Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions
We report on depairing critical currents in submicron YBa₂Cu₃O₇₋δ microbridges. A small-angle bicrystal grain boundary junction is used as a tool to study the entrance of vortices induced by a transport current and their influence on the I–V curves. The interplay between the depairing and the vo...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1194742017-06-08T03:06:06Z Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions Ivanov, Z.G. Fogel, N.Ya. Yuzephovich, O.I. Stepantsov, E.A. Tzalenchuk, A.Ya. Свеpхпpоводимость, в том числе высокотемпеpатуpная We report on depairing critical currents in submicron YBa₂Cu₃O₇₋δ microbridges. A small-angle bicrystal grain boundary junction is used as a tool to study the entrance of vortices induced by a transport current and their influence on the I–V curves. The interplay between the depairing and the vortex motion determines a crossover in the temperature dependence of the critical current. The high entrance field of vortices in very narrow superconducting channels creates the possibility of carrying a critical current close to the depairing limit determined by the S–S–S nature of the small-angle grain boundary junction. 2004 Article Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇δ microbridges and bicrystal junctions / Z.G. Ivanov, N.Ya. Fogel, O.I. Yuzephovich, E.A. Stepantsov A.Ya. Tzalenchuk // Физика низких температур. — 2004. — Т. 30, № 3. — С. 276-281. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 74.60.Jg, 74.60.Ec, 74.72.Bk http://dspace.nbuv.gov.ua/handle/123456789/119474 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| spellingShingle |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Ivanov, Z.G. Fogel, N.Ya. Yuzephovich, O.I. Stepantsov, E.A. Tzalenchuk, A.Ya. Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions Физика низких температур |
| description |
We report on depairing critical currents in submicron YBa₂Cu₃O₇₋δ microbridges. A small-angle
bicrystal grain boundary junction is used as a tool to study the entrance of vortices induced by
a transport current and their influence on the I–V curves. The interplay between the depairing and
the vortex motion determines a crossover in the temperature dependence of the critical current.
The high entrance field of vortices in very narrow superconducting channels creates the possibility
of carrying a critical current close to the depairing limit determined by the S–S–S nature of the
small-angle grain boundary junction. |
| format |
Article |
| author |
Ivanov, Z.G. Fogel, N.Ya. Yuzephovich, O.I. Stepantsov, E.A. Tzalenchuk, A.Ya. |
| author_facet |
Ivanov, Z.G. Fogel, N.Ya. Yuzephovich, O.I. Stepantsov, E.A. Tzalenchuk, A.Ya. |
| author_sort |
Ivanov, Z.G. |
| title |
Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions |
| title_short |
Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions |
| title_full |
Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions |
| title_fullStr |
Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions |
| title_full_unstemmed |
Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇₋δ microbridges and bicrystal junctions |
| title_sort |
depairing critical currents and self-magnetic field effects in submicron yba₂cu₃o₇₋δ microbridges and bicrystal junctions |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2004 |
| topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119474 |
| citation_txt |
Depairing critical currents and self-magnetic field effects in submicron YBa₂Cu₃O₇δ microbridges and bicrystal junctions / Z.G. Ivanov, N.Ya. Fogel, O.I. Yuzephovich, E.A. Stepantsov A.Ya. Tzalenchuk // Физика низких температур. — 2004. — Т. 30, № 3. — С. 276-281. — Бібліогр.: 12 назв. — англ. |
| series |
Физика низких температур |
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Fizika Nizkikh Temperatur, 2004, v. 30, No. 3, p. 276–281
Depairing critical currents and self-magnetic field effects
in submicron YBa2Cu3O7–� microbridges and bicrystal
junctions
Z.G. Ivanov
Department of Physics, Chalmers University of Technology and University of G�teborg
S-412 96 G�teborg, Sweden
N.Ya. Fogel
Solid State Institute, Technion 32100, Haifa, Israel
Department of Physics, Chalmers University of Technology and University of G�teborg
S-412 96 G�teborg, Sweden
E-mail: nfogel@techunix.technion.ac.il
O.I. Yuzephovich
B.Verkin Institute for Low Temperature Physics and Engineering National Academy of Sciences of
Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: yuzephovich@ilt.kharkov.ua
E.A. Stepantsov and A.Ya. Tzalenchuk
Institute of Crystallography, Russian Academy of Sciences, Moscow 117333, Russia,
Department of Physics, Chalmers University of Technology and University of G�teborg
S-412 96 G�teborg, Sweden
Received February 24, 2003, revised July 30, 2003
We report on depairing critical currents in submicron YBa2Cu3O7–� microbridges. A small-an-
gle bicrystal grain boundary junction is used as a tool to study the entrance of vortices induced by
a transport current and their influence on the I–V curves. The interplay between the depairing and
the vortex motion determines a crossover in the temperature dependence of the critical current.
