in section 4.
This material review, although certainly not exhaustive, gives an idea of the large
number of systems investigated and of the broad range of materials which can be grown
heteroepitaxially.
2.2. Deposition techniques
In this part of the review, we describe briefly the most commonly used techniques for
growing high-Tc films and multilayers. The interested reader can refer to the original work
cited in the references. A wide range of deposition techniques has been tested to prepare
artificial oxide multilayers, including sputtering (DC and RF, on- and off-axis) (Triscone
et al 1989, Jakob et al 1992, Chan et al 1993, Eom 1991, Eom et al 1990, 1991, Li Z Z et al
1994), laser ablation (Li Q et al 1990, Lowndes et al 1990, Gupta et al 1990, Ariosa et al
1994b), laser molecular beam epitaxy (MBE) (Kanai et al 1990, Li X et al 1994), reactive
electron beam evaporation (Terashima et al 1990, 1991, Obara et al 1991), and thermal
MBE (Bozovic et al 1992, Eckstein et al 1992a, b, Lagües et al 1993, Locquet et al 1996).
All these techniques have been successfully used for growing oxides and multilayer oxide
structures. The very general features, advantages, and disadvantages of these techniques are
described below.
Usually, sputtering and laser ablation deposition techniques use single stoichiometric
targets for the starting materials. To grow multilayer structures one can either move
the substrate from one deposition area to another, or one can rotate targets into place.
Figure 2 shows a schematic picture of a typical sputtering system used for preparing highTc multilayers. In this particular technique, the substrate temperatures (Ts ) are in the range
500–850 ◦ C, depending on the oxide. A mixture of O2 and Ar (or pure O2 ) is used with
Superlattices of high-temperature superconductors
1679
Figure 2. A typical sputtering system used to prepare multilayer structures. The heated
substrates can rotate to face each sputtering gun. Stoichiometric targets are generally used, and
the composition transfer from the target to the film requires unusually high deposition pressures.
For both YBa2 Cu3 O7 and PrBa2 Cu3 O7 , typical deposition parameters are Ts ≈ (750 ◦ C,
PO2 ≈ 60 mTorr, PAr ≈ 600 mTorr, with the deposition of a unit cell of YBa2 Cu3 O7 ≈ 12 Å)
taking about a minute. (From Miéville 1995.)
typical pressures of several mTorr to several Torr. The multilayer structure is obtained by
sequentially going from one sputtering gun to another. Calibrated deposition rates allow one
to control the thicknesses by the time spent in front of each gun. For 123 materials, using
on-axis sputtering, typical parameters are Ts ≈ 750 ◦ C, PO2 ≈ 60 mTorr, PAr ≈ 600 mTorr,
with the deposition of one unit cell of YBa2 Cu3 O7 (≈12 Å) taking about a minute. Postdeposition measurement of the film thickness is usually performed by using x-ray analysis,
as discussed below.
In the MBE approach each material is supplied individually from metallic sources. In
principle, this approach is more flexible since the stoichiometry can be easily changed. The
difficulty is that calibration and rate control is rather complex and difficult. In addition, the
amount of oxygen which can be supplied during the deposition is low, and more reactive
oxygen sources like atomic oxygen, ozone, and NO2 are used to increase the oxidation
efficiency, leading to a shift of the stability line in the Hammond–Bormann PO2 –substrate
temperature phase diagram (Bormann and Nölting 1989, Hammond and Bormann 1989),
allowing the formation of the phase at a lower oxygen pressure for a given temperature. The
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J-M Triscone and Ø Fischer
advantage of the single target deposition technique is that it is compatible with high oxygen
pressure, and both calibration and rate control are readily obtained. The right choice of
pressure also leads to homogeneous composition over a rather large area (typically 3×3 cm2
for the off-axis sputtering technique using a 200 target). One disadvantage of single target
techniques is that high deposition pressures forbid the use of any in situ characterization such
as low-energy electron diffraction (LEED) or reflection high-energy diffraction (RHEED),
which are widely used in the MBE approach (see, for instance, Terashima et al (1990, 1991),
Obara et al (1991), Bozovic et al (1992), Ahn et al (1995)). These in situ techniques are
particularly important tools for the characterization of very thin layers (Ahn et al 1995) and
in the realization of layer-by-layer type growth described in section 4.
2.3. Characterization
It is particularly important for the further development and understanding of high-Tc
heterostructures to pursue complete material characterization of these multilayers and to
acquire knowledge about the basic growth mechanism. High-Tc superlattices have been
extensively characterized using x-ray analyses, scanning tunnelling microscopy (STM),
transmission electron microscopy (TEM), Rutherford backscattering spectroscopy (RBS),
and in situ analyses like LEED and RHEED. The purpose of this section is not to go into
the details of these techniques, but rather to give an idea of the information one gets using
these different analytical tools.
For a long time, x-ray characterization has been a key tool for the study of thin film
structures because it is non-destructive and yields structural information. Furthermore,
with modelling, it sheds light on strain and interfacial interdiffusion (see McWhan 1985,
Fullerton et al 1992). Figure 3 (top) shows one of the first x-ray diffractograms obtained on
a DyBa2 Cu3 O7 /YBa2 Cu3 O7 multilayer (Triscone et al 1989). This figure is a θ –2θ x-ray
scan around the (001) and (002) 123 reflections (the material grows with the c-axis parallel
to the growth direction and thus only (00l) reflections are visible). When compared to
pure YBa2 Cu3 O7 and DyBa2 Cu3 O7 films (shown in figure 3, middle and bottom spectra),
the superlattice diffractogram has additional satellite peaks which are the signature of a
modulated structure. These satellites occur close to the usual Bragg reflections and are
related to the modulation wavelength 3 by (see, for instance, Schuller (1980)):
3=
λx
2(sin θn − sin θn+1 )
(1)
where λx is the x-ray wavelength, and θn and θn+1 are the positions of two consecutive
satellites. Using this formula, one can verify after deposition that the wavelength 3
corresponds to the desired one. One can also use these satellite peaks for rate calibration.
Furthermore, analysis of such diffractograms through modelling allows one to make an
estimate of the interdiffusion at the interfaces, a crucial concern with multilayers. Using a
simple x-ray model to analyse samples with different periods, it was concluded (Triscone
et al 1990a) that interdiffusion is restricted to planes adjacent to the interfaces with
roughly 20% mixing. In such an analysis, though, one cannot easily differentiate between
interdiffusion and steps at the interfaces. Since YBa2 Cu3 O7 grows unit cell by unit cell,
the top surface may very well consist of incomplete YBa2 Cu3 O7 layers forming 12 Å
thick islands. When covering this surface (and thus completing the last layer) with
PrBa2 Cu3 O7 , one will find at the interfaces a layer containing ‘sections’ of YBa2 Cu3 O7
and PrBa2 Cu3 O7 . Thus, in the rare earth interfacial plane, one will cross regions with
yttrium and regions with praseodymium. This situation is very different in nature from
Superlattices of high-temperature superconductors
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Figure 3. X-ray θ–2θ diffractograms of a YBa2 Cu3 O7 film (bottom), a DyBa2 Cu3 O7 film
(middle), and a 60 Å wavelength YBa2 Cu3 O7 /DyBa2 Cu3 O7 superlattice (top). One sees satellite
peaks (marked with arrows) around the (001) and (002) reflections that are related to the
synthetically derived periodicity. The peaks marked with stars are due to an incommensurate
modulation, discussed in Triscone et al (1989). (From Triscone et al 1989.)
a thermal interdiffusion layer. A more sophisticated x-ray model has been developed by
Fullerton et al (1992) where thickness fluctuations, strain, and interdiffusion are taken into
account. Their estimate of interdiffusion is close to the value of 20% for the interfaces
mentioned above. In addition, they find that in one unit cell thick YBa2 Cu3 O7 layers
separated by PrBa2 Cu3 O7 , the c-axis length of YBa2 Cu3 O7 shortens (about 1% for 10
unit cell separations) as the PrBa2 Cu3 O7 thickness increases, suggesting that this change
in lattice constant should be taken into account in the discussion of the Tc of ultra-thin
layers. Further confirmation of the weak interdiffusion has been given by Pennycook
et al (1991), who performed Z-contrast high-resolution scanning transmission electron
microscopy (HRSTEM) on YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers. Figure 4 shows a Zcontrast STEM image of a 3 × 5 (3 unit cells YBa2 Cu3 O7 × 5 unit cells PrBa2 Cu3 O7 )
superlattice. One sees that the contrast is not only abrupt in the c-direction, but also in the
ab plane at the interfaces, suggesting an even more strikingly weak interdiffusion along the
rare earth plane.
Figure 5 shows one of the most spectacular TEM photographs obtained by Jia et al
(1993) of a 1 × 6 (1 unit cell YBa2 Cu3 O7 × 6 unit cells PrBa2 Cu3 O7 ) multilayer grown
by DC sputtering. The TEM image shows very continuous layers over large distances.
However, if one looks at this image in detail, one notices that the YBa2 Cu3 O7 single layers
are in fact not always continuous from the left to the right of the picture, but occasionally
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J-M Triscone and Ø Fischer
Figure 4. A Z-contrast STEM image of an interface step in a 3 × 5 (3 unit cells or ≈36 Å/5
unit cells or ≈60 Å) YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattice showing compositional abruptness
on the order of one lattice parameter in the ab plane, suggesting weak interdiffusion. (From
Pennycook et al 1991.)
‘jump’ from one layer to another. These discontinuities are the result of the unit cell by
unit cell growth. Nevertheless, this TEM image gives an idea of the quality which can
be achieved in these structures. The quality and flatness of the layer can also be studied
by x-ray diffraction using the finite size effect. In thin layers, typically 20 to 40 unit
cells thick, additional reflections are observed around the main Bragg reflections. These
peaks, along with the broadening of the main diffracted peaks, are related to the finite
number of diffracting cells. These effects can be used to calibrate the deposition rates.
Figure 6 shows a finite size effect obtained on a thin GdBa2 Cu3 O7 film (Nakamura et al
1992). One can observe around the main reflections numerous additional peaks which can
be indexed and modelled. Their positions and intensity allow an accurate (within 5–10%)
rate calibration, and one can also obtain an estimate of the surface roughness (Nakamura
et al 1992). Another estimate of the thickness for thin films can be obtained by simply
measuring the widths of the reflections and inserting these widths into the Scherrer formula
(see, for instance, Cullity (1967)):
1(2θ) =
0.9λx
d cos θ
(2)
Superlattices of high-temperature superconductors
1683
Figure 5.
A cross section TEM image of a 1 × 6 (1 unit cell/6 unit cells)
YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattice. Along the c-axis, a unit cell thick PrBa2 Cu3 O7 layer
gives rise to two white fringes separated by a dark fringe, while the single YBa2 Cu3 O7 layer
yields a single broader white fringe. As is visible from the photograph, some steps resulting
from the growth mode can be noticed at the YBa2 Cu3 O7 /PrBa2 Cu3 O7 interfaces. (From Jia
et al 1993.)
where λx is the x-ray wavelength and θ is the angular position of the reflection
(in
q principle, one has to correct for the experimental width by) 1(2θ )real =
1(2θ )2measured − 1(2θ)2experimental ). From this expression, one can extract d, which turns
out to be the film thickness if the x-ray coherence length is larger than d. For high-quality
thin films (200–400 Å) one finds that the thicknesses obtained by finite site effect analysis
and by estimates from the Scherrer formula agree in general to within a unit cell.
Another useful tool for estimating surface roughness is scanning tunnelling microscopy
analysis, which has revealed the spiral growth observed on thick 123 films (Gerber et al
1991, Hawley et al 1991). Figure 7(a) is an STM image (Maggio-Aprile 1996) obtained
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J-M Triscone and Ø Fischer
Figure 6. An x-ray θ–2θ diffractogram of a 232 Å GdBa2 Cu3 O7 thin film prepared on SrTiO3 .
