Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects
The fluctuation-induced conductivity (paraconductivity) measured in YBa₂Cu₃O₇₋d (YBCO) films grown on 10° miscut SrTiO₃ (001) substrates is analyzed using various theoretical models describing weak fluctuations in high-Tc superconductors and considering both Aslamazov-Larkin and Maki-Thompson fluctu...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2002
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irk-123456789-1287202018-01-14T03:03:22Z Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects Solovjov, A.L. Свеpхпpоводимость, в том числе высокотемпеpатуpная The fluctuation-induced conductivity (paraconductivity) measured in YBa₂Cu₃O₇₋d (YBCO) films grown on 10° miscut SrTiO₃ (001) substrates is analyzed using various theoretical models describing weak fluctuations in high-Tc superconductors and considering both Aslamazov-Larkin and Maki-Thompson fluctuation contributions in the clean limit approach. The analysis reveals a highly anisotropic pair-breaking caused by structural defects produced. This result is in favor of an idea that pseudogap in high-Tc oxydes is mainly governed by the fluctuating pairing. 2002 Article Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects / A.L. Solovjov // Физика низких температур. — 2002. — Т. 28, № 11. — С. 1138-1149. — Бібліогр.: 30 назв. — англ. 0132-6414 PACS: 74.40.+k http://dspace.nbuv.gov.ua/handle/123456789/128720 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
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The fluctuation-induced conductivity (paraconductivity) measured in YBa₂Cu₃O₇₋d (YBCO) films grown on 10° miscut SrTiO₃ (001) substrates is analyzed using various theoretical models describing weak fluctuations in high-Tc superconductors and considering both Aslamazov-Larkin and Maki-Thompson fluctuation contributions in the clean limit approach. The analysis reveals a highly anisotropic pair-breaking caused by structural defects produced. This result is in favor of an idea that pseudogap in high-Tc oxydes is mainly governed by the fluctuating pairing. |
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| author |
Solovjov, A.L. |
| author_facet |
Solovjov, A.L. |
| author_sort |
Solovjov, A.L. |
| title |
Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects |
| title_short |
Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects |
| title_full |
Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects |
| title_fullStr |
Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects |
| title_full_unstemmed |
Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects |
| title_sort |
fluctuation conductivity in y-ba-cu-o films with artificially produced defects |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2002 |
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Свеpхпpоводимость, в том числе высокотемпеpатуpная |
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http://dspace.nbuv.gov.ua/handle/123456789/128720 |
| citation_txt |
Fluctuation conductivity in Y-Ba-Cu-O films with artificially produced defects / A.L. Solovjov // Физика низких температур. — 2002. — Т. 28, № 11. — С. 1138-1149. — Бібліогр.: 30 назв. — англ. |
| series |
Физика низких температур |
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AT solovjoval fluctuationconductivityinybacuofilmswithartificiallyproduceddefects |
| first_indexed |
2025-07-09T09:45:13Z |
| last_indexed |
2025-07-09T09:45:13Z |
| _version_ |
1837162105299533824 |
| fulltext |
Fizika Nizkikh Temperatur, 2002, v. 28, No. 11, p. 1138–1149
Fluctuation conductivity in Y–Ba–Cu–O films with
artificially produced defects
A. L. Solovjov
B. Verkin Institute for Low Temperature Physics and Engineering,
National Academy of Sciences of Ukraine, 47 Lenin Ave., 61103 Kharkov, Ukraine
E-mail: solovjov@ilt.kharkov.ua
Received March 14, 2002
The fluctuation-induced conductivity (paraconductivity) measured in YBa2Cu3O7–�
(YBCO) films grown on 10� miscut SrTiO3 (001) substrates is analyzed using various theore-
tical models describing weak fluctuations in high-Tc superconductors and considering both
Aslamazov–Larkin and Maki–Thompson fluctuation contributions in the clean limit ap-
proach. The analysis reveals a highly anisotropic pair-breaking caused by structural defects
produced. This result is in favor of an idea that pseudogap in high-Tc oxydes is mainly go-
verned by the fluctuating pairing.
PACS: 74.40.+k
1. Introduction
The pseudogap (PG) phenomenon in high-Tc su-
perconductors (HTSC) is widely debated at present
[1]. Measurements taken with a wide variety of
techniques demonstrate that the pseudogap is pre-
sent in both the spin and charge channel but theo-
retical views of the problem are still rather contro-
versial. One point of view which stands out in the
context of experimental evidence is the idea of pre-
formed pairs [1] considered to be the fluctuating
Cooper pairs which are believed to be present in
HTSC well above Tc [2,3]. As structural defects
are known to deeply affect the pair-breaking me-
chanism in high-Tc oxides [2], investigation of the
influence of systematically produced structural de-
fects on the fluctuation conductivity is to clarify
the issue.
Measurement of the fluctuation conductivity
(FC) is known to be a powerful method of getting
reliable information about the normal charge scat-
tering and superconducting coupling mechanisms in
HTSC just in the PG temperature region [4–11].
Using FC analysis, such microscopic parameters as
the coherence length along the c axis, � c( )0 , and
the phase relaxation time of fluctuating pairs,
��(100 K), can be determined. It also gives the
possibility to address more fundamental issues such as
the contribution from or absence of Maki–Thompson
(MT) type fluctuations [12]. The question is of re-
markable importance, since the MT fluctuation
process is strongly dependent on the pairing mecha-
nism [12,13].
Fluctuation conductivity, � � �� � ( ) ( )T TN , ari-
ses from excess current carried by fluctuation-crea-
ted Cooper pairs above the superconducting transi-
tion temperature Tc, as has been shown by
Aslamazov and Larkin (AL) [14]. The additional
contribution to FC, introduced by Maki and
Thompson [12] to extend the AL theory, is treated
as arising from interaction of the fluctuating Coo-
per pairs with normal electrons resulting in the
pair-breaking process. Finally, the fluctuation con-
ductivity is taken to be
� � �
( ) [ ( ) ( )] [ ( ) ( )]T T T / T TN N , (1)
where
( ) ( )T Txx� is the actually measured longi-
tudinal resistivity and
�N T T b( ) � � is the ex-
trapolated normal-state resistivity. According to
the nearly antiferromagnetic Fermi liquid (NAFL)
model [15] the linear-in-T
xx T( ) dependence at
high temperatures can be considered as a true sign
of the normal state of the system, a state which is
characterized by stability of the Fermi surface and,
hence, by stability of the normal-carrier scattering
rate. As T is lowered,
xx T( ) deviates downward
from the T-linear dependence at some representa-
tive temperature T*0 >> Tc, giving rise to the ex-
cess conductivity which is usually considered as a
© A. L. Solovjov, 2002
pseudogap [1,15]. However, in the temperature in-
terval Tc < T < Tñ0 the excess conductivity is well
described by the conventional fluctuating theories
[12–14] and is usually treated as ��( )T [4–10,16].