The high entrance field of vortices in very narrow superconducting channels creates the possibility
of carrying a critical current close to the depairing limit determined by the S– �S –S nature of the
small-angle grain boundary junction.
PACS: 74.60.Jg, 74.60.Ec, 74.72.Bk
1. Introduction
An understanding of the limitations of supercurrent
transport in high-Tc superconductors (HTS) is impor-
tant from fundamental and applied points of view.
The upper limit for the critical current density, jcp, in
the superconductors is determined by the mechanism
of Cooper pair breaking. High nondissipative currents
of the order of jcp, however, can only be attained in
some special cases. One of the main mechanisms re-
sponsible for the observed reduced values is the mo-
tion of vortices, which leads to energy dissipation. The
critical current density, jc, in such a case is deter-
mined by vortex pinning. Pinning in an HTS is weak
because of the small coherence length, �, and to hinder
the vortex motion a special approach is needed. This
may be achieved by employing narrow superconduct-
ing channels. In such a channel the penetration of
magnetic field and the vortex motion can be blocked
by a surface barrier, which may be an effective
additional pinning source in the case of a large
surface-to-volume ratio. Experiments on narrow
© Z.G. Ivanov, N.Ya. Fogel, O.I. Yuzephovich, E.A. Stepantsov, and A.Ya. Tzalenchuk, 2004
YBa2Cu3O7–� (YBCO) microbridges with widths W
of 2–13 µm showed a tendency to increase jc while de-
creasing W [1]. It was suggested that in the limit of
very narrow microbridges with W < �eff the jcp may
be attained due to the increasing role of the surface
barrier [1]. Here, � ��eff � 2 L/d is the effective mag-
netic field penetration depth for the superconducting
film, �L is the London penetration depth, and d is the
film thickness. Experimentally, such a behavior has
been until now confirmed only in one experiment [2].
Authors report on jc of 109
�/cm2 measured at 77 K
in a 50 nm wide YBCO microbridge. Similar micro-
bridges prepared on the same chip showed a two or-
ders of magnitude lower critical current density. Al-
though a submicron processing may give a random
structural degradation, the reason for such a spread in
jc values is not completely understood. Thus, the limi-
tation of critical current densities in high-Tc oxides,
especially in a case of narrow filaments, continues to
be an unresolved issue and requires further investiga-
tion. In particular, large vortex entrance fields for
narrow superconducting channels [3] and the influ-
ence of inhomogeneities in the case of a restricted ge-
ometry have not been investigated.
In this paper, we report on supercurrent transport
in submicron YBCO microbridges, with and without a
predetermined grain boundary. An asymmetric 4�
grain boundary is exploited as a tool to study the en-
trance of vortices and their influence on jc and the
I–V curves. A self-magnetic field, which is due to the
transport current, serves as a source of vortices in the
grain boundary, and therefore one can determine the
value of the current at which the self-induced vortices
start to contribute to dissipation. This characteristic
current separates two different regimes, where de-
pairing and flux-flow effects are the dominating mech-
anisms limiting the magnitude of the supercurrent.
The interplay of these two mechanisms determines the
unusual temperature dependence of jc observed in our
experiments.
2. Experimental details
We investigated YBCO microbridges 0.5–1 µm
wide and 10 µm long. C-axis oriented YBCO thin
films with thickness d of 120 nm were grown by laser
deposition on Y-ZrO2 bicrystal substrates. The films
had a superconducting transition temperature Tc of
89–90 K with �Tc of 1 K before patterning. Three
microbridges were patterned across the bicrystal bo-
undary and two microbridges on both sides of the
boundary. A mask of e-beam resist SAL601 and Ar ion
milling were used to pattern microbridges and elec-
trodes for four-point measurements. The samples were
ion milled at –20 °C and the Tc of the microbridges de-
creased by 3–5 K in respect to the as-deposited films.