One can observe between the main reflections (indexed (00l)) numerous additional peaks due to
finite size effects. Modelling of such a spectrum allows one to determine the average thickness
and the flatness of the film. (From Nakamura et al 1992.)
on a 1000 Å thick film of YBa2 Cu3 O7 prepared on SrTiO3 . The scan dimensions are
5000 Å × 5000 Å, and the image clearly reveals the spiral growth in thick YBa2 Cu3 O7
films. Each step is 12 Å high, corresponding to one unit cell. Figure 7(b) is an STM image
(Maggio-Aprile 1996) on a thinner film of about 220 Å. Here, the surface quality is much
higher, although a few steps are still visible. This result demonstrates that the surfaces of
these materials are not completely perfect and that one has to take this imperfection into
account when discussing the physical properties of these films. However, it is important
to notice that the roughness, even in the worst cases, is nevertheless small, and the picture
shown in figure 7(b) demonstrates that, with some care, it is possible to obtain very high
surface quality, especially for thin layers.
In this section we have considered mainly 123 superlattices. However, examples of
high-quality structures can be found in (La2−x Srx )CuO4 (Williams et al 1994, Cretton et al
1994), in BiSrCaCuO films and multilayers (Matsushima et al 1990, Kanai et al 1990,
Bozovic et al 1992, Eckstein et al 1992a, b), and in infinite layer structures (Adachi et al
1995, Gupta et al 1995, Fàbrega et al 1996a).
For MBE-type growth, additional characterization can be performed in situ using
RHEED. This technique is particularly interesting for layer-by-layer growth giving
information on the growth type, epitaxial relations, and the completeness of a layer. RHEED
oscillations have been used to control precisely the thickness of 123 layers (Terashima et al
1990, 1991).
3. Using multilayers as model systems for probing fundamental properties of high-Tc
superconductors
3.1. High-Tc and low dimensionality
The high-temperature superconductors are all characterized by a layered crystal structure,
as shown in figure 1, which results in strongly anisotropic properties. One is therefore led
to ask the obvious question about the role played by this quasi 2D nature in the unusual
Superlattices of high-temperature superconductors
1685
Figure 7. (a) An STM image of a 1000 Å thick film of YBa2 Cu3 O7 prepared on SrTiO3 .
The 5000 Å × 5000 Å image reveals a spiral growth. Each step is 11.7 Å high, corresponding
to a unit cell. (b) An STM image on a thinner film of about 220 Å. On this image, also
5000 Å × 5000 Å, the surface quality is much higher, although a few steps are still visible.
(From Maggio-Aprile 1996.)
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J-M Triscone and Ø Fischer
superconductivity found in these compounds. For instance, what is the critical temperature
of a single unit cell thick YBa2 Cu3 O7 layer? If these materials are actually 2D, one would
expect that the properties of such a unit cell layer would essentially be the same as those of
the bulk crystal. On the other hand, if the coupling between the unit cell layers in a thicker
film or a crystal is of importance, the properties of a unit cell thick layer might be very
different from those of thicker layers. Another way to express this question is to ask about
the influence of the anisotropy of the high-temperature superconductors on their various
properties. For instance, YBa2 Cu3 O7 is clearly less anisotropic than Bi2 Sr2 CaCu2 O8 , but
how can one study systematically the evolution of the properties as one goes from an
anisotropy corresponding to that of YBa2 Cu3 O7 to the extreme case of Bi2 Sr2 CaCu2 O8 ?
The fabrication of superlattices of such materials has opened up the possibility to
systematically investigate these questions and others as well. In this section we shall
review the extensive investigations that have already been carried out and also illustrate
how such materials can be used in the future to answer many of the still open questions
about the high-temperature superconductors. Most of these investigations have been carried
out on YBa2 Cu3 O7 -based multilayers, so we shall to a large extent be concerned with such
structures. However, recently there have been an increasing number of measurements on
BiSrCaCuO-based multilayers, and we shall discuss these as well.
This section is organized as follows: first, we shall discuss the behaviour of ultrathin layers in the 2D limit in sections 3.2.1 and 3.2.2 and examine how the reduced
dimensionality reflects itself in the experimental data. As we shall see, a possible explanation
of the data is that 2D fluctuations dominate the behaviour in the thinnest layers. The
experiments have mostly been carried out on YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattices where
the PrBa2 Cu3 O7 layers are thick enough to completely isolate the individual YBa2 Cu3 O7
layers. A natural question which arises in this context will be if and how coupling
between the YBa2 Cu3 O7 layers can be mediated across the PrBa2 Cu3 O7 layers. This
question will be discussed in sections 3.2.1 and 3.2.3. We also discuss experiments using
a less insulating spacer material like (Y1−x Prx )Ba2 Cu3 O7 which can, depending on the
yttrium concentration, be superconducting or insulating (see, for instance, Neumeier and
Maple (1992)). In section 3.2.4 we will compare results obtained on ultra-thin layers of
YBa2 Cu3 O7 and Bi2 Sr2 CaCu2 O8 . All of these experiments suggest that the mechanism
leading to superconductivity is not essentially weakened in ultra-thin layers compared to
the bulk, but that it is fluctuations which dominate the change in the properties in the thinnest
layers. Of course, this conclusion has the corollary that the vortex dynamics will change
drastically when one goes to ultra-thin layers, and that therefore these superlattices may
be ideal to study the unusual vortex dynamics of the high-temperature superconductors. In
section 3.3, we discuss the vortex dynamics and the vortex state phase diagram of high-Tc
heterostructures. The understanding of the vortex phase diagram is of primary importance,
both for applications, where one needs the highest possible irreversibility line, and for
basic physics studies, where one wants to understand the nature of the low-temperature
solid vortex phase. The difference in nature between the low- and high-Tc vortex phase
diagrams have been discussed by Huse et al (1992), and extensive reviews on the vortex
properties of high-Tc materials have been written by Blatter et al (1994) and Brandt (1995).
In addressing these properties, we are once again led to examine the properties of isolated
thin YBa2 Cu3 O7 films in YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers. As we shall see, the issue
of coupling between thin superconducting layers will arise. By modifying the nature of
the spacer material through the use of materials such as the alloy (Y1−x Prx )Ba2 Cu3 O7 ,
we find that it is possible to control and modify the material anisotropy. This approach
gives one a unique tool to investigate the vortex phase diagram for different anisotropies
Superlattices of high-temperature superconductors
1687
between the ideal 2D case and the 3D case of bulk YBa2 Cu3 O7 . A surprising effect is that
coupling between the YBa2 Cu3 O7 layers is observed through rather thick films of the alloys
(Y1−x Prx )Ba2 Cu3 O7 . One thus finds a rather unconventional long-range coupling through
these materials which remains to be explained. This coupling has been observed in different
experiments and by different groups, and we will summarize these findings.
We will also present a possible explanation of the different experimental facts which
suggest that the physics of ultra-thin films, especially the Tc behaviour, is very similar
in YBa2 Cu3 O7 and Bi2 Sr2 CaCu2 O8 . This explanation is based on the assumption that
the measured properties are intrinsic to the materials. As we will see, this viewpoint is
supported by the consistency of the data, which follow well defined predictions for how
the observed behaviour should depend on thickness (extrinsic effects should be more likely
sample dependent). Of course the reader should keep in mind that the materials are certainly
not perfect, and additional experiments might be required to prove or disprove the point of
view promulgated here.
Figure 8. The critical temperature of YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattices with a YBa2 Cu3 O7
thickness of one unit cell, as a function of the insulating PrBa2 Cu3 O7 thickness. (From Triscone
et al 1990b.)
3.2. The critical temperature of ultra-thin high-temperature superconducting layers
3.2.1. The critical temperature of 12 Å YBa2 Cu3 O7 /d Å PrBa2 Cu3 O7 superlattices. After
the first success in making a synthetically modulated multilayer consisting of YBa2 Cu3 O7
and DyBa2 Cu3 O7 , it was quickly realized that the insulating material PrBa2 Cu3 O7 could be
used as a spacer to separate thin YBa2 Cu3 O7 layers and thus allow the study of ultrathin layers of YBa2 Cu3 O7 . Figure 8 illustrates the results of the first study of such
multilayers (Triscone et al 1990b). In these materials, one unit cell thick YBa2 Cu3 O7
layers are separated by insulating PrBa2 Cu3 O7 layers of specified thickness (d Å) (12 Å
YBa2 Cu3 O7 /d Å PrBa2 Cu3 O7 ). What is shown is the critical temperature Tc , defined as
Tc = T (ρ(T ) = 10%ρ(Tconset )), as a function of the PrBa2 Cu3 O7 thickness. The surprising
result is that Tc decreases strongly as the PrBa2 Cu3 O7 thickness increases, and that this
decrease takes place over 60–70 Å, suggesting that some coupling takes place over relatively
1688
J-M Triscone and Ø Fischer
thick layers of the insulator. This observation raises two questions: why does Tc decrease
and for what reason does the decrease continue even when the YBa2 Cu3 O7 layers are
separated by several unit cells of the insulator? We shall come back to these questions in
sections 3.2.2 and 3.2.3.
Subsequent investigations (Li Q et al 1990, Lowndes et al 1990, Antognazza et al
1990) showed that beyond a PrBa2 Cu3 O7 thickness of about 60–70 Å, Tc saturates and that
this value corresponds to the critical temperature of a single unit cell thick YBa2 Cu3 O7
layer sandwiched between PrBa2 Cu3 O7 layers. This finding was clearly demonstrated
by Terashima et al (1991), who reported a Tc of 25 K for a single unit cell layer of
YBa2 Cu3 O7 (not a multilayer) sandwiched between PrBa2 Cu3 O7 buffer and capping layers.
This general behaviour has been observed by a number of groups who all agree about the
overall behaviour of these multilayers, although the value quoted for the single unit cell
Tc varies between 10 and 30 K. There are thus some differences in the detailed behaviour
reported in the literature, and we shall comment on these discrepancies in section 3.2.3.
One might be inclined to ask why it is preferable to use mulitlayers for this study,
rather than ultra-thin layers grown directly on the substrate. The answer is that the first
few unit cells of YBa2 Cu3 O7 are perturbed by the substrate, and thus, in general, one unit
cell thick YBa2 Cu3 O7 (≈12 Å) (or half a unit cell of Bi2 Sr2 Ca1 Cu2 O8 ≈ 16 Å) is not
superconducting when deposited onto a bare substrate. The lattice mismatch between the
film and the substrate and the presence of steps on the substrate surface are two factors
that are responsible for the suppression of Tc to zero. By using a buffer layer consisting
of a few unit cells of PrBa2 Cu3 O7 (or YBa2 Cu3 O7 ), these imperfections heal out, and
thus the multilayer produces its own ‘perfect’ substrate. Also, it has been found that it
is necessary to protect the top surface of the ultra-thin superconducting layer with another
buffer layer. Terashima et al (1991) found that the last unit cell of YBa2 Cu3 O7 is not
superconducting when it is not covered by at least one unit cell of PrBa2 Cu3 O7 . Finally, by
using a multilayer instead of just a single YBa2 Cu3 O7 layer, the inevitable imperfections
in any given single layer can be compensated for by the other layers in the multilayer,
resulting in fewer deviations from the ideal single layer behaviour.
In what follows, we shall first be concerned with the properties of individual YBa2 Cu3 O7
layers as a function of their thickness, using multilayers containing PrBa2 Cu3 O7 to fully
separate the YBCO layers. Figure 9 shows the evolution of Tc (= T (ρ(T ) = 10%ρ(Tconset ))
as a function of the YBa2 Cu3 O7 thickness. As expected, Tc increases and reaches a bulk
value only around 200 Å. Again, this result is surprising; why is it necessary to make the
YBa2 Cu3 O7 film as thick as 200 Å before the bulk Tc is found?
The three first points in figure 9 correspond to one, two and three unit cell thick layers of
YBa2 Cu3 O7 . An interesting question to ask is: how will this curve look if one tries to make
nominally intermediate thicknesses (i.e. not a multiple of a unit cell)? Such a study was
reported by Cieplak et al (1993) and by Triscone et al (1993). Figure 10 shows the results
reported by Cieplak et al. In this experiment, the Tc of single layers (again deposited on top
of a buffer and capped by PrBa2 Cu3 O7 ) is plotted as a function of the YBa2 Cu3 O7 thickness,
but here the average thicknesses of the layers are not multiples of a unit cell. Since the
material grows locally unit cell by unit cell, the top layer will ideally consist of islands.