Tc0 = (100 ± 5) K is the temperature which de-
termines the pair-breaking parameter � th �
� ( )T T /Tc c c0 [12,13]. The possibility of the fluc-
tuating pairing in HTSC at Tc0 < T < T*0 is widely
debated at present [1–3].
As we have recently shown [16], the ��( )T de-
pendence of well-structured optimally doped (OD)
and strongly underdoped (UD) YBCO films al-
ways consists of two temperature regions with dif-
ferent FC behavior, separated by the dimensional
crossover at T0. Accordingly, above T0 this is the
two-dimentional (2D) fluctuation region common-
ly described by the MT term of the Hikami –Larkin
theory (HL) [13], and at Tc < T < T0 it is the re-
gion of three-dimentional (3D) fluctuations always
described by the 3D term of the AL theory [14].
The Lawrence–Doniach (LD) model [17], proposed
to describe FC in any layered superconducting sys-
tem, was found to fail in fitting experiment in this
case. Really, the LD model predicts a smooth,
gradual transition from 2D AL fluctuation behavior
to 3D AL behavior as the temperature approaches
Tc, and it considers the MT contribution to be van-
ishing. This kind of FC behavior has been shown
to be typical for badly structured high-Tc oxides
[2]. However, in most of the previous papers de-
voted to the problem, FC fitted by the LD model
alone is reported [4–9], suggesting the presenñå of
different structural defects in the samples studied.
The conclusion is corroborated by measurements of
the critical current densities jc of thin epitaxial
YBCO films, which are known to be at least an or-
der of magnitude larger than that for high-quality
YBCO single crystals [18]. The main reason for
that is strong flux pinning in the films caused by
specific defects such as point defects in the CuO2
planes [19], screw dislocations [20], and twin
boundaries [21], expected to be also responsible for
observed ��( )T dependence of the LD type. How-
ever, the properties of high-quality modern thin
epitaxial HTSC films prepared by pulsed laser de-
position [22] are believed to be mostly determined
by some slight degree of miscut growth of the
films, resulting in the appearance of specific
growth-related defects [23,24]. These defects have
been identified as effective pinning centers [23] and
have been found to produce an appreciable aniso-
tropy of the resistivity, magnetic flux penetration,
and critical current densities in miscut-grown
YBCO films [24]. However, a systematic study of
the effect of specific growth-related defects on the
fluctuating pairing in HTSC is still lacking.
In this paper we presented measurements of the
fluctuation conductivity in the c-axis-oriented
YBa2Cu3O7–� (YBCO 123) films grown on 10�
miscut SrTiO3 (001) substrates. The expected
strong anisotropy of the scattering of the fluctuat-
ing pairs due to growth-related defects influence is
revealed. The results are treated using a recently
developed approach to FC analysis in YBCO films
[2,16].
2. Experimental techniques
YBCO films with a thickness of 240 to 2400 Å
were grown on vicinal SrTiO3 (001) substrates by
pulsed laser deposition (PLD) as described in de-
tail in Ref. 24. The SrTiO3 substrates were cut and
polished 10� off the (001) plane towards [010], as
confirmed by Laue diffraction. After the PLD pro-
cess the deposition chamber was pumped to a pres-
sure of less than 10–7 mbar and the samples were
transferred to the scanning tunneling microscopy
(STM) stage without exposure to air. To provide
measurements of expected resistivity anisotropy the
samples were patterned in two different directions.
These two directions are denoted in the text by L
and T, respectively, since they coincide with the di-
rections longitudinal to and transverse to the film
step edges. To get the resistivity data, standard
4-probe dc measurements were performed using a
fully computerized setup. It should be emphasized
that a certain care in the sample preparation pro-
cess enables to obtain highly reliable and system-
atic data despite the evident complexity of the sam-
ples’ structure.
Combined STM and cross-sectional transmission
electron microscopy (TEM) measurements estab-
lished a close relationship between the film mor-
phology and defect microstructure [24]. It has been
shown that almost periodic surface and defect
structure is generated for YBCO films grown on 10�
miscut SrTiO3 substrates. The TEM image has re-
vealed a significantly disturbed YBCO lattice. The
step structure persists on the YBCO surface due to
the step flow growth mechanism. This generates a
multitude of translational boundaries (TB), ex-
tending throughout the entire film thickness. The
crystal lattice is slightly tilted across the defects.
Numerous stacking faults (SF) are also created, re-
sulting in a general waviness of the unit-cell-high
layers as observed in the TEM image. A strong
strain field is associated with this specific defect
structure. Some extended defects (ED) with a
structural width of 20–30 Å, penetrating most of
Fizika Nizkikh Temperatur, 2002, v. 28, No. 11 1139
Fluctuation conductivity in Y–Ba–Cu–O films with artificially produced defects
the film thickness, are also present. All defects, and
especially TB, are found to contribute to the strong
flux pinning in the films. It has also been shown
[24] that the close correspondence between the
STM and TEM results suggests that most defects
are aligned along the direction L of the regular film
step edges. This one-dimentional nature of the de-
fects is found to be resposible for observed aniso-
tropy of the resistivity, magnetic flux penetration,
and critical current densities [24]. Naturally, one
can expect to reveal an anisotropy of the pair-brea-
king mechanism in the films, resulting in the aniso-
tropy of the fluctuation conductivity. If pseudogap
in high-Tc oxides is really governed by the fluctuat-
ing pairing different temperature regions of the PG
behavior have to be observed, depending on whe-
ther measurements are perfomed in the L or in T di-
rection.
3. Results and discussion
3.1. Transport properties
To obtain more information, two films with dif-
ferent thicknesses commonly used in experiment,
d0 = 1900 Å (sample M23) and d0 = 900 Å (sample
M35), were chosen for analysis. Both films exhibit
a sharp resistive transition at Tc
90 K in both di-
rections (see the Table), i.e., can be considered
as apparent representatives of OD YBCO systems.