The submicron bridges had a well-defined trapezoid
geometry with a slope of the edges of about 55�, and
according to SEM investigations no YBCO «foot»
was observed around them.
Standard four-point probe measurements were per-
formed on all microbridges. The critical current Ic was
determined from current–voltage characteristics at
the voltage level of 1 µV, and its density jc was calcu-
lated using the geometrical cross-sectional area with-
out taking into account the real current distribution.
3. Results and discussions
Current–voltage characteristics were measured at
different temperatures. The Ic vs T dependence for a
microbridge with a 4� bicrystal grain boundary junc-
tion (GBJ) is shown in Fig. 1. Two well-defined re-
gions with different temperature dependences can be
distinguished. Close to Tc the Ic(T) dependence is de-
scribed by a relation Ic � (1 – T/Tc)
3/2. This behav-
ior is further illustrated in Fig. 2,a using the coordi-
nates jc
2/3 and reduced temperature T/Tc. Such
behavior is similar to that expected for the depairing
critical current, but it was observed only in a limited
temperature range. At temperatures around T* =
= 81 K, Ic becomes unstable. Below T* the tempera-
ture dependence of Ic changes radically. Simulta-
neously, a change of I–V characteristics takes place.
Above T* the I–V curves are smooth, but at T < T*
regular steps appear in the I–V curves which are peri-
odic in current (Fig. 3). These steps are only observed
Depairing critical currents and self-magnetic field effects in submicron YBa2Cu3O7–� microbridges
Fizika Nizkikh Temperatur, 2004, v. 30, No. 3 277
70 75 80 85
0
20
40
60
80
100
I
cp
(1–T/T
c
)
3/2
Ic (1–T/T )
1/2
T = 81 K
I c
,
m
A
T, K
Fig. 1. Ic(T) dependence for a YBCO microbridge (W =
= 500 nm) with a 4� bicrystal grain boundary junction. The
solid line corresponds to the dependence Jc � (1–T/Tc)
3/2
and the dotted one to Jc � (1 – T/T*)1/2. Note the
large spread in Ic within the crossover region.
in a limited temperature range of 2–4 K, where also a
large spread in jc values was noted. At lower tempera-
tures, the I–V characteristics are of the flux flow type
with V � (I–Ic)
2.
The maximum value of Ic at T � T* corresponds to
a high current density of 3·107 A/cm2. We will show
below that the critical current densities in the temper-
ature range between T* and Tc are very close to the
depairing critical current not only qualitatively but
quantitatively as well. As shown in Fig. 2,b, the criti-
cal current densities of the microbridge in the body of
the grain are close to the jc of the GBJ at the same re-
duced temperatures.
To explain the Ic(T) dependence measured for
microbridges with GBJ in the whole temperature
range and the high values of jc, two assumptions were
made. First, the barrier of the small-angle GBJ may be
described as a «weak» superconductor ( �S ), with a Tc
lower than in the electrodes. Values of jc approaching
the depairing limit can be reached only in weak links
with large transparency, and the S– �S –S model may
than explain the high jc values in our experiments in
the vicinity of Tc. Another important assumption con-
cerns the absence of vortices in the microbridge at
T > T*. As was shown by Likharev [3], the vortex en-
trance field, HV, becomes width dependent when the
microbridge width is comparable to �eff and it may at-
tain large values exceeding the first critical field Hc1
even in bulk superconductors. For a narrow
microbridge [3]:
H
/ W W/ W
/ W /V �
( )ln( )
( )ln( )
2 40
2
0
� � �
� � � �
at eff
eff eff at effW ��
�
�
�� �
. (1)
Here
0 is the magnetic flux quantum. The HV � W –2
dependence was observed for narrow microbridges of
conventional superconductors [4]. If the microbridge
edges are smooth, the entrance field may even exceed
the calculated HV values due to the surface barrier
[3]. Large entrance fields governed by the surface
barrier and exceeding HV have also been observed ex-
perimentally [5].
The properties of S– �S –S weak links have been in-
vestigated theoretically [6]. The authors considered a
model of a weak link, �S , which only differed in its
properties relative to those of the bulk electrodes, S,
in a shorter electron mean free path l. The weakness of
the link was defined by a parameter � � �Wl��el, � be