Depending on the percentage of coverage, one expects through percolation arguments to
get the Tc of either an n or an n + 1 unit cell thick film. From this simple argument, one
expects as a function of the average thickness to observe a steplike behaviour with plateaus
corresponding to the Tc of 1, 2, 3, etc unit cell thick films. As one sees in figure 10, this
behaviour seems to be observed, suggesting that Tc is a function of the number of unit cells
in the layer. Also, as the thickness is reduced, not only does the onset of the transition go
Superlattices of high-temperature superconductors
1689
Figure 9. The critical temperature of YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattices as a function of
the YBa2 Cu3 O7 thickness for thick PrBa2 Cu3 O7 layers. As expected, the critical temperature
increases rapidly as a function of the YBa2 Cu3 O7 thickness and reaches the bulk value around
200 Å. (From Triscone et al 1990a.)
Figure 10. The critical temperature of PrBa2 Cu3 O7 /YBa2 Cu3 O7 /PrBa2 Cu3 O7 trilayers as a
function of the YBa2 Cu3 O7 thickness. This thickness is chosen not to be a multiple of a unit
cell. The open circles are the transition onsets, the points the estimated mean field transition,
and the full circles the Kosterlitz–Thouless transition temperature obtained from a fit of the
resistivity. (From Cieplak et al 1993.)
down, but the width also increases markedly. An essentially similar result has been found
by Triscone et al (1993b).
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J-M Triscone and Ø Fischer
Figure 11. Normalized resistance R(T )/R(100 K) against temperature for trilayers consisting
of 72 Å of PrBa2 Cu3 O7 , l = 1, 2, 3, 5, 10 unit cell thick YBa2 Cu3 O7 layers, and 72 Å of
PrBa2 Cu3 O7 on top. As can be seen, a shift of the transition, along with a broadening, occur
when the YBa2 Cu3 O7 thickness is reduced. (From Terashima et al 1991.)
3.2.2. The critical temperature of ultra-thin YBa2 Cu3 O7 layers. We shall address here the
question of the variation of the critical temperature with the thickness of the individual
layers of YBa2 Cu3 O7 . For this problem, it is useful to look at the resistance as a
function of temperature for different thicknesses. In figure 11 the resistive transitions of
single YBa2 Cu3 O7 layers reported by Terashima et al (1991) are shown. As is evident,
the character of the transition is largely dominated by a broadening which increases
systematically with decreasing thickness. In addition, we see that there is a small shift
in the onset of the transition, Tconset . This behaviour has been reported by many groups
and suggests an intrinsic Tc behaviour in these multilayers. In fact the Tc experiments on
‘intermediate’ thicknesses discussed above also point out that the reduction of Tc in ultrathin films is not obviously related to material problems such as steps at the interfaces, since
the latter would produce a monotonic decrease of the critical temperature as the thickness
is reduced, and not the observed steplike behaviour. It is important to stress here that
the YBa2 Cu3 O7 films, although not perfect, do show surfaces with large terraces that are
typically a few thousand Å wide. However, structural imperfections such as interdiffusion,
strain, and interface steps are still present in these materials and cannot be neglected. These
will certainly play a role in the progressive suppression of Tc , and some of the differences
in the detailed results between the various groups may be related to these problems. As
mentioned above, we will present here an explanation based on the assumption that the
overall observed behaviour is essentially intrinsic.
Now, it is clear from the results of figure 11 that when comparing Tc values, one
has to carefully consider the precise definition of Tc . Unless specified, we shall take as
Superlattices of high-temperature superconductors
1691
a conventional definition for Tc the temperature at which ρ(Tc ) = 10%ρ(Tconset )). This
criterion is of course sensitive to both the shift and the broadening of the transition, and
we use it here only to make a connection with values given in the literature. The detailed
analysis of the transitions will give more precise and physically justified definitions.
We believe that the shift in the onset of the transitions, Tconset , reflects changes in
the microscopic interactions in the sample. Charge transfer between the PrBa2 Cu3 O7
layers and the YBa2 Cu3 O7 layers is one possible origin. For example, transfer of oxygen
from YBa2 Cu3 O7 to PrBa2 Cu3 O7 across the interface or band bending at the interfaces
could occur. Experiments testing these ideas have been reported, for instance, by Norton
et al (1991), Affronte et al (1991), Cieplak et al (1994), and Ravelosona (1996). The
more striking and dominant feature of the transitions shown in figure 11, however, is the
systematic broadening with decreasing YBa2 Cu3 O7 thickness. As we shall demonstrate
below, 2D fluctuations, which in an ideal case lead to a Kosterlitz–Thouless transition,
provide an alternate explanation for this behaviour.
In an ideal 2D film, it is expected that a superconductor will undergo a Kosterlitz–
Thouless (KT) transition (Kosterlitz and Thouless 1973, Beasley et al 1979) at a temperature
TKT well below the mean field transition Tc0 (the transition obtained in mean field
theory, neglecting fluctuations). This Tc0 is situated somewhat below the onset of the
transition. The actual occurrence of the KT transition is a subtle phenomenon, and a
convincing demonstration that this transition actually occurs as predicted requires a detailed
investigation of several properties and so far has yet to be made in these materials. One
difficulty is that this demonstration requires an ideal behaviour at long length scales close
to the transition, and a complex microstructure in ultra-thin films may actually prevent the
observation of the expected signatures of the transition. For instance, percolative behaviour
can be misinterpreted as a KT transition, as shown by Leemann et al (1990).
However, as one goes away from the transition temperature, this problem gets less
critical and therefore it makes sense to look at the behaviour above TKT . The essence of the
argument here is that the difference Tc0 − TKT represents a measure for the transition width
and that this quantity increases with decreasing 2D superfluid density. An analysis of the
resistive transitions following this line of thought was presented by Fischer et al (1992a).
The starting point here is that the temperature dependence of the resistance just above the
KT transition calculated by Halperin and Nelson (1979),
A
(3)
R(T ) = RN exp − √
X(T ) − 1
can also be used in a broad temperature interval above TKT , as demonstrated by Minnhagen
and coworkers using a Coulomb gas scaling approach (Minnhagen 1987, 1989, Minnhagen
and Olsson 1991). Here A is a constant of the order unity, and
(Tc0 − TKT )T
.
(4)
X(T ) =
(Tc0 − T )TKT
Following the scheme proposed by Minnhagen (1987, 1989), it is possible to determine Tc0
and TKT from the experimental resistive transition curves. Using the Kosterlitz–Thouless
relation
φ02 d
(5)
TKT =
8kB πµ0 λ2 (TKT )
and approximating λ(T )
λ0
λ(T ) = √
1 − (T /Tc0 )
1692
J-M Triscone and Ø Fischer
as we find
φ02 d
TKT Tc0
=
.
Tc0 − TKT
8kB πµ0 λ20
(6)
The left-hand side of equation (6), which is essentially proportional to the inverse of the
transition width, should increase linearly with the thickness d. Figure 12 shows this quantity,
using the TKT and Tc0 values determined from the transition curves, plotted as a function
of the YBa2 Cu3 O7 thickness in decoupled multilayers where the PrBa2 Cu3 O7 layers were
either 96 Å or 144 Å thick (these data are shown as diamonds; the triangles represent
coupled multilayers with a PrBa2 Cu3 O7 thickness of 12 or 24 Å, which will be discussed
later). This result demonstrates that the broadening of the transitions can be understood in
terms of dissipation due to the thermal creation of unbound vortex–antivortex pairs. More
recent experiments are discussed in Fivat et al (1996b).
Figure 12. TKT Tc0 /(Tc0 − TKT ) as a function of the YBa2 Cu3 O7 thickness (in unit cells).
Uncoupled YBa2 Cu3 O7 layers are shown with diamonds for fixed 96 Å PrBa2 Cu3 O7 separation
thickness. Coupled YBa2 Cu3 O7 layers are shown with triangles for YBa2 Cu3 O7 /PrBa2 Cu3 O7
thicknesses of 12 Å/12 Å, 24 Å/12 Å, and 24 Å/24 Å. For decoupled layers, TKT Tc0 /(Tc0 −TKT )
is proportional to the YBa2 Cu3 O7 thickness, as expected and discussed in the text. For thin
PrBa2 Cu3 O7 separation a deviation occurs, showing that coupled samples behave with an
effective YBa2 Cu3 O7 thickness larger than that of the individual layers in the multilayer. (From
Fischer et al 1992a.)
Since the proportionality shown in figure 12 extends up to YBa2 Cu3 O7 thicknesses
of several hundred Å, it implies a 2D behaviour. One consequence is that the vortex–
antivortex pairs, which are the excitations, must extend over the thickness of the film in a
rigid fashion. This result, furthermore, implies that the energy of creating smaller vortex
loops is larger than the energy of creating vortex–antivortex pairs. The same should be
true for the dynamics of the field induced vortices, which is what is observed, as discussed
below in section 3.3.
Another consequence of this result is that, in principle, all isolated ultra-thin films should
show a similar broadening, since this effect should be present in all films. Unfortunately,
Superlattices of high-temperature superconductors
1693
the numbers will depend strongly on the actual carrier concentration determining λ0 . In the
experiments presented in figure 12, the films were probably slightly underdoped, and Hall
effect measurements suggest a carrier concentration only half of that of an ideally doped
crystal. This lower carrier density could be the result of mismatch strain. Consequently,
the λ0 corresponding to the data in figure 12 was about 2400 Å. In more optimally doped
samples, the broadening could turn out to be considerably reduced, which is another possible
explanation of different Tc and 1Tc values reported by different groups.
Figure 13. The superconducting transitions of superlattices containing one unit cell thick
YBa2 Cu3 O7 layers separated from the next by 16 unit cells of PrBa2 Cu3 O7 (open circles),
(Y0.3 Pr0.7 )Ba2 Cu3 O7 (squares), and (Ca0.5 Pr0.5 )Ba2 Cu3 O7 (diamonds). As is clear from the
figure, the broadening of the transition is strongly affected by the material surrounding the thin
YBa2 Cu3 O7 layers. (From Norton et al 1991.)
3.2.3. Coupling between the YBa2 Cu3 O7 layers: the role of the spacer material. We
have seen that a sufficiently thick layer of insulating PrBa2 Cu3 O7 between YBa2 Cu3 O7
layers separates the latter so that each of the YBa2 Cu3 O7 layers in the multilayer behave
as an isolated 2D layer. What happens when we replace PrBa2 Cu3 O7 by a more
conducting material? Figure 13 shows the effect of replacing pure PrBa2 Cu3 O7 by either
(Y0.3 Pr0.7 )Ba2 Cu3 O7 or (Pr0.5 Ca0.5 )Ba2 Cu3 O7 (Norton et al 1991). As one can see, the
Tconset remains about the same, but the transition width decreases strongly as the material
surrounding the thin YBa2 Cu3 O7 layers becomes more conducting. Within the context of the
above discussion, these multilayers behave as if the superconducting layers have a larger
effective thickness or a higher carrier concentration. This behaviour has been observed
systematically by several groups whenever the spacer layer is less insulating (Li Q et al
1994, Cieplak et al 1994, Fivat 1996a).
In order to investigate this question further, the original experiment reported in figure
8 was repeated, but this time using a more conducting spacer. In figure 14, the Tc against
spacer thickness for the multilayer series YBa2 Cu3 O7 /(Y0.45 Pr0.55 )Ba2 Cu3 O7 is shown,
together with the results reported in figure 8 (a result for a higher PrBa2 Cu3 O7 spacer
thickness is also shown (Fivat 1996a)). In agreement with the results shown in figure 13,
the Tc values are higher when a less insulating material is used as the spacer. However, we
also see that the Tc variation continues up to spacer thicknesses of several hundred Å. This
1694
J-M Triscone and Ø Fischer
Figure 14. Critical temperatures, defined as the temperature at which the resistance of the
film is 10% of the normal state resistance, for two series of superlattices containing 12 Å
thick YBa2 Cu3 O7 layers separated by insulating PrBa2 Cu3 O7 (squares) and semiconducting
(Y0.45 Pr0.55 )Ba2 Cu3 O7 (circles). (From Fivat et al 1996a.)
result suggests that a kind of coupling now exists between the YBa2 Cu3 O7 layers. As we
shall see in section 3.3, this hypothesis is confirmed by experiments on the vortex dynamics
in such multilayers.