Figure 1 shows
xx as a function of tempera-
ture for sample M23 measured in the L and T
directions, respectively. As can be readily seen,
T L( ) ( .100 100 3 2K K)/
in this case. Moreover,
a value
T L( ( .100 100 9 5K) K)/
is measured for
sample M35, suggesting the strong influence of the
growth-related defects on the normal charges scat-
tering. However, despite of the considerable in-
crease of the resistivity, the width of the resistive
transition �T
1.2 K is estimated for M23 in both
directions (Table), a value typical for well-cha-
racterized OD systems. The representative tempera-
ture T*0L, marked by the arrow on the graphs, is
also found to be in good agreement with the predic-
tion of the NAFL model for OD films. According to
the NAFL model, the T-linear resistivity above T*0,
extrapolated towards Tc (as shown by the dashed
lines in the figure), is treated as the sample nor-
mal-state resistivity
N(T) used to determine �� (T)
from Eq. (1). However, resistivity buckling, which
is uncharacteristic of OD systems, is distinctly ob-
served for both samples at higher temperatures
(Fig. 1). The result suggests the presence of a
somewhat enhanced electron–electron interaction
in the films [15], likely caused by the defect struc-
ture.
But the most striking result is the fact that mea-
sured for both films representative temperatures
T*0L and T*0T appear to be noticeably different
(Fig. 1 and the Table). As it is clearly seen from
the figure, the larger resistivity, the shorter is the
T-linear resistivity region but the shorter becomes
the PG temperature range too, what is difficult to
explain in terms of the normal charges scattering
only. To account for the finding, measurements of
1140 Fizika Nizkikh Temperatur, 2002, v. 28, No. 11
A. L. Solovjov
Table
The sample parameters
Sample d
0
, Å T
c
, K �T, K Tc
mf , K
(100K), ���cm
(300K), ���cm d
/dT, ���cm �K–1 T
*0
, K
M23-L 1975 90.0 1.0 90.14 88 287 0.93 130
M23-T 1900 89.9 1.2 90.19 278 628 1.6 108
M35-L 900 89.7 2.0 90.60 204 600 1.86 150
M35-T 900 89.5 2.2 90.85 1948 3325 6.06 105
Fig. 1. Resistivity as a function of temperature for
sample M23 measured in the L and T direction; the
dashed lines is the extrapolated normal-state resistivity.
FC, sheding light on the fluctuating pairing, are
evidently required.
3.2. Fluctuation conductivity
3.2.1. Theoretical overview. The fluctuation
conductivity ��( )T is computed from the resistivity
measurements (Fig. 1) using Eq. (1), as discussed
above. The experimental FC data are analyzed
using the HL theory [13], considering both the AL
and MT fluctuation contributions. In the absence
of magnetic field H the AL theory yields
� � �� � �
ÀL e / d[ ( )]( ) /2 1 2 116 1 2� (2)
and
�
� �
� � � �
�
� �
�
�
� � �
� � �
ÌÒ
e
d /
/
2
1 2
8 1
1 1 2
1 1 2
� ( )
ln
( )[ ( ) ]
[ (
/
�
�
) ]
,
/1 2
1�
�
�
�
�
�
(3)
where d
11.7 Å is the distance between conducting
CuO2 planes, � � � �� � 2 2 02 2 2 1
c cT /d /d( ) [ ( ) ] is
a coupling parameter,
� � � � ���1203 0 16 0 2. ( ( ))( )[ ( ) ]l/ / /d k Tab c B� (4)
is a pair-breaking parameter, and � �
ln ( )T/Tc
mf
( )T T /Tc
mf
c
mf is a reduced temperature. Here
T Tc
mf
c� is the critical temperature in the me-
an-field approximation actually separating the FC
region from the critical fluctuation region. The fac-
tor 1203 0. ( ( ))l/ ab� (Eq. (4)) is introduced by
Bieri, Maki, and Thompson (BMT) [25], who have
extended the HL theory to incorporate the clean
limit approximation. This seems to be reasonable,
as the mean free path l ab� � ( )0 for YBCO sys-
tems, where � �ab c� is the intraplane coherence
length. But when H � 0 the only difference with the
HL theory is that � � �BMT ab HLl/�1203 0. ( ( )) , as-
suming that nonlocal effects can be ignored [25].
Actually, Eq. (2) reproduces the result of the
LD model [17], with allowance for the presence of
Josephson-like pair tunneling between conduc-
ting layers [26], which is mainly pertinent to
the 3D region, as � c T d( ) � near Tc. Accordingly,
the MT contribution gains importance at
k T T /c
mf( ) �� � �� [13], where no intraplane tun-
neling is expected, as � c T d( ) � (2D region)
[10,26]. Thus the HL theory predicts both 2D–3D
and MT–LD crossovers as the temperature ap-
proaches Tc. The 2D–3D crossover should occur at
the temperature
T T /dc c0
21 2 0� �{ [ ( ) ] }� (5)
at which � � 1/2, i.e., � �c d/( ) ( ) /0 2 0
1 2� . The
MT–LD crossover should occur at the temperature
� � � ��0 1203 0 8� ( ) [ . ( ( ))( )]� / l/ k Tab B , (6)
where � �
, and this gives an opportunity to esti-
mate ��. No significant difference between the two
crossover temperatures is considered [13]. In con-
trast to the HL theory, the 3D fluctuation region in
well-structured YBCO films [16] has been found to
be described by the 3D term of the AL theory [14],
� � �� �
AL ñe / h{ [ ( )]} /2 1 232 0 . (7)
No LD fluctuation mechanism is observed in this
case, as was mentioned above. It is clear on physi-
cal grounds that with increasing temperature the
3D fluctuation regime will persist until � ñ T d( ) �
[16]. Hence, in this case the 2D–3D crossover
should occur at � ñ T d( )
or at
� �ñ d( ) /0 0
1 2
, (8)
which is twice as large as predicted by the LD and
HL theories (Eq. (5)). Besides, the crossover at T0
prooves to be of the MT–AL type [16].