The puzzling question that remains is the nature of this coupling. The spacer is
not metallic; it is situated on the insulating side of the metal–insulator transition in the
(Y1−x Prx )Ba2 Cu3 O7 system. One possibility is that the localization length in this material
could be relatively long. The alloy could actually have a metallic behaviour on a length scale
comparable to the thickness so that a proximity effect would couple the superconducting
layers. There is still, however, a problem. In a classical proximity effect calculation,
Tc as a function of the metallic spacer distance decreases over a distance equal to the
superconducting coherence length ξ in the normal layer perpendicular to the layers. An
estimate of the c-axis coherence length that we could expect for this alloy at the temperatures
considered here can be obtained from the measurements on the superconducting alloy
(Y0.6 Pr0.4 )Ba2 Cu3 O7 . This alloy has a Tc of 30 K and a ξc = 30 Å (Antognazza 1992).
This value is ten times less than what is necessary to explain the result reported in figure 14.
Although we do not yet have a satisfactory explanation of the observed behaviour, several
other experiments also report this ‘long range proximity effect’ in such systems (Li Q et al
1994, Cieplak et al 1994). We note that because these experiments were performed in
systems with large separation distances between the superconducting layers, an explanation
due to material problems is unlikely.
Experiments have also been performed using other materials as spacers. One such
interesting material is (Sr, Ca)RuO3 . This compound, which is well lattice matched to
YBa2 Cu3 O7 , is a metallic perovskite that is also ferromagnetic below 150 K (Kanbayasi
1978). Partial substitution of Ca for Sr allows one to progressively decrease the
magnetic transition temperature (Kanbayasi 1978), making this system interesting to
probe the influence of magnetism on this long-range coupling. Multilayer structures of
SrRuO3 /YBa2 Cu3 O7 and CaRuO3 /YBa2 Cu3 O7 have been achieved (Antognazza et al 1993,
Dömel et al 1995, Miéville et al 1996a, b), and investigations of the coupling are underway.
Superlattices of high-temperature superconductors
1695
Another system where it is interesting to study the coupling is (La,Sr)2 CuO4 . In this
system one can modulate the Sr doping to change the properties of the layers and to study
the coupling through the non-superconducting material. Work in this direction is being
performed by Locquet et al 1996 (see also Cretton et al (1994) and Williams et al (1994)).
3.2.4. Comparison with the behaviour of ultra-thin Bi2 Sr2 CaCu2 O8 layers. How do the
results obtained on the behaviour of ultra-thin YBa2 Cu3 O7 films compare with measurements
on other high-temperature superconductor materials like Bi2 Sr2 CaCu2 O8 ?
Figure 15. The resistance against temperature for a Bi2 Sr2 Cu1 O6 film, a Bi2 Sr2 CaCu2 O8 film,
and multilayers of the two materials containing half a unit cell (15.5 Å) of Bi2 Sr2 CaCu2 O8
separated by n = 1, 2, and 5 molecular layers (each n × 12.5 Å thick) of Bi2 Sr2 Cu1 O6 . As
can be seen, the critical temperature of the multilayers does not seem to be affected by the
separation. (From Eckstein et al 1992a.)
Figure 15 shows a spectacular result obtained by Bozovic et al (1992). What is shown
is the resistance against temperature for a Bi2 Sr2 CuO6 film, a Bi2 Sr2 CaCu2 O8 film, and
multilayers of the two materials containing half a unit cell (15.5 Å) of Bi2 Sr2 CaCu2 O8
separated by n = 1, 2, and 5 layers (each n×12.5 Å thick) of Bi2 Sr2 CuO6 . These films were
grown in an atomic layer-by-layer fashion, a technique which can lead to the preparation
of numerous metastable phases (see section 4). As can be seen, the critical temperature
of the multilayer does not seem to be affected by the separation. There is thus apparently
an important discrepancy between the behaviour of ultra-thin layers of Bi2 Sr2 CaCu2 O8 and
YBa2 Cu3 O7 . However, a major difference between the experiment of Eckstein et al and that
presented above is that the spacer material used by Eckstein et al has a high conductivity,
and is in fact superconducting below 10 K. As we pointed out in section 3.2.3, the transition
width in YBa2 Cu3 O7 is extremely sensitive to the conductivity of the adjacent material. In
YBa2 Cu3 O7 we have no direct equivalent material to Bi2 Sr2 CuO6 . However, the experiment
of Norton et al (1991) illustrated in figure 13 shows that a single unit cell thick layer of
YBa2 Cu3 O7 separated from the next by 16 unit cells of (Pr0.5 Ca0.5 )Ba2 Cu3 O7 , a material
with a higher resistivity (≈2 m cm at 15 K with an incomplete superconducting transition
1696
J-M Triscone and Ø Fischer
at 4.2 K (Norton et al 1991)) than Bi2 Sr2 Cu1 O6 , nevertheless has a transition ending around
60 K. This value can be compared to the 20 K obtained in the same experiment when the
spacer material is PrBa2 Cu3 O7 . One can also ask the question in another way: what does
the transition of ultra-thin Bi2 Sr2 CaCu2 O8 look like when sandwiched between an insulating
material? The answer to this question has been given by Li Z Z et al (1994), who grew
a series of BiSrCaCuO multilayers where they did observe a marked broadening of the
transition as the separation material between ultra-thin Bi2 Sr2 CaCu2 O8 layers was changed
from metallic Bi2 Sr2 CuO6 to insulating Bi2 Sr2 CuO6 .
This experiment is illustrated in figures 16(a) and 16(b). Figure 16(a) shows the
superconducting transitions of Bi2 Sr2 CuO6 (2201 on the figure) and Bi2 Sr2 CaCu2 O8 (2212
on the figure) films, grown with deposition conditions that yield metallic low-Tc Bi2 Sr2 CuO6
material, along with the superconducting transition of a multilayer containing one unit cell
thick Bi2 Sr2 CaCu2 O8 separated by two unit cells of Bi2 Sr2 Cu1 O6 . In this case, the Tc of
the sample is high, being in fact higher than for the Bi2 Sr2 CaCu2 O8 film, and the transition
is sharp, a result close to that of Eckstein et al. Figure 16(b) shows similar transitions for
Bi2 Sr2 CaCu2 O8 and Bi2 Sr2 Cu1 O6 films, the latter grown with deposition conditions that
yield ‘insulating’ Bi2 Sr2 CuO6 material, along with a transition for a multilayer containing
two unit cell thick Bi2 Sr2 CaCu2 O8 layers separated by two unit cells of Bi2 Sr2 CuO6 . For
this sample, although the Bi2 Sr2 CaCu2 O8 layer is thicker, the transition is very broad, with
an onset that is essentially unchanged. The transition width can be roughly compared to
what is observed on ultra-thin YBa2 Cu3 O7 separated by PrBa2 Cu3 O7 . On the basis of this
set of data, we are led to conclude that in comparable situations ultra-thin Bi2 Sr2 CaCu2 O8
layers behave similarly to YBa2 Cu3 O7 layers, although a detailed analysis has not yet been
performed on the former system.
In their recent review, Bozovic and Eckstein (1996) arrive at the conclusion, using
the same set of data, that 2D fluctuations are unimportant in these materials, and that the
reduced Tc observed in ultra-thin YBa2 Cu3 O7 layers is mostly related to extrinsic effects. We
believe that the experiments discussed above do not lead obviously to this conclusion, since
it does not account for the consensus coming from the large body of data on YBa2 Cu3 O7 ,
including the experiments reporting Tc against thickness that reveal steps in Tc , or for the
recent results of Li Z Z et al (1994) on Bi2 Sr2 CaCu2 O8 . We believe that the broadening of
the transition observed both in ultra-thin layers of YBa2 Cu3 O7 and Bi2 Sr2 CaCu2 O8 is an
intrinsic phenomenon related to 2D fluctuations, and that the broadening can be explained
by these fluctuations, as demonstrated by the Coulomb gas scaling analysis presented in
section 3.2.2.
One apparent problem with the interpretation promoted here is that if one considers
only phase fluctuations, as in a 3D X–Y model (see, for instance, Schneider et al (1996)),
the maximum change in Tc between a 2D and a 3D system is only about 30%. However,
as shown by Schneider et al (1991, 1992), for example, when both phase and amplitude
fluctuations are taken into account, a much larger reduction of Tc is expected for a decoupled
system, allowing one to explain the behaviour of the broad transitions of ultra-thin layers of
YBa2 Cu3 O7 (and Bi2 Sr2 CaCu2 O8 ). The striking reduction of the transition width observed
in Bi2 Sr2 CaCu2 O8 , and to a smaller degree in YBa2 Cu3 O7 , when the spacer material is
conducting implies either that even a very weak coupling is enough to reduce fluctuations
markedly, or that the metallic nature of the surrounding material suppresses 2D fluctuations,
thus reducing the transition width. In other words, the high conductivity of the adjacent
layers would inhibit the 2D nature of these ultra-thin layers and the associated fluctuations,
implying that the screening properties of the environment play a crucial role in reducing
fluctuations.
Superlattices of high-temperature superconductors
1697
Figure 16. The superconducting transitions of (a) Bi2 Sr2 CaCu2 O8 and Bi2 Sr2 CuO6 films
grown with deposition conditions producing metallic low-Tc Bi2 Sr2 CuO6 material, along with
a multilayer containing one unit cell thick Bi2 Sr2 CaCu2 O8 layers separated by two unit cells
of Bi2 Sr2 CuO6 . (b) Bi2 Sr2 CaCu2 O8 and Bi2 Sr2 CuO6 films grown with deposition conditions
producing ‘insulating’ Bi2 Sr2 CuO6 material, along with a multilayer containing two unit cell
thick Bi2 Sr2 CaCu2 O8 layers separated by two unit cells of Bi2 Sr2 CuO6 . As can be seen, the
transition of the multilayer containing metallic Bi2 Sr2 CuO6 is higher and sharper than that
containing insulating Bi2 Sr2 CuO6 , even though for the case of the metallic Bi2 Sr2 CuO6 layer
the Bi2 Sr2 CaCu2 O8 is only one unit cell thick. (From Li Z Z et al 1994.)
1698
J-M Triscone and Ø Fischer
Ariosa and Beck (1991) consider the effect of electrostatic energy on quantum phase
fluctuations, taking into account the electrostatic coupling between the metallic layers in
YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers. They stress that this energy varies with the distance
between the layers because of the screening properties of the adjacent layers, and that the
larger the capacitance between the metallic layers, the more strongly phase fluctuations
are suppressed, resulting in a higher Tc when compared to a single isolated YBa2 Cu3 O7
layer. This model does not assume any Josephson-like coupling between the groups of
CuO2 planes. Based on these ideas, Ariosa and Beck could explain the relatively slow
decrease of Tc with PrBa2 Cu3 O7 thickness, as reported in figure 8, as well as the large
difference in Tc between the bulk value and that obtained in an ultra-thin isolated layer.
This model, which has been further extended (Ariosa et al 1994a, b), thus points to an
essential difference between an insulating spacer and a metallic spacer, with the metallic
one strongly suppressing the phase fluctuations. Experiments with metallic spacers should
not show such important fluctuation effects, in agreement with the observations discussed
here. More experiments are necessary to clarify definitively these issues, but if the ideas
discussed above turn out to give the correct picture, they would give a simple and unified
view of the behaviour of ultra-thin superconducting oxide layers.
3.3. Vortex dynamics and vortex state phase diagrams of multilayers
3.3.1. Vortex state phase diagram of high-Tc superconductors. The vortex state phase
diagram of high-Tc superconductors is an important area of research (see, for instance,
the review of Blatter et al (1994)). The interplay of high temperature, large anisotropy,
and disorder produce important changes in the nature of the vortex phase. While in low-Tc
superconductors a solid Abrikosov lattice is generally found between Hc1 and Hc2 , the highTc superconductors have, in contrast, a large liquid and essentially reversible region above
a characteristic temperature. In this liquid region, the dissipation is dominated by plastic
deformations of the vortex structure, leading to linear current–voltage (I –V ) characteristics
at low currents (Geshkenbein et al 1989), and thus to zero superconducting critical current.
The transition from the vortex liquid to the vortex solid will be a melting in a clean system,
and probably a glass transition in the presence of disorder. The details of this phase diagram
are still under debate, although the gross features are basically understood. These issues
are important, since above the irreversibility line the critical current is zero, making the
materials useless for applications. The understanding of the vortex dynamics and of the
B–T phase diagram is thus an important question both for fundamental reasons as well as
for potential applications of high-Tc superconductors. In the following sections we will see
how superlattices can help address some of these issues. The main advantage offered by
these structures is that they provide a way to control and modify the material parameters
and thus the vortex phase diagram. Anisotropy, dimensionality, and pinning can all be
changed, allowing one to track the effects of such changes on specific physical properties.
Clear predictions (see, for instance, Fisher et al (1991)) have been made on the nature of
the low-temperature vortex state depending on its dimensionality, making these multilayers
a perfect testing ground for the theory.
3.3.2. Vortex dynamics in thin YBa2 Cu3 O7 layers, H perpendicular to the ab plane.
We shall start with a discussion of the vortex dynamics in isolated ultra-thin films in
the liquid phase, i.e. close to Tc . The experiments reported here were performed on
YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattices, with the PrBa2 Cu3 O7 layers being eight unit cells
thick (Brunner et al 1991, Fischer et al 1992a). These 96 Å of ‘insulating’ PrBa2 Cu3 O7 are
Superlattices of high-temperature superconductors
1699
sufficient to essentially decouple the superconducting layers (as will be discussed below,
magnetic coupling is irrelevant to this study). The behaviour of these multilayers can thus
be ascribed to the behaviour of single layers. The experiment is performed in the liquid
phase above the irreversibility line in the regime of linear I –V characteristics.
The main idea is to measure the resistive transitions in a magnetic field parallel to
the c-axis. For low-Tc superconductors, one observes a shift of the transition temperature
related to the upper critical field. In contrast, high-Tc superconductors show a broadening
of the transition with a long thermally activated tail (see, for instance, Iye et al (1987) and
Palstra et al (1990)). This behaviour is ascribed to flux flow and thermally activated flux
flow (Palstra et al 1990). From these resistive transitions one can extract the activation
energy U for flux motion as a function of the YBa2 Cu3 O7 thickness and magnetic field.
This activation energy corresponds to the process with the smallest energy that allows for
flux motion. In a bulk material this process will correspond to the jump of a segment of
length lc of a flux line (or a flux line bundle with a diameter Rc in the collective pinning
picture (see Blatter et al 1994 ch 8)). This correlation length lc will be determined by a
minimization of the cost in energy for a vortex segment to jump. The line energy, which
is proportional to the length of the vortex, and the elastic energy due to the bending of the
vortex line (Kramer 1973, Brandt 1993) are both involved in this process. Since this elastic
energy involves the tilt modulus C44 of the vortex lattice, it depends on the anisotropy
and thus on the Josephson coupling between the individual CuO2 layers. The weaker this
coupling is, the smaller lc is, and finally, when there is no coupling, lc should be equal to
the thickness of the individual layers. Since the activation energy for thermally activated
flux flow is proportional to lc (Palstra et al 1990), one expects in the case of a purely 2D
material that U should be independent of the film thickness, since lc is equal to or smaller
than a unit cell. With coupling, one expects U to be proportional to the film thickness ds
for ds smaller than lc (in other words, lc is cut off by the finite thickness). A measurement
of the activation energy U as a function of the film thickness will thus provide information
on the coupling between the groups of CuO2 planes, i.e. on the stiffness of the vortices in
the material. As we will see, this technique will turn out to be a powerful tool for studying
coupling in the c-direction.
The activation energies are obtained from a measurement of the resistivity ρ as a function
of temperature and magnetic field using standard four point measurements. If the resistivity
ρ has a thermally activated behaviour, ρ(T ) can be expressed very generally as
−U (B, T , J )
ρ(T ) = ρ0 exp
kB T
with U (B, T , J ) being the activation energy which might depend on temperature, magnetic
field, and current. However, for low currents, U is current independent in the liquid,
which has been explained as being due to the dominant contribution of plastic deformations
(Geshkenbein et al 1989). As is clear from the formula, when ρ(T ) is represented in an
Arrhenius plot, ln ρ against 1/T , the activated character of the resistivity becomes clear,
with ln ρ proportional to −1/T . The activation energy can thus be determined from the
slope. The temperature dependence of U may complicate its determination from the slope
of the Arrhenius plot. However, as is apparent, if U varies as U0 (1 − T /Tc ), the slope gives
U0 . Thus, only deviations from a linear temperature dependence introduce a correction. A
detailed discussion of this temperature dependence is given by Palstra et al (1990), Brunner
(1993), and Triscone et al (1994). It is shown that these corrections are small and cannot
modify the essential conclusions of this section. The activation energies quoted here are the
average slope of the Arrhenius plots, denoted Ū .
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J-M Triscone and Ø Fischer
Figure 17. Arrhenius plots of the resistivity for a YBa2 Cu3 O7 film (top), a 96 Å/96 Å
YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayer (middle), and a 24 Å/96 Å YBa2 Cu3 O7 /PrBa2 Cu3 O7
multilayer (bottom). The different curves are for magnetic fields of 0, 1, 3, 6, and 9 T. The
inset shows I –V characteristics for the 24 Å/96 Å multilayer, showing that the measurements
are performed in the linear regime. (From Brunner et al 1991.)
Superlattices of high-temperature superconductors
1701
Figure 17 shows a typical Arrhenius plot of the resistivity, from which one can extract
the activation energy for flux motion. The top figure is a measurement of ρ(T ) for different
magnetic fields for 1000 Å YBa2 Cu3 O7 films. As can be seen, when comparing this top
figure with the middle and the bottom ones, which show data for superlattices containing
96 Å and 24 Å thick YBa2 Cu3 O7 layers, respectively, the effect on U of reducing the
thickness is a dramatic demonstration that the interlayer coupling is strong in YBa2 Cu3 O7 .
In particular, one sees directly that U changes by a factor of four between the 96 Å
YBa2 Cu3 O7 and the 24 Å YBa2 Cu3 O7 , and thus U is proportional to the YBa2 Cu3 O7
thickness in this range. The inset shows I –V characteristics for the 24 Å/96 Å multilayer,
showing that the measurements are performed in the linear regime.
Figure 18. The behaviour of the activation energies Ū as a function of the YBa2 Cu3 O7 thickness
in the multilayer and the magnetic field. As can be seen, Ū is proportional to the YBa2 Cu3 O7
thickness up to 264 Å, and the activation energy values of a thick film are obtained for an
extrapolated thickness of about 300 to 400 Å. (From Brunner et al 1991.)
Figure 18 shows a central result, where Ū is plotted as a function of the YBa2 Cu3 O7
thickness. Here, Ū is proportional to the YBa2 Cu3 O7 thickness for each magnetic field for
thicknesses up to 300 to 400 Å. The scaling of the activation energy with the YBa2 Cu3 O7
thickness reflects the fact that there is a relatively strong Josephson coupling between the
individual unit cell layers in YBa2 Cu3 O7 , and that the tilt modulus C44 is correspondingly
large, giving a large lc . Comparing these results with the activation energy of a thick
film (1500 Å) allows one to estimate lc to be about 400 Å. In the solid vortex phase at
low temperatures and high critical current densities, the vortex correlation length has been
measured using quantum flux creep. It was found to be much shorter, with an estimated
value of about 24 Å (Van Dalen et al 1993, 1996).
This result has important implications concerning the dimensionality of the vortex lattice
in the liquid phase. In thin films with thicknesses smaller than lc (=400 Å), the vortices
will be essentially straight lines, so that the dynamics is determined by the movement in the
ab plane, implying that the vortices are to be considered as 2D. Only when the thickness is
larger than lc does bending play a role so that the vortex lattice is 3D. Recently, Suzuki et al
1702
J-M Triscone and Ø Fischer
Figure 19.
The magnetic field dependence of Ū for 24 Å/96 Å and 96 Å/96 Å
YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers. For all the thicknesses investigated (up to 264 Å), it
was found that Ū is proportional to − ln(B) while a power-law behaviour is observed in bulk
materials. (From Brunner et al 1991.)
have been able to study vortex dynamics in a-axis YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattices
(Suzuki et al 1994), which in principle yields information on the correlation length of a
vortex along the ab plane.
In Bi2 Sr2 CaCu2 O8 , no such experiment has been performed up to now. However,
measurements of kinetic inductance by Rogers et al (1992) show that a similar scaling of
the activation energy, i.e. U ≈ d, does take place in Bi2 Sr2 CaCu2 O8 for up to at least two
unit cell thick films, where the measurements were stopped. This result demonstrates a
non-negligible coupling in Bi2 Sr2 CaCu2 O8 in zero field.
A second important finding of these vortex dynamics experiments is that the activation
energy depends logarithmically on the applied magnetic field, instead of the usually observed
power-law dependence. More precisely, it was found by Brunner et al (1991) that
Ū = −α log B + β.
Figure 19 shows this behaviour for different multilayers with superconducting layer
thicknesses going from 24 to 264 Å. This behaviour is also observed in thin single
YBa2 Cu3 O7 layers (Brunner 1993), in Mo/MoGe artificial multilayers (White et al 1993),
and more recently in a-axis YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayers (Suzuki et al 1994).
The origin of this log B dependence of the activation energy is still an open question
at the moment. It should be noticed that this behaviour is different from the U ∼ B −α
behaviour often observed in bulk materials, and is thus specific to thin films. At least three
ideas have been proposed to explain this particular field dependence. In the 2D collective
pinning theory of Feigel’man et al (1990), it was proposed that the interaction between two
dislocations is logarithmic up to distances of the order of R0 + Rc (R0 ≈ a02 /ξ ), with a0
being the vortex–vortex separation and Rc being the vortex translational correlation length.
For larger distances, it decreases exponentially, so that the energy to activate a dislocation
Superlattices of high-temperature superconductors
1703
Figure 20. The resistive transitions for a 24 Å/96 Å YBa2 Cu3 O7 /PrBa2 Cu3 O7 multilayer as a
function of magnetic field up to 19.5 T. The measurements are performed with the field parallel
to the ab plane and, as can be seen, the transition is not noticeably affected by the magnetic
field. (From Fischer et al 1992b.)
pair becomes finite and equal to:
φ02 d
Rc
a0
ln
+
U=
16π 2 µ0 λ2
a0
ξ
where d is the film thickness, φ0 the flux quantum, ξ the coherence length, and λ the
penetration depth. It was noted by Brunner et al (1991) that for a short translational
correlation length
Rc , the free energy to create a dislocation pair is reduced to U ∝ ln(a0 /ξ ).
√
Since a0 ≈ φ0 /B, we see that the activation energy U is proportional to −α log B + β.
This interpretation was also adopted to explain the behaviour of Mo/Ge superlattices (White
et al 1993) and a-axis superlattices (Suzuki et al 1994, 1995).
Jensen et al (1992) have proposed that the logB behaviour may have a different origin,
namely that the dominant contribution to the dissipation is from thermally generated vortex–
antivortex pairs. Here, the idea is that the field-induced vortices can screen the vortex of
the thermally generated vortex–antivortex pair. In this case, the mean vortex–antivortex
distance is about a0 , the vortex lattice constant. Since the energy between a vortex and an
antivortex is proportional to the logarithm of the separation, one gets U ≈ −α ∗ log B + β ∗ .
Finally, in a recent publication, Burlachkov et al (1994) suggest that this effect might be
related to surface barriers. To discriminate between these different interpretations, one needs
more experiments, since all the predictions are rather close, although the fit to the dislocation
activated behaviour is clearly better.
3.3.3. Vortex dynamics in thin YBa2 Cu3 O7 layers, H parallel to the ab plane. In this
section we want to briefly describe the behaviour of some superlattices in magnetic fields
parallel to the layers. This discussion of the activation energy will be relevant for
section 3.3.6, where we discuss the critical current and angular scaling of the critical current.
As observed by Fischer et al (1992b) in YBa2 Cu3 O7 /PrBa2 Cu3 O7 superlattices, an
applied magnetic field parallel to the layers has no effect on the resistive transition when the
multilayer contains thin decoupled superconducting layers. Figure 20 shows the resistive
transition of a 24 Å YBa2 Cu3 O7 /96 Å PrBa2 Cu3 O7 multilayer in fields up to 20 T. No
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J-M Triscone and Ø Fischer
discernible effect of the field is observed on the transition. It turns out that the low resistivity
part of the transition is not affected either. A more complete study shows that as long as
the applied field is smaller than about φ0 /d 2 the material has a field-independent behaviour.