Actually, Eq. (7) depends only on � ñ( )0 , which
is independently determined by the measured va-
lue of �0 (Eq. (8)), thus noticeably reducing
the number of fitting parameters. However, ��
(Eq. (6)) still remains uncertain, since neither l
nor � ab( )0 is directly measured in the FC experi-
ment. To circumvent this problem we have desig-
nated 1203 0. ( ( ))l/ ab� �� [16]. As before, to further
evaluate ��(100 K) it is assumed that ��( ) ~T /T1
and ��T � const [7,15,16,27]. Hence, Eq. (6) can
be rewritten as follows:
� � � � �� T / k AB� �
� ( )8 0 0
1, (9)
where A / kB� � � �� ( ) .8 2 988 10 12 s. Now the pa-
rameter ��(100K)� is strictly determined by the
measured value of �0 and can be used in the fitting
procedure together with � ñ( )0 . Besides � �th ( )0 2�
(Eq. (4)). Thus, the only fitting parameter now re-
mains a C-factor introduced to take into account
the structural imperfection of the sample [5]. But
in contrast to Oh et al. [5], we introduce C as a
factor by which Eqs. (2), (3) and (7) must be mul-
tiplied to fit the experimental data. It is clear that
the farther C is from 1, the more influence of de-
fects is expected [2]. However, independently of
the measured values of the C factors, the ratio
C C /C* ( . . )� � �3 2 182 0 2D D was found for all
well-structured YBCO films with different oxygen
concentration [2,16], as a result of the layered na-
ture of HTSC.
Fizika Nizkikh Temperatur, 2002, v. 28, No. 11 1141
Fluctuation conductivity in Y–Ba–Cu–O films with artificially produced defects
Compared to OD YBCO films, the MT fluctua-
tion mechanism in films with Tc 82 K (so-called
80-kelvin samples) is somewhat suppressed and
partly substituted by the LD one because of the ap-
pearance of structural defects mostly produced by
oxygen vacancies in the CuO chains, as described
in detail in Ref. 2. The more defects, the more pro-
nounced is the LD part of the ��( )T dependence
and the greater is the suppression of the MT contri-
bution. Nevertheless, the ��( )T dependence near Tc
is still described by the 3D term of the AL theory
(Eq. (7)). Naturally, ��( )T exhibits two dimensional
crossovers in this case but just the second LD–AL
(3D) crossover at �0 has been shown to determine
� c( )0 and ��(100 K)� in 80-kelvin samples [2].
3.1.2. Fluctuation conductivity analysis. Out-
side the critical region ��( )T is a function of
�
( )T T /Tc
mf
c
mf only. Thus the determination of
Tc
mf is of primary importance to the determination
of ��( )T . As before [2,16], Tc
mf is defined by ex-
trapolating the linear 3D region of the �� ! vs T
plot down to the T axis, since �� ( )T should diverge
as ( ) /T Tc
mf 1 2 (Eq. (7)) as T approaches Tc
mf .
Figure 2 shows �� !(T) for samples M23 and M35
measured in the L and T directions. As expected,
the each plot is characterized by a pronounced 3D
region fitted by the straight line to determine Tc
mf .
Above T0 the data measured for M23-L (Fig. 2,a,
dots) and the data measured for both samples in the
T direction (Fig. 2,a and 2,b, circles) deviate to the
left from the line. The fact means the absence of
any MT fluctuation mechanism in this case [16].
On the other hand, the data measured for M35-L
(Fig. 2,b, dots) demonstrate an evident rightward
deviation from the line at T0, thus suggesting the
presence of the MT fluctuation mechanism in the
sample in the latter case. But, strictly speaking,
the deviation is relatively small in comparison
with the well-structured OD films [16]. But the
more striking result is the fact that the 3D region
measured for M23-T turns out to be extremely short
(Fig. 2,a, circles), resulting in T T0 0L T
0.9 K
(Fig. 2,a). Possible reasons for this finding will be
discussed below.
Figure 3,a shows a plot of ln �� vs ln � (dots)
for sample M23-L in comparison with the LD
term of the HL theory (Eq. (2)) (curve 2) and the
3D term of the AL theory (Eq. (7)) (curve 3),
as no MT fluctuation contribution is expected
(Fig. 2,a). The LD–AL (3D) crossover, marked by
the arrow on the figure, is distinctly seen on the
plot at ln �0
–3.98 (T0
91.83 K). Now the values
� c( ) ( . . )0 16 0 01
� Šand � ��( .100 16 03 10 13K)
� s
can easily be determined using the measured �0 and
Eqs. (8) and (9), respectively. The two parameters
found enable us to reasonably fit the data in the
whole temperature region of interest (Fig. 3,a). Be-
sides, the value � �th ( )0 2
is computed using
Eq. (4), in good agreement with the above theore-
tical consideration. It has been established [16] that
� �th ( )0 2� only when �0, which determines both
�c(0) and ��(100 K)�, is properly chosen. This crite-
rion plays a significant role in the fitting procedure,
especially when no MT contribution is observed.
Above T0 the LD term with CLD = 0.82 per-
fectly fits the data up to ln .� c0 2 98
(Tc0
94.72 K) (Fig. 3,a, curve 2). In accordance with
the analysis for the 80-kelvin samples [2], observa-
tion of a fluctuation mechanism of the LD type can
1142 Fizika Nizkikh Temperatur, 2002, v. 28, No. 11
A. L. Solovjov
Fig. 2. � � 2 vs Ò for samples M23 (a) and M35 (b)
measured in the L (dots) and T (circles) direction, re-
spectively; the solid lines is extrapolated 3D fluctuation
regions.
be considered as an evident sign of structural im-
perfection of a sample. Thus there should be a scat-
ter of the intraplane distances in the sample even in
the L direction as a result of the influence of de-
fects throughout the relatively thick film. This con-
clusion is in good agreement with the results of the
defect microstructure study discussed above. Simple
algebra yields d /c c
* /( )�
� �0 0
1 2 7.2 Å, and, as be-
fore, d � 11.7 Å at �0 is assumed [2]. Thus, the scat-
ter appears to be just the same as had been found
for 80-kelvin films [2]. Whether this is a coinci-
dence or not has yet to be settled.
Below T0 the LD model fails to fit the data be-
cause there is a rather pronounced linear 3D fluc-
tuation region here, perfectly described by the 3D
term of the AL theory with C3D � 0.73 (Fig. 3,a,
curve 3). Thus, the observed crossover at T0 is just
of the LD–AL(3D) type expected to be responsi-
ble for the parameters of fluctuation analysis in the
presence of defects [2]. For more assurance the MT
term calculated using the found values for � c( )0
and ��(100 K)� is also plotted (Fig. 3,a, curve 1).
As expected [2], when drawn withC C /2D 3D�
182.
0 401. , it intersects the data just at the crossover
point, accordingly marked as ln �0 on the graph.
This result once again comfirms the universality of
the C* . .� �182 0 2 ratio for the high-Tc oxides [2].
Nevertheless, the real MT fluctuation mechanism is
completely suppressed here, being replaced by the
LD one because of the presence of growth-related
defects. The result of the structural imperfection is
the observed diminution of the C3D factor, ex-
pected to be close to 1 for well-structured OD
YBCO systems [16]. We think that the �� ( )T de-
pendence found without any MT contribution but
with clear LD–AL(3D) crossover appears to be ty-
pical for YBCO films with highly ordered defects.
When defects are randomly distributed in the sam-
ple the crossover is never observed. In the latter
case the data are traditionally fitted using the LD
model alone [4–9], as was mentioned above.
Despite the fact that the set of defects in sample
M35 was found to be the same [24], the FC beha-
vior measured for sample M35-L appears to be
rather different. Figure 4,a shows a ln �� vs ln �
plot (dots) for sample M35-L compared with the
theory in the established manner. Here the 3D re-
gion is somewhat shorter and the crossover at
ln � "
–4.39 (T0
91.72 K) becomes clear only
when the corresponding theoretical curves are pro-
perly drawn. Using the measured �0, the values
� c( ) ( . . )0 1 3 0 01� � Å, � ��( ) .100 24 24 10 13K
� s,
and � �th ( )0 2
can easily be derived from the ex-
periment. The parameters found enable one to rea-
sonably fit the data in the whole temperature re-
gion of interest (Fig. 4,a). As before, the 3D
fluctuation region near Tc is well described by the
3D AL term (Fig. 4,a, curve 3) with C3D
0.31.
However, above T0 the fitting process turns out to
be more complicated than before. As can be easily
seen from the figure, the LD term (curve 2), re-
duced to the crossover temperature, does not fit the
Fizika Nizkikh Temperatur, 2002, v. 28, No. 11 1143
Fluctuation conductivity in Y–Ba–Cu–O films with artificially produced defects
Fig. 3. a — ln �� vs ln � (dots) for sample M23-L
(Òc
mf � 90.14 K) compared with fluctuation theories:
curve 1 — ÌÒ term (Ñ2D � 0.401, d � 11.7 Å), 2 — LD
term (ÑLD � 0.82, d � 11.7 Å ), 3 — ÀL(3D) term
(Ñ3D � 0.73). b — ln �� vs ln � (dots) for sample M23-T
(Òc
mf � 90.19 K) compared with fluctuation theories:
curve 1 — ÌÒ term (Ñ2D � 0.07, d � 17.34 Å), 2 — LD
term (ÑLD � 0.178, d � 35 Å), 3 — ÀL(3D) term
(Ñ3D � 0.127).
data in any temperature region. To complete the
analysis the MT term, calculated using the values
for found � c( )0 and ��(100 K)�, is traditionally
plotted (Fig. 4,a, curve 1). As before, when drawn
with C C /2D 3D�
182 0172. . , it also intersects the
data just at the crossover point. But in spite of the
fact that the presence of the MT fluctuation contri-
bution is evident from Fig. 2,b, the MT term also
does not meet the case. Actually, all three theoreti-
cal mechanisms evidently fail to fit the data in the
2D fluctuation region. In the end, all the way up to
ln . (� c cT0 0315
94.48 K), the data are found to
be well fitted by the summary curve MT+LD
(Fig. 4,a, curve 4).
Fluctuation behavior of the MT+LD type but
without crossover, likely overlooked by the au-
thors, is reported for single crystals [7] and some
YBCO films [9]. Thus a certain amount of the
growth-related defects, likely produced by twins
[7] or a slight degree of substrate miscut [9], has to
be present in the samples. In our case the structural
imperfection is apparently much stronger because
of using the specific 10° miscut substrates, as is con-
firmed by the very small values of the C factors
measured in the experiment. Besides, �T and
(100 K) are about 2.2 times the value found for
M23-L, whereas the ratio
T L( ) ( )100 100K K/ is
3 times larger, respectively (Table). All these facts
evidently indicate the enhanced role of the defects
in the sample. That is why even the partial observa-
tion of the MT fluctuation contribution here turns
out to be somewhat controversial.
At first sight the observed �� ( )T dependence of
the MT+LD type is difficult to explain in terms of
the FC approach discussed here. Indeed, as is well
established now [2], the MT fluctuation mechanism
gains importance in the distinct 2D fluctuation re-
gion and requires CuO2 planes to be intact and re-
gularly situated with an intraplane distance
d Tc
117. ( )Å > � , whereas the LD mechanism is
found to be typical for samples with a noticeable
spread of the intraplane distances and somewhat
deteriorated planes. Thus, one have to assume that
the growth-related defects result in some very spe-
cific sample structure, in which both the MT and
LD fluctuation mechanisms are able to exist in pa-
rallel when measurements are performed in the L
direction. As follows from a structural analysis
[24], the sample surface looks like a remarkably
regular, row-like terrace structure. The observed
FC behavior makes it sure that between the rows
the planes are presumably fully intact, giving rise
to the MT fluctuation contribution. On the other
hand, the planes are expected to be badly deterio-
rated on the tops of the rows. These parts of the
sample are to be responsible for the appearance of
the LD fluctuation mechanism. Despite the fact
that the measurements are carried out in the L di-
rection, the measuring current should evidently
pass through both sample regions discussed, giving
rise to the observed MT+LD combined fluctuation
1144 Fizika Nizkikh Temperatur, 2002, v. 28, No. 11
A. L. Solovjov
Fig. 4. a — ln �� vs ln � (dots) for sample M35-L
(Òc
mf � 90.60 K) compared with fluctuation theories:
curve 1 — ÌÒ term (Ñ2D � 0.172, d � 11.7 Å), 2 —
LD term (ÑLD � 0.353, d � 11.7 Å), 3 — ÀL(3D) term
(Ñ3D � 0.31), 4 — MT+LD term (C � 0.116, d � 11.7 Å).
b — ln �� vs ln � (dots) for sample M35-T (Òc
mf �
� 90.85 K) compared with fluctuation theories: curve 1
— ÌÒ term (Ñ2D � 0.00714, d � 11.7 Å), 2 — LD term
(ÑLD � 0.0238, d � 35 Å), 3 — ÀL(3D) term (Ñ3D �
� 0.013).
behavior (Fig. 4,a, curve 4). Thus, influence of the
defects appears to be rather specific in this case.