Above this field, broadening of the transition appears and the activation energy becomes
field dependent, with U ≈ B −1/2 (Triscone et al 1991). This result suggests that vortices
enter in the layers only above this characteristic field. Indeed, Hc1 can be very high for thin
layers, and an estimate of Hc1 yields (see, for instance, Orlando and Delin (1991))
2λab φ0
d
ln
Hcl =
√
πλc d 2
ξab ξc
with λab , λc , ξab , and ξc being the ab plane and c-axis penetration depths and coherence
lengths, respectively. From this formula, one sees that for a 24 Å thick layer Hc1 is about
60 T, using standard parameters for YBa2 Cu3 O7 (ξab = 15 Å, ξc = 3 Å, λab = 1500 Å,
λc = 7000 Å). The picture here is that the magnetic field essentially penetrates the structure,
but vortices will enter the superconducting layers only above Hc1 . Below Hc1 , no vortices
are in the layers, and thus no dissipation is observed.
Even more interesting is the case of coupled systems.
Both in the case of
YBa2 Cu3 O7 /(Y1−x Prx )Ba2 Cu3 O7 (Fivat et al 1994a) and YBa2 Cu3 O7 /SrRuO3 (Miéville
et al 1996a), it was found that field-dependent dissipation occurs at much lower fields. In
these systems the field will enter the regions between the YBa2 Cu3 O7 planes as in the above
case. However, because of proximity coupling, the field will enter in the form of vortices in
the ‘normal’ layer. Since the energy difference between sitting in the normal material and the
superconductor is smaller than between an insulator and a high-temperature superconductor
(such as in YBa2 Cu3 O7 /PrBa2 Cu3 O7 ), the vortices can now enter the superconductor at
a lower field. This behaviour is precisely what one observes, as shown in figure 21 for
a YBa2 Cu3 O7 /(Y0.45 Pr0.55 )Ba2 Cu3 O7 multilayer, where Ū is plotted as a function of the
magnetic field on a log–log scale. Thus, this limiting field represents a kind of ‘artificial
intrinsic pinning’ such as described by Feinberg and Villard (1990a, b), and Feinberg (1990).
These experiments therefore demonstrate again that there is a significant coupling between
the superconducting layers, in agreement with the experiments described in sections 3.2.3
and 3.3.2. As can be seen in the figure, the activation energies are field independent only
up to 1 T. Above this value, a field-dependent activation energy Ū ≈ B −0.2 is observed.
3.3.4. Probing the coupling between superconducting layers using activation energies. One
of the motivations for making superlattices is to modify in a controlled manner the anisotropy
of the material. In the superlattices described above, the spacer separates completely the
superconducting layers, making the vortex lattice effectively 2D, so that in this sense these
materials have an infinite anisotropy. In order to have a finite anisotropy, one has to choose
the spacer material such that there remains a finite coupling between the layers. One way
to do this would be to reduce the thickness of the PrBa2 Cu3 O7 layers. Starting from the
24 Å YBa2 Cu3 O7 /96 Å PrBa2 Cu3 O7 multilayer and reducing the PrBa2 Cu3 O7 thickness, we
expect the activation energies to stay constant as long as there is no coupling between the
layers. When the coupling sets in, however, we expect the activation energies to increase,
since the movements of the pancake vortices in one layer will now be coupled to those
in the neighbouring layers. In the investigations of Brunner et al (1991), this idea was
tested, and it was found that at a separation of two unit cells of PrBa2 Cu3 O7 there is
still some coupling, but beyond a four unit cell separation the activation energies become
independent of the PrBa2 Cu3 O7 thickness. Therefore, one way to produce materials with
an increased anisotropy compared to YBa2 Cu3 O7 would be to make, for example, 24 Å
Superlattices of high-temperature superconductors
1705
Figure 21. The magnetic field dependence of Ū for a coupled 24 Å YBa2 Cu3 O7 /96 Å
(Y0.45 Pr0.55 )Ba2 Cu3 O7 multilayer. In this case the activation energy is field independent only
below 1 T, as compared to decoupled multilayers, where this field is above 20 T. (From Fivat
et al 1994a.)
YBa2 Cu3 O7 /12 Å PrBa2 Cu3 O7 and 24 Å YBa2 Cu3 O7 /24 Å PrBa2 Cu3 O7 superlattices and
study their properties. Investigations on such structures have been carried out, and figure
12 shows a Coulomb gas scaling analysis of these results. Clearly, they behave as if the
YBa2 Cu3 O7 layers had a larger effective thickness, indicating coupling. Unfortunately,
since it is not possible to avoid the presence of steps and screw dislocations in these films,
it is very hard to control the local thickness everywhere on these films with a precision of
one unit cell. We therefore looked for another way to introduce coupling between the layers.
As we have seen in section 3.2.3, the replacement of PrBa2 Cu3 O7 by an alloy, (Y1−x
Prx )Ba2 Cu3 O7 , does introduce some coupling over large thicknesses. As pointed out above,
the Tc dependence on the spacer thickness could also be explained by purely electrostatic
arguments, at least for PrBa2 Cu3 O7 . Thus, the question arises as to how we can test directly
that there is a Josephson-like coupling across these layers. One way would be to make direct
current measurements perpendicular to the layers, but this kind of measurement is difficult
to do with accuracy on these thin films.
Another way is to use the activation energy analysis discussed above. A study of
this type has been reported by Triscone et al (1994) on a series of samples made in
the following way. The spacer materials used were the alloys (Y0.6 Pr0.4 )Ba2 Cu3 O7 and
(Y0.45 Pr0.55 )Ba2 Cu3 O7 , as well as PrBa2 Cu3 O7 . The former is metallic and superconducting
below 30 K. These measurements were carried out above the critical temperature of the
alloy. The second alloy is just on the insulating side of the metal–insulator transition; its
resistance in the investigated temperature interval is, however, several orders of magnitude
below that of PrBa2 Cu3 O7 . Each sample was deposited on a buffer made of the chosen
spacer material. The N = 1 sample had one 24 Å thick superconducting DyBa2 Cu3 O7
layer (DyBa2 Cu3 O7 was used in this study, and its properties are similar to YBa2 Cu3 O7 ),
with a 96 Å layer of spacer material deposited on top. In the N = 2 sample, a second
24 Å DyBa2 Cu3 O7 layer was added on top of the 96 Å spacer layer, followed by a second
layer of 96 Å spacer material. This series was continued up to N = 15. Because lc for
YBa2 Cu3 O7 (and DyBa2 Cu3 O7 ) was found above to be about 400 Å, the vortices in an
isolated 24 Å DyBa2 Cu3 O7 layer will behave as 2D pancake vortices.
1706
J-M Triscone and Ø Fischer
Figure 22. Arrhenius plots of the resistivity, i.e. ln R against 1/T , for fields of 1, 3, 6, and
9 T and for two different samples, N = 1, N = 2, as illustrated in the inset. The N = 1
sample contains one 24 Å thick DyBCO layer deposited onto a ≈220 Å (Y0.6 Pr0.4 )Ba2 Cu3 O7
buffer layer, followed by a protection layer of 96 Å of the same buffer material. The N = 2
sample is built similarly, by depositing a second 24 Å DyBa2 Cu3 O7 layer and ‘protective’ 96 Å
(Y0.6 Pr0.4 )Ba2 Cu3 O7 layer. (From Triscone et al 1994.)
We first concentrate on a comparison of the N = 1 and N = 2 samples. If PrBa2 Cu3 O7
is used as the spacer material, the two samples have the same activation energies simply
because the pancake vortices in each layer move independently of each other. When the
two alloys are used, the results are very different. Figure 22 shows the Arrhenius plots
for the N = 1 and N = 2 samples with (Y0.6 Pr0.4 )Ba2 Cu3 O7 as the spacer material. We
see that the activation energies for each magnetic field have considerably increased for the
N = 2 sample compared to the N = 1 sample. In fact, an analysis of these results show that
U (N = 2) = 2 U (N = 1). This result can easily be understood. If the coupling between
pancake vortices in the two layers in the N = 2 sample is strong enough, the vortices in
the two layers will move together, and the activation energy for the N = 2 sample will be
exactly twice that for the N = 1 sample. It is interesting to note that this result is also
found for the (Y0.45 Pr0.55 )Ba2 Cu3 O7 alloy, although this one is non-metallic.
These measurements clearly demonstrate that a coupling takes place across the 96 Å
alloy layer. What happens when the number of layers is increased, and what happens when
the thickness of the alloy is increased? The answer to the first question is shown in figure 23
(Fischer et al 1994). Here the activation energy is plotted as a function of N for the alloy
(Y0.45 Pr0.55 )Ba2 Cu3 O7 . Beyond N = 3 the activation energy saturates, showing that the
correlation length lc corresponds to about three layers of DyBa2 Cu3 O7 . This result implies
that the vortex lattice is 3D for N > 3, and in the next section we shall discuss the vortex
phase diagram for such a 3D sample (N = 15). The answer to the question regarding the
alloy thickness is not yet known in detail. An N = 2 sample with a spacer layer of 220 Å
still showed U (N = 2) = 2 U (N = 1), whereas with a spacer of 750 Å the activation energy
of one layer was found. Thus the coupling clearly extends over several hundreds of Å.
Another question that can be raised here concerns the magnetic coupling between the
pancake vortices. Because this question does not depend on the nature of the spacer material,
Superlattices of high-temperature superconductors
1707
Figure 23. Activation energies Ū for DyBa2 Cu3 O7 /(Y0.45 Pr0.55 )Ba2 Cu3 O7 as a function of N
and for fields of 0.25, 0.5, 1.0, 3.0, 6.0, and 9.0 T. As can be seen for N < 3–4, Ū depends on
N linearly, while for larger N a saturation is observed. The full curves are a guide to the eye.
(From Fischer et al 1994.)
the answer should be the same for all three materials considered here. The fact that no
coupling is observed for PrBa2 Cu3 O7 as a spacer material excludes magnetic coupling as
the origin of the observed behaviour in the alloys. In fact, calculations on systems with only
magnetic coupling show that this energy is of the order of Tc (Bulaevskii et al 1991) and
is thus much lower than the activation energies observed here. Therefore, we do not expect
that the magnetic coupling can be seen in these experiments, and the coupling must be of
a Josephson type in the broad sense that the phases of the pair-wavefunctions of different
layers are correlated.
3.3.5. The vortex state phase diagram of N = 15 DyBa2 Cu3 O7 /(Y0.45 Pr0.55 )Ba2 Cu3 O7
superlattices. The general idea behind this section is to show how multilayers can be
used as a tool to understand the vortex state phase diagram of high-Tc superconductors. As
mentioned before, there is a large difference in anisotropies between YBa2 Cu3 O7 , which
is a rather strongly coupled system, and Bi2 Sr2 CaCu2 O8 , which is much more anisotropic.
Multilayers can be used to systematically investigate systems with anisotropies that are
intermediate between YBa2 Cu3 O7 and Bi2 Sr2 CaCu2 O8 to gain further understanding of the
vortex state phase diagram.
In recent papers, Cubitt et al (1993) and Lee S L et al (1993) probed the phase diagram
in Bi2 Sr2 CaCu2 O8 single crystals by neutron diffraction and muon spin relaxation. The
striking feature they observe is the disappearance, in the solid part of the phase diagram, of
the neutron diffraction pattern above a field of 0.06 T. This disappearance is clearly related
to the destruction of long-range order in the vortex lattice. This result raises the question of
the nature of the vortex state above this field and, in addition, how this characteristic field
depends on anisotropy, disorder, finite size effects, etc. To address these issues, multilayer
systems are ideal.
1708
J-M Triscone and Ø Fischer
As an example, we shall here present the results of a study of an N = 15 sample of
the 24 Å DyBa2 Cu3 O7 /96 Å (Y0.45 Pr0.55 )Ba2 Cu3 O7 multilayer discussed above. To probe
the vortex state phase diagram, activation energies have been measured in the liquid phase
(Fivat et al 1994b, Triscone et al 1994); current–voltage (I –V ) characteristics and critical
scalings have been used to probe the boundary between the liquid and the solid phase
(Andersson et al 1994, 1996); and, at low temperatures, I –V analysis, using a collective
flux creep or a vortex glass picture, has been performed to study the dynamics of the solid
phase (Obara et al 1994, 1995).