With increasing sample thickness (e.g., for the
sample M23-L) the regions with mixed planes are
likely to overlap. Naturally, no MT fluctuation
mechanism will be observed in this case (Fig. 3,a).
Whether or not the difference in the FC behavior
found for the miscut-grown films is really due
solely to the more than twofold difference in the
samples thickness has yet to be settled.
Unfortunately, miscut-grown films for Hall effect
measurements have not been prepared. As a result,
the absolute value of � �~ ( )l/ ab 0 remains unknown,
giving us no possibility of directly deriving the ex-
plicit value of ��(100 K) from experiment. However,
for sample M23-L there is an evident correlation be-
tween the ratio Tc(M23-L)/Tc( ) .F1 103� and
� �c c/( )( ) ( )0 1 0F (M23-L) = 1.031, respectively, sug-
gesting that the value found for � c(0) is in good
agreement with the conventional superconducting the-
ory [28] as to the relationship between � and Tc:
� �0 0~ [ ( )]�v /F � , (10)
where vF is the Fermi velocity and �( )0 is the or-
der parameter at T � 0 K (F1 is the well-structured
YBCO film with Tc � 87.8 K (Ref. 16), considered
to be the principal sample). Assuming � �0 0� c( )
and taking into account that 2 0 5�( )
k TB c for
YBCO systems [29], one can rewrite Eq. (10) as
� ñ cG/T( )0 � , where G K v / kF B� 2 5� ( )� and K
0,12 is the coefficient of proportionality. A plot
of � c( )0 as a function of Tc is shown in Fig. 5 (solid
line) for the value G � � � 1 46 10 6. Å K computed for
F1 [2]. The dots are the experimentaly measured
� c( )0 values for samples M23, M35, and four
YBCO films with different oxygen concentrations
(samples F1–F6 from Ref. 2, 16). With increasing
Tc the value � c( )0 gradually decreases in accor-
dance with the theory (Fig. 5, dots), thus clearly
suggesting the conclusion that the coupling mecha-
nism of high-Tc superconductivity to a certain de-
gree follows the conventional superconducting theo-
ry. At the same time the parameter ��(100K) �,
computed for the same samples, is found to be a lin-
ear function of Tc (Fig. 5, circles). All the data are
normalized to the value � ��( ) .100 5 9 10 13K
� s
for sample F6 (Ref. 16) in this case in order
to make scales coinside. Since both � c( )0 and
��(100K) � are determined solely by �0, which is
strictly determined by the crossover, the depen-
dences found appear to be an inherent property of
YBCO high-Tc oxides. As is clearly seen from the
figure, sample M23-L perfectly matches both de-
pendences shown at the highest temperature, in this
way playing the role of the real OD system.
Summarizing the facts, it seems to be rather rea-
sonable to ascribe to M23-L the same ��( )100K
�3 35 10 13. – s as was found for all other films [16].
The assumption could explain the fact that no sig-
nificant diminution of the PG region is observed in
this case (Fig. 1). Taking found �� into account
one can easily derive the value �
4.785 from the
measured � ��( )100K . Since � ab( )0 13� Šfor F1
[16], the values � ab( )0 � 13/1.03 = 12.62 Å and
l /ab� �� �( ) .0 1203 51.7 Šcan easily be obtained
for M23-L. Both calculated � and l are in good
agreement with the FC analysis [16], for which evi-
dent increase of � and l with increasing Tc is
observed. The result evidently confirms the as-
sumption and suggests the conclusion that the fluc-
tuating coupling mechanism in HTSC, leading to
the appearance of fluctuation conductivity, has the
same physics for all samples studied. But, on the
other hand, the result looks somewhat surprising in
view of the expected influence of the defects on the
sample structure, and the estimated l
51.7 Å looks
suspiciously large for the same reason. To avoid
this problem one have to assume that influence of
the growth-related defects on the scattering of the
normal charge carriers (which is responsible for the
resistivity) and on the fluctuating pairing (which
determines Tc) is not very considerable here, at
least when measurements are performed in the L di-
rection. This conclusion seems reasonable since
sample M23-L has the lowest resistivity, the high-
est Tc, and relatively large values of the C factors
as compared to the samples F1–F6 [2,16]. Besides,
Fizika Nizkikh Temperatur, 2002, v. 28, No. 11 1145
Fluctuation conductivity in Y–Ba–Cu–O films with artificially produced defects
Fig. 5. �c( )0 as a function of Tc (dots); the solid line
represents the theory. Circles — � ��( )100K vs Tc; the
dashed line is a guide for the eye.
the resistive transition is very narrow (Table) and,
additionally, found T*0 130
K is very close to that
predicted by the NAFL theory for OD YBCO sys-
tems [15]. The only exception is the absence of a
clear MT fluctuation mechanism, which unexpect-
edly turns out to be the only evidence of the pres-
ence of defects in this case.
Strictly speaking, both � c( )0 and � ��( )100 K
found for M35 are not inconsistent with the
dependences shown in Fig. 5. However, as it is easi-
ly seen from the figure, the absolute values of the
parameters evidently do not match any of the plots
shown. Especially � ��( ) .100 24 24 10 13K
� s pro-
ves to be extremely large. As a result, there are no
reasonable assumptions as to how to get credible
values of � and ��( )100 K in this case. Neverthe-
less, ��( )100 K is expected to be rather high. As a
result, the PG temperature region determined by
the measured T*0 150L
K is the same as usually
observed for OD YBCO films [3,9].
As expected, results of the FC measurements,
obtained from the T-direction experiment, appear
to be noticeably different. Figure 4,b shows a plot
of ln �� vs ln � (dots) for the sample M35-T com-
pared with the fluctuation theories. As it is easi-
ly seen, the absolute value of �� is deeply sup-
pressed, and, as expected, the C factors are
extremely small, evidently reflecting the enhanced
role of the defects in this case. It is easy to compute
that S* � ��L (92 K) # ��T (92 K) = 28.8, whereas
* ( )� T 92 K /
L ( )92 K � 10.48 only. The corres-
ponding values of S * and
*, found for samp-
le M23, are 8.48 and 3.44, respectively. Here
T � 92 K is chosen as a representative temperature
which is close to the measured T0 for each sample.
Despite the fact that the absolute values of the pa-
rameters are noticeably different, the ratio S /* *
is approximately the same for both samples, namely
2.75 and 2.47, respectively. The finding apparently
means that the relative diminution of the paracon-
ductivity is approximately the same for both of the
films discussed suggesting that the same mechanism
of FC suppression occurs in each sample. It should
be noted that [ ( ) ( )]
N T T (Eq. (2)), measured
for both films in both directions, is of the same or-
der. Hence, the observed diminution of �� is actual-
ly the consequence of the corresponding increase of
the T resistivity, as �� $
1/ TN[ ( )] (Eq. (2)). Be-
sides, �� ( )T drops to zero at T*0
105 K (Table),
which is much lower than that measured in the L
direction. Thus, the PG temperature range turns
out to be rather limited in this case, as was men-
tioned above.
Nevertheless, despite the strong influence of de-
fects, the standard linear �� ( )T dependence, well
described by the 3D AL term, but withC3D � 0.013
only, is observed near Tc (Fig. 4,b, curve 3). As
before, the LD–AL (3D) crossover is distinctly
seen on the plot at the same ln � %&'('
as was
measured for M35-L. Thus, the same values � c( )0
�( . . )1 3 0 01 Å, � ��( ) .100 24 24 10 13K
� s, and
� th
2 are derived from the analysis, which seems
reasonable. To check the type of crossover, the MT
term calculated using the values found for � c( )0
and � ��( )100 K is also plotted (Fig. 4,b, curve 1).
As before, when drawn with C C /2D 3D�
182.
0 0072. , it intersects the data just at the crossover
point, accordingly marked as ln �0 on the graph.
This finding indicates that the crossover is of just
the type that has to determine the parameters of the
fluctuation analysis [2], and it once again confirms
the universality of the ratio C*
1.82 found for
YBCO oxides [16]. Nevertheless, the MT curve
runs far away from the experimental data, which is
not surprising since the CuO2 planes are expected
to be badly mixed in the T direction. But, sur-
prisingly, the LD term (not shown to prevent
obscuring the graph) when drawn with � c( )0
�( . . )1 3 0 01 Å and the value d � 11.7 Å commonly
used in the FC analysis does not fit the data in any
temperature region below or above T0. After many
trials it was eventually found that above T0, all the
way up to ln . (� c cT0 03 3
94.2 K), the data can
be perfectly extrapolated by the LD term with
� c( ) ( . . )0 1 3 0 01
� Å but d � �( )35 1 Å (Fig. 4,b,
curve 2). At first sight the result looks somewhat
puzzling, but sample M23-T demonstrates exactly
the same FC behavior above T0 (Fig. 3,b, curve 2).
Moreover, the similar �� ( )T dependence above T0,
fitted by the LD term with d
35 Å, was recently
found for YBCO films which structure was artifi-
cially deteriorated to increase the critical currents
[30]. Thus, the specific temperature dependence
found for the fluctuation conductivity above T0 ap-
pears to be universal for the YBCO oxides with de-
fected structure. As the CuO2 planes are expected
to be badly mixed in the T direction, it seems rea-
sonable to consider this temperature region as a
pseudo-two-dimensional one.
To account for this finding one have to assume
that any new structure with the intraplane distance
d
35 Å is realized in the films as a result of the
growth-related defects presence. However, this
most simple explanation proves to be somewhat
contradictory since the L-direction measurements
indicate that d � 11.7 Å, and just this value of d is
used in computing � c( )0 and � ��( )100 K from the
1146 Fizika Nizkikh Temperatur, 2002, v. 28, No. 11
A. L. Solovjov
T-direction experiment. Unfortunately, the 3D AL
term (Eq. (7)) does not depend on d and cannot
help solve the problem. Finally, before proceeding
with assumptions it seems rather reasonable to find
out the features of the FC behavior common to
both of these films above T0. Such a feature is the
faster diminution of �� with T in this temperature
interval as compared with the L-direction ex-
periment. As a result, �� ) *T steepens, suggesting
enhanced pair-breaking in the pseudo-two-dimen-
tional region. In accordance with the discussion of
the 80-kelvin films [2], this �� ) *T dependence is to
be described solely by the LD model, as a large
spread of the intraplane distances in the T direction
is expected. Strictly speaking, it is difficult to dis-
tinguish any predominant distance in this case.
Taking all of the above remarks into account, the
value d � 35 Å is obviously not to be considered as
the distance between the conducting layers but has
only to reflect the fact that the scattering rate of
the fluctuating pairs, measured in the T direction
above T0, is at least 3 times that measured in the L
direction (see Eq. (2)). As a result, the pseudogap
temperature range measured in the T direction for
both films turns out to be rather limited (Fig. 1),
with T T* *0 0L T
20–45 K (Table). This finding
permits to conclude that the PG phenomenon, at
least in OD YBCO oxides, is mainly governed by
the fluctuating pairing.
At first sight sample M23-T exhibits just the
same FC behavior (Fig. 3,b, dots). Above T0, all
the way up to ln . (�0 03 7
Tc 92.41 K), the �� ( )T
curve is well described by the LD model with
d � 35 Å (Fig. 3,b, curve 2), as mentioned above.
But the LD–AL(3D) crossover unexpectedly oc-
curs at T T0 0T L� , resulting in the extremely short
3D region in this case. Really, only the leftmost
few data points can be fitted by the 3D AL term
with C3D � 0.127 (Fig. 3,b, curve 3) now. It looks
as if all the data are shifted towards low tempera-
tures compared with the L-direction experiment.
The shift is distinctly seen on the graph as the dif-
ference between ln �0T and ln �0L , also shown in
the figure. The matter of whether we could again
ascribe the shift to twice the difference in the sam-
ples thickness or whether it is an intrinsic feature
of sample M23 has yet to be settled, leaving this an
open question. Since the FC parameters are strictly
determined by the �0, the shift evidently suggests
the change of both � c( )0 and � ��( )100 K compare
with those measured for M23-L. Using the value
found for ln . ( .�0 04 766 90 95
T K), one can
easily compute the values � c( ) ( . . )0 108 0 01
� Å
and � ��( ) .100 35 21 10 13K
� s, suggesting the
anisotropy of the parameters. But the anisotropy of
� c( )0 and the enlargement of ��, appear to be
rather unusual.