First, let us discuss the liquid phase. The new effect observed in these coupled systems
is that the activation energy for flux motion varies as −α ln B + β (a signature of thin film
behaviour, as observed and discussed above for thin single decoupled layers) only at low
fields. Above a characteristic field H ∗ , we observe a deviation which corresponds to a
relative increase of Ū . For large N samples, the activation energy seems to turn into a
power law with Ū ≈ H −α above H ∗ , as observed in bulk materials. Depending on the
samples, the values of α range from 0.45 to 0.65, but mostly values close to 0.5 were found.
In addition, it was observed that the crossover field depends on the number of layers in
the sample, i.e. the total thickness. Even if small fluctuations in the activation energies
complicate the precise determination of the crossover field, one finds that the thicker the
sample (or the larger N is), the smaller the crossover field. This situation is illustrated in
figure 24, where Ū (H ) is shown for N = 5 and N = 15 samples, i.e. two samples with
similar parameters except for the large difference in total thickness. As can be seen, H ∗
is about three times larger for the N = 5 sample. We also find that H ∗ depends on the
anisotropy, with larger anisotropy resulting in a smaller H ∗ .
Figure 24. The field dependence of the activation energy for two samples with similar parameters
but with very different total thickness. The N = 15 sample contains 15 24 Å thick DyBa2 Cu3 O7
layers separated by 96 Å of alloy material, while the N = 5 sample contains only five
DyBa2 Cu3 O7 layers, and thus is about three times thinner. As can be seen, H ∗ is roughly
inversely proportional to the total thickness. (From Fivat et al 1994b.)
What could be the origin of this crossover? What we observe is a deviation from the
log H behaviour at a field which depends on the total thickness. Above this characteristic
field, the measured activation energies are higher than what a continuation of the logH
dependence would have given. The crossover field is certainly not the decoupling field,
at which intralayer interactions dominate the interlayer interactions, leading to an effective
Superlattices of high-temperature superconductors
1709
decoupling of the layers, since above H ∗ one does not at all recover the behaviour of a
single layer N = 1 sample. One possibility is that the observed behaviour is the result of an
entanglement of the vortices, as discussed by Nelson (1988) and Nelson and Seung (1989).
The idea is that the logH behaviour may not only be a characteristic of 2D systems, but
more generally the characteristic of disentangled systems. As long as the vortices are rigid,
entanglement is clearly impossible. For thin 3D samples and at low fields, the vortices are
too separated to entangle; as the field increases the distance between vortices decreases and
entanglement becomes possible, resulting in an increase of the activation energy due to the
flux line crossing energy.
The expression for the entanglement field is (Nelson (1988), Nelson and Seung (1989))
Mab
λab
ln
,
H = φ03 (8πµ0 lz kB T λ2ab )−1
Mz
ξab
where lz is the sample thickness, λab the in-plane penetration depth, ξab the in-plane
coherence length, T the temperature, and Mab and Mz the effective masses. Setting
λab = 1400 Å, ξab = 12 Å, T = 50 K, and using a mass ratio Mab /Mz = 10−2 (this
value is a rough estimate of the mass ratio), one gets H = 1200(lz (Å))−1 (T), where the
entanglement field is in Tesla for lz in Å. For the N = 15 sample we have lz = 1800 Å,
leading to an entanglement field of ≈0.7 T, precisely in the range where we observe the
crossover in figure 24. The 1/ lz dependence predicted by the above formula is consistent
with the data, although large uncertainties arise in the determination of the crossover field.
It is also interesting to notice that Vinokur et al (1990) have predicted a B −0.5 behaviour
of the activation energy, as observed here at high fields, in the case of a very viscous flux
lattice with large barriers associated with thermally activated plastic motion in the vortex
structure. They also note that such large barriers can arise due to entanglement and crossing
of vortex lines.
To probe the boundary between the solid and the liquid phase, I –V characteristics have
been performed. Figure 25 shows an I –V characteristic for an N = 15 sample at 1 T. In
the region of high temperature, low voltage, and low current, one gets linear I –V ’s, which
is where we determine the activation energies. When the temperature is lowered, one can
observe that the I –V ’s become progressively nonlinear, and one can define a temperature
TG at which the curvature of the I –V changes from positive to negative. We take this
temperature as the characteristic temperature separating the vortex liquid state from the
vortex solid. Andersson et al (1994, 1996) have shown that a critical scaling analysis can
be performed around the transition temperature in a narrow temperature range, suggesting a
second-order phase transition. From this analysis we find critical exponents consistent with
a vortex glass transition. In addition, one finds that as the field is increased, TG decreases
continuously and that this scaling analysis can be performed up to 9 T, suggesting 3D
correlations even at high fields. The detailed features of these I –V ’s, including the Sshape, are discussed in Andersson et al (1996).
In the low-temperature solid vortex phase (below TG ) one can perform an analysis
based on a vortex glass description and extract some characteristic parameters. Fitting the
experimental I –V ’s through the vortex glass relations
J0 µ
(E/J ) = ρ0 exp
−
J
allows one to unambiguously extract J0 , µ, and ρ0 as a function of field and temperature (for
a complete picture, see Blatter et al (1994), ch 7). The field and temperature dependences
of these parameters turn out to be sensitive to changes in the vortex dynamics. Figure 26
1710
J-M Triscone and Ø Fischer
Figure 25. I –V characteristics for an N = 15 sample. At high temperatures, low currents, and
low voltages, linear I –V ’s are observed. As the temperature is lowered, a curvature appears,
and at TG a change from positive to negative curvature is observed. This temperature is taken
as the boundary between the liquid and solid part of the vortex state. (From Andersson et al
1996.)
shows J0 as a function of field and temperature for the N = 15 sample. As can be seen, at
low temperatures, the J0 value decreases abruptly at a magnetic field of about 1 T. As the
temperature is increased, the onset field of this transition, Hon , changes, while the endpoint
Hs∗ (the reason for this notation will become apparent below) is constant. When such an
analysis is performed on a sample with different total thickness (the N = 5 sample for
instance), one finds that Hon (T ) is sample independent, while Hs∗ is inversely proportional
to the total thickness. This result suggests that we are seeing a double transition, which
is reflected in a temperature-dependent, thickness-independent onset and a temperatureindependent, thickness-dependent Hs∗ . Furthermore, one finds that Hs∗ ≈ Hl∗ , measured in
the liquid phase. To understand the physics of this transition, it is interesting to relate J0 ,
µ, and Jc (the measured critical current) to the collective pinning energy Uc . One finds,
upon comparing the vortex glass and collective flux creep expressions (Obara et al 1995),
µ
J0
.
Uc = kB T
Jc
What is found (Obara et al 1995) is that the abrupt change in J0 is related to a decrease of
Uc around Hs∗ , implying a reduction of the correlated volume and a softening of the vortex
structure.
If one records all this information on a B–T diagram, one ends up with the phase
diagram illustrated in figure 27. We now discuss the physics behind the different regions
of the phase diagram. Clearly these materials display a large liquid region separated from a
low-temperature solid of vortices, very probably a vortex glass phase. Both liquid and solid
regions are ‘cut’ by a horizontal line at a field H ∗ . Above H ∗ bulk behaviour is observed
in the different physical properties measured. Below H ∗ , a typical thin film behaviour is
observed, with Ū ≈ −α ln B + β in the liquid and Jc ≈ −a ln B + b in the solid. H ∗ is
proportional to the inverse of the total thickness, which means that for thick samples the
Superlattices of high-temperature superconductors
1711
Figure 26. Magnetic field dependence of the scaling current density J0 at several temperatures
for the N = 15 sample. (From Obara et al 1995.)
‘thin film’ region naturally shrinks. In the vortex solid, another line, Hon (T ), complicates the
picture. One possible interpretation is that below Hon (T ), the vortices are rigid but probably
do not form a lattice since the disorder in the films is rather high. This phase would be the
analogue (with disorder added) of the region where a neutron diffraction pattern is observed
in Bi2 Sr2 CaCu2 O8 . At Hon (T ), the in-plane interactions start to dominate the inter-plane
interactions, and a partial decoupling of the vortices occurs. This transition depends only
on in-plane against inter-plane interactions and should not depend on the total thickness.
At this transition, any neutron diffraction pattern will disappear since long-range order
is destroyed. At a higher field Hs∗ , the vortices are no longer rigid and might entangle,
forming an entangled solid. This latter transition must depend on total thickness, as is
experimentally observed. It is interesting to note that as the total thickness d increases, Hs∗
(≈1/d) decreases, and thus for thick samples the two transitions will turn into one, which
is very probably what is observed in Bi2 Sr2 CaCu2 O8 single crystals. It is also interesting to
note that since we see two transitions, Hon (T ) cannot correspond to a complete decoupling
of the vortices, since in this case no thickness dependence of H ∗ should be observed.
We have described in this section measurements on a multilayer system with an
anisotropy intermediate between that of YBa2 Cu3 O7 and Bi2 Sr2 CaCu2 O8 . By studying
the behaviour as a function of N, important information has been gained about the nature
of the transitions. Clearly, one sees that this approach opens up the door for a number of
other investigations on such structures, which could clarify the fascinating properties of the
vortex structure in the high-temperature superconductors.
3.3.6. Testing flux pinning models using high-Tc superlattices. Another interesting model
experiment has been performed by Li Q et al (1992) on YBa2 Cu3 O7 /(Y0.6 Pr0.4 )Ba2 Cu3 O7
coupled multilayers. The idea behind this work is to probe flux pinning models using
superlattices as a tool. The structures investigated consist of one unit cell thick YBa2 Cu3 O7
separated by 96 Å of alloy material. The key point is that, depending on the temperature
at which the critical current measurement is performed, the separation material is either
normal or superconducting. Figure 28 shows Jc as a function of the angle for two different
temperatures; for the top graph, T = 25 K, which is below the Tc of the alloy, while for the
bottom graph, T = 52 K, which is above the critical temperature of this alloy. As one can
see, the theoretical predictions of Tachiki and Takahashi (1989) and Kes et al (1990) are
very easily tested using such an approach. At low temperatures, the model of Tachiki and
1712
J-M Triscone and Ø Fischer
Figure 27. The proposed H –T phase diagram of the N = 15 superlattice obtained from
the experiments described in the text. The full circles are Hs∗ in the vortex solid, and the
hatched area is Hl∗ , determined from activation energy measurements. The curvature of the
I –V characteristics changes at the full curve, which is considered to be a vortex glass transition
line TG (H ). Full squares represent Hon (T ) of the J0 transition. The dashed lines are a guide to
the eye. (From Obara et al 1995.)
Takahashi, which assumes a dissipation dominated by the motion of segments perpendicular
to the ab plane and takes as an angle θ stepwise vortex lines with segments along and
normal to the ab plane, fits the data very nicely, suggesting a vortex line configuration
close to that of bulk YBa2 Cu3 O7 . At higher temperatures, the data are well described
by the expression given by Kes et al (1990), which states that Jc (B, θ ) = Jc (B cos θ, 0),
implying no dissipation of the parallel component of the field.
4. Exploratory systems: new systems and new materials
In this section we want to discuss the atomic layer-by-layer construction of materials,
exploratory systems such as BaCuO2 , BaCuO2 /CaCuO2 , and BaCuO2 /SrCuO2 , where
superconductivity has been found, and new experiments based on the possibilities of
growing epitaxial heterostructures containing materials with similar crystalline structures
but very different physical properties. As an example, we will discuss the observation of a
ferroelectric field effect in ferroelectric/SrCuO2 heterostructures.
4.1. Layer-by-layer growth of oxide materials
The idea of atomic layer-by-layer growth is to take advantage of the naturally layered
structure of the high-Tc oxides in order to grow these materials by supplying in sequential
fashion the different atomic constituents. This approach allows one to envisage going beyond
thermodynamically stable compounds. The primary difficulty, however, is to control the
amount of materials deposited very accurately, typically to within 1% (Bozovic et al 1994).
Furthermore, one must find the appropriate temperature–oxygen pressure window which
allows one to obtain sufficient lateral surface mobility to promote good crystallinity without
substantial bulk diffusion in the vertical direction. In essence, one has to find the conditions
for kinetically controlled growth, as opposed to thermodynamically controlled growth.