There are two possible approaches to esti-
mation of � c( )0 in the given case. The value
� c( ) ( . . )0 108 0 01
� Å is computed from Eq. (7)
taking d � 11.7 Å. The other possibility is the likely
modification of d as a result of the influence of de-
fects, considering � c( )0 to be stable. Simple alge-
bra (Eq. (8)) yields d
17.34 Å in the latter case.
Analysis of the defect microstructure [24] evidently
shows that the crystal lattice is slightly tilted
across the defects, and numerous stacking faults
could result in a general change of the unit-cell
height. That is why the second approach seems to
be better, as it is difficult to see any physics behind
the possible anisotropy of � c( )0 depending on the
measuring current direction in the ab plane. Final-
ly, the AL and MT terms in the figure are drawn
using d � 17.34 Å, and accordingly � c( )0 � 1.6 Å
and � ��( ) .100 35 21 10 13K
� s. The only excep-
tion is d � 35 Å used for the LD fit. As expected,
the AL and LD fits prove to be rather good in this
case. And, as before, the MT term, drawn with
C C /2D D�
3 182 0 07. . , intersects the data just at
the crossover point (Fig. 4,b, curve 1). Thus, it ap-
pears that, despite the strong influence of defects,
the FC approach developed in Ref. 16 enables the
reasonable description of the data in all of the tem-
perature region of interest. As far as the noticeable
enhancement of � ��( )100 K is concerned, we think
the �� should be the same as calculated for M23-L,
since the same Tc is measured in both directions
(Table), suggesting the fluctuating pairing in the
3D region to be independent of the presence of de-
fects. The conclusion is confirmed by the fact that
the temperature range of the 3D fluctuations ob-
served for M35-T is the same as measured in the L
direction (Fig. 4,b). Thus, the influence of defects
is evidently much more stronger for the thicker
sample. Therefore, to account for the enhancement
of � ��( )100 K one can assume the enlargement of
� �~ ( )l/ ab 0 . Naturally, some speculations as to the
likely anisotropy of l, � ab, and, finally, of the
Fermi surface due to defect structure seem to be
rather possible, but more experiments are evidently
required to shed light on the problem.
4. Conclusion
As expected, the structural defects produced by
10° miscut growth of YBCO films [24] appear to
deeply affect the fluctuation conductivity of the
films, ultimately resulting in a rather complicated
and somewhat contradictory picture of the FC be-
Fizika Nizkikh Temperatur, 2002, v. 28, No. 11 1147
Fluctuation conductivity in Y–Ba–Cu–O films with artificially produced defects
havior (Figs. 3 and 4). Nevertheless, the results are
shown to be reasonably described within the frame-
work of the FC analysis developed for the well-
structured YBCO films [2,16].
Noticeable anisotropy of the FC behavior is
found for both films studied, depending on whether
measurements are performed in the L or in T direc-
tion. The FC measured in the T direction appears to
be deeply suppresed. Moreover, above T0 the scat-
tering rate of the fluctuating pairs is estimated to
be three times as large as measured in the L di-
rection, suggesting enhanced pair-breaking in this
case. As a result, the pseudogap temperature range
measured in the T direction for both films (Fig. 1)
turns out to be rather limited with T T* *0 0L T
20 45 K (Table). The finding permits to con-
clude that the PG phenomenon, at least in OD
YBCO oxides, is mainly governed by the fluctuat-
ing pairing.
In the fluctuation region below T0, where the 3D
volume FC is realized, the pair-breaking mechanism
appears to be the same for all samples studied, re-
sulting in the same and very high Tc‘s. As a result,
independently of the direction of measurements,
the FC in the 3D fluctuation region near Tc is always
fitted by the 3D term of the AL theory [14] and in all
cases the ratio C C /C* ( . . )�
�3D 2D 182 0 2 is held,
as a result of the layered structure of HTSC. We
think that both findings suggest the same fluctuat-
ing pairing mechanism near Tc for all YBCO oxides,
independently of the presence of defect structure.
However, despite the fact that the same set of
growth-related defects was found for both films
studied [24], the FC behavior, especially that mea-
sured in the L direction, turns out to be rather dif-
ferent. Most likely the result can be attributed to
the noticeable difference in the sample thickness
d0, as the difference in Tc is negligible (Table). In-
deed, in the relatively thin film (sample M35) the
influence of the defects on FC is not so pro-
nounced. As a result, the fine structure of the �� ( )T
dependence, including all three AL, MT, and LD
fluctuation contributions, is distinctly revealed on
the plot (Fig. 4,a). In contrast with the FC results
an enhanced scattering rate of the normal carriers,
leading to a very high resistivity measured in the T
direction, is observed in this case (Fig. 1). As a re-
sult, d dT d dT
#
#( ) ( )M35 Ì23
2 is found, and,
besides, the wider is �+, the larger is
)+* and the
ratio
#
T L (Table).
With increasing film thickness (sample M23)
the sample regions responsible for the different
fluctuation contributions have to overlap (see the
text), apparently leading to the averaging of the in-
fluence of defects on �� ( )T . As a result, the smooth
�� ( )T dependence described by the LD model alone
is observed in this case (Fig. 3,a). At the same
time, all resistivity parameters, including d dT
#
(Table), measured in the L direction turn out to be
practically the same as those usually reported for
the OD YBCO oxides [2,4–9]. Accordingly,
T ( )100 K is about 6 times as less as measured for
M35-T. We think all the findings have to corrobo-
rate this assumption.
Summarizing the facts, one may conclude that
investigation of fluctuation conductivity addition-
ally provides a useful method of getting reliable in-
formation on the inhomogeneity of the sample
structure. Depending on what kind of �� ( )T de-
pendence is observed, additional information as to
the type of defects and intensity of their influence
on the resistivity and FC can easily be obtained.
The method appears to be especially useful when no
thorough structural analysis is unavailable.
Acknowledgements
The author acknowledges the staff of MPI-
Stuttgart where experimental part of this work was
done for their hospitality. He is also grateful to
Prof. H.-U. Habermeier for stimulation of the stu-
dy and fruitful suggestions, to T. Haage for films
preparation and to Prof. V. M. Dmitriev for valu-
able comments in a discussion of the results of this
study.
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Fluctuation conductivity in Y–Ba–Cu–O films with artificially produced defects
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