One demonstration of this type of growth has been provided by Bozovic et al (1992)
and Eckstein et al (1992a, b, 1994), who have developed a deposition system with thermal
Superlattices of high-temperature superconductors
1713
Figure 28. The angular dependence of Jc for a 12 Å YBa2 Cu3 O7 /96 Å (Y0.6 Pr0.4 )Ba2 Cu3 O7
multilayer. The results for (a) were taken at a temperature of 25 K, lower than the
Tc of (Y0.6 Pr0.4 )BCO, while (b) is for a temperature of 52 K, higher than the Tc of
(Y0.6 Pr0.4 )Ba2 Cu3 O7 . (From Li Q et al 1992.)
evaporation sources providing atomic fluxes of the different elements. The rates are
controlled by atomic absorption spectroscopy, and the growth is followed in situ by RHEED.
By using this complex technology, one is able to obtain the required rate control and to
determine the ‘sweet spot’ in the temperature–pressure phase diagram, allowing for layerby-layer growth. This technique can be extremely powerful, not only to produce single
phase compounds of BiSrCaCuO 2201 and 2212, but also 2223 and larger n compounds
such as 2278, which are essentially impossible to obtain in phase pure form with other
techniques, since all these phases are energetically very close. Another obvious possibility
is to produce a vertical modulation in the growth direction, not by changing the target, as
with single target laser ablation or sputtering, but by changing the deposition sequence.
Figure 29 shows a cross section TEM image of a BiSrCaCuO film grown in layer-by-layer
fashion, where a single BiSrCaCuO 2278 layer has been embedded between thick layers
of Bi2 Sr2 CaCu2 O8 . This striking picture illustrates the large potential of this technology
1714
J-M Triscone and Ø Fischer
very well. The next step will be to produce artificial compounds and new structures by
using these advanced technologies. A recent review on high-Tc superlattices by Bozovic
and Eckstein (1996) covers this subject in detail.
Figure 29. The cross section TEM image of a single unit cell thick layer of 2278 BiSrCaCuO,
sandwiched between thick Bi2 Sr2 CaCu2 O8 layers. (From Eckstein et al 1994.)
4.2. Infinite layer based superlattices
Copper oxides ACuO2 (A = alkaline earth) with the infinite layer structure have stimulated
great interest in the past few years because the infinite layer structure is the simplest
structure containing the CuO2 planes that are essential for superconductivity. Furthermore,
superconductivity has been reported in bulk samples with Tc as high as 110 K in
(Sr0.7 Ca0.3 )1−y CuO2 (Azuma et al 1992). In these samples, however, TEM analyses
reveal the presence of ‘superlattice’ defect layers, which might play the role of a charge
reservoir. It is thus rather natural to investigate synthetically modulated multilayer structures
containing the infinite layer material. Figure 30 shows a cross section TEM image of
a (Sr, Ca)RuO3 /(Sr, Ca)CuO2 superlattice, grown by Satoh et al (1994), with individual
thicknesses down to 35 Å and 28 Å for (Sr, Ca)RuO3 and (Sr, Ca)CuO2 , respectively. The
quality of the artificial structure is obvious from the TEM image. Figure 31 shows a
θ –2θ x-ray diffractogram of a 36 unit cell/18 unit cell (Sr, Ca)CuO2 /SrCuO2 multilayer
(Fàbrega et al 1996a), along with the theoretical spectrum for an ideal structure. These
two examples, among others, demonstrate that high-quality structures can be grown with
these compounds. These two structures, however, were not superconducting. On the other
hand, superconductivity in very similar systems has been reported by Li X et al (1994) in
BaCuO2 /CaCuO2 and by Norton et al (1994) in SrCuO2 /BaCuO2 superlattices with very
short periods, typically a few unit cells of each material. It is worthwhile noting that infinite
layer BaCuO2 cannot be obtained in bulk form. Figure 32 shows the resistivity against
temperature for different multilayer samples (BaCuO2 )n /(SrCuO2 )m . One possibility to
Superlattices of high-temperature superconductors
1715
explain superconductivity in these materials is that some oxygen atoms are present in the Ba
planes, providing apical oxygens to the Cu, which is the reason for the notation used in figure
32; (BaCuO2 )n /(SrCuO2 )m is indexed as Ban Srm Cun+m O2(m+n)+δ . Another possibility is
that some carbon groups are contained in these films. Oxycarbonate intercalation layers
would again provide apical oxygens, and superconductivity in such materials has been
reported with Tc in the observed range (Allen et al 1995). Further work is necessary to
answer these questions and to understand the origin of superconductivity in these artificial
structures.
Figure 30. The TEM cross section of a (Sr, Ca)RuO3 /(Sr, Ca)CuO2 superlattice with individual
thicknesses down to 35 Å and 28 Å for (Sr, Ca)RuO3 and (Sr, Ca)CuO2 , respectively. The
interface quality for this multilayer made of constituents with different crystal structures is
remarkable. (From Satoh et al 1994.)
4.3. New material combinations
As mentioned in the introduction, the techniques developed mainly at first for the growth
of oxide superconductors are now widely used for the growth of other types of oxides such
as ferroelectrics and giant magneto-resistance compounds. In addition, the possibility of
combining materials with similar crystalline structures but different properties in epitaxial
structures opens new perspectives for experiments and devices. As an example of this
promising field, we mention the recent report by Ahn et al (1995) of an all epitaxial
ferroelectric field effect device made of ferroelectric Pb(Zr1−x Tix )O3 and a thin layer of
SrCuO2 . The idea of the experiment is to use the surface electric field produced by a
ferroelectric layer to modify the number of carriers at an interface. In this experiment, a 40 Å
SrCuO2 layer was deposited on a thick Pb(Zr1−x Tix )O3 and characterized in situ. Figure 33
shows the structures used and the principal result of the experiment. Four point resistivity
measurements give the resistivity of the thin overlayer as a function of the polarization
of the ferroelectric layer. As can be seen, a non-volatile 3.5% resistivity change of the
1716
J-M Triscone and Ø Fischer
SrCuO2 film is observed, depending on the polarization state of the ferroelectric. This
change is related to the modification of the carrier concentration in the SrCuO2 layer at
the interface. Recent experiments (Ahn et al 1997a) show that a 10% resistivity change
effect can be obtained in a 30 Å thick SrRuO3 film, and that the magnitude of the effect is
consistent with the change in carrier concentration. This effect was non-volatile for up to
several days, which was the duration of the experiment. These results imply an interface
quality high enough that the field effect is not substantially reduced by electronic traps
at the interface, revealing an interesting new approach for electronic doping experiments.
Finally, Ahn et al (1997b) have demonstrated the possibility of using this ferroelectric field
effect, in conjunction with scanning probe microscopy, to modify the electronic properties
of complex oxides on submicrometre length scales in a non-volatile, reversible fashion that
does not require any permanent electrical contacts or lithographic processing.
Figure 31. A θ–2θ x-ray diffractogram of a 36 unit cell/18 unit cell (3 = 182 Å)
(Sr, Ca)CuO2 /SrCuO2 superlattice. The satellite peaks around the (002) reflections of the pure
infinite layer structure reveal the modulated structure. The calculated ideal spectrum is very
close to the experimental one. The splitting of the Kα1 and Kα2 reflections is also a signature
of the excellent quality of the sample. (From Fàbrega et al 1996a.)
Figure 32. Resistivity against temperature for different multilayer samples (BaCuO2 )n /
(SrCuO2 )m , indexed as Ban Srm Cun+m O2(m+n)+δ . The striking point here is that neither of
the constituent materials is superconducting. (From Norton et al 1994.)
Superlattices of high-temperature superconductors
1717
Figure 33. Room temperature resistivity of a 40 Å SrCuO2 -Pb(Zr0.52 Ti0.48 )O3 film deposited
on Nb-SrTiO3 as a function of the polarization of the Pb(Zr0.52 Ti0.48 )O3 layer. The pulse train
shown is used to switch the polarization of the Pb(Zr0.52 Ti0.48 )O3 . This experiment demonstrates
that the resistivity changes are non-volatile and reversible. In the inset, repeated pulses of the
same polarity do not alter the resistivity state of the material. To the right of the graph is a
schematic of the heterostructure and the measurement geometry. (From Ahn et al 1995.)
5. Conclusions
In this review, we have attempted to illustrate that the epitaxial growth of perovskite-like
oxides has opened a wide field of research in synthetic multilayers. Since heteroepitaxial
growth is often possible in this category of materials, a large choice of constituent
compounds for such multilayers exists. This fact is illustrated by the large number of
multilayer structures already realized based on YBa2 Cu3 O7 , BiSrCaCuO, (La, Sr)CuO4 ,
SrCuO2 , SrRuO3 , Pb(Zr, Ti)O3 , etc. The new and exciting possibility of fabricating epitaxial
heterostructures with materials having essentially the same crystallographic structures but
very different electronic properties, ranging from dielectric insulators and ferroelectrics to
metals, ferromagnets, and superconductors, represents a great potential for new physics and
new devices in the future.
We have also discussed in detail the use of oxide superlattices as model systems to
probe the physics of high-Tc superconductivity. A large part of the existing experiments are
concerned with the critical temperature of ultra-thin layers and the relation between highTc superconductivity and low dimensionality. The conclusion of our analysis is that the
critical temperature of ultra-thin layers of YBa2 Cu3 O7 or BiSrCaCuO is markedly reduced
in comparison to thick layers. This reduction can be understood in terms of 2D fluctuations
in the framework of the 2D Coulomb gas scaling approach by considering quantum phase
fluctuations. The nature of the spacer material was discussed, and several experiments
clearly show that when this spacer is more metallic the transition width is considerably
reduced, suggesting that the screening properties of the environment plays an important role
in reducing fluctuations.
The use of superlattices for studying vortex dynamics was presented, with experiments
testing the dimensionality of the vortex structures as well as the vortex phase diagram in
coupled multilayer systems being discussed. In YBa2 Cu3 O7 , a c-axis vortex correlation
length of about 400 Å is found in the liquid vortex phase, implying 2D vortex behaviour
for films thinner than this characteristic length. In the solid phase, at low temperatures
1718
J-M Triscone and Ø Fischer
and high current densities, this correlation length is much smaller, about 24 Å. By using
multilayers containing ultra-thin layers of YBa2 Cu3 O7 separated by a non-insulating spacer
material, one can design systems with a controlled anisotropy. New features in the vortex
dynamics have been observed suggesting a transition to a partially decoupled state of the
vortices along the c-axis, and then to an entangled state, as the magnetic field is increased.
Critical current measurements in superlattices can be used to probe different theories, since
the anisotropy and coupling between thin layers can be modified as desired. An example
of 2D and anisotropic 3D behaviour has been shown.
Finally we discussed briefly the layer-by-layer construction of oxides, allowing the
realization of metastable compounds. This approach represents an exciting new avenue to
new materials and holds promise for new results in the coming years.
Acknowledgments
We would like to especially thank C H Ahn for a careful reading of the manuscript, L Fàbrega
and P Fivat for their comments, and G Bosch and A Stettler for technical support. We would
like also to thank numerous former or actual collaborators in Geneva who worked and shared
with us the excitment of this research, M Affronte, M Andersson, L Antognazza, O Brunner,
A Cretton, M Decroux, L Fàbrega, P Fivat, M G Karkut, E Koller, L Miéville, H-H Obara,
R Perez-Pinaya, and S Reymond. We would like also to thank the numerous scientists who
have contributed to this review through their work and numerous discussions, H Adrian,
D Ariosa, Y Bando, M R Beasley, H Beck, G Blatter, I Bozovic, L N Bulaevskii, K Char,
M Z Cieplak, J R Clem, J P Contour, J N Eckstein, O Eibl, C B Eom, D Feinberg, D Fork,
T H Geballe, V B Geshkenbein, R Griessen, A Gupta, R H Hammond, A Inam, Y Jaccard,
H J Jensen, A Kapitulnik, M Kawai, T Kawai, A E Koshelev, C Kwon, Q Li, P Lindenfeld,
J-P Locquet, D H Lowndes, A F Marshall, J A A J Perenboom, P Martinoli, V Matijasevic,
P Minnhagen, D Norton, S J Pennycook, H Raffi, D Ravelosona, C T Rogers, T Schneider,
I K Schuller, D Schlom, K Setsune, Y Suzuki, M Tachiki, T Terashima, A J J Van Dalen,
P Van der Linden, T Venkatesan, K Wasa, W White, E Williams, X X Xi. This work was
supported by the Swiss National Foundation of Scientific Research.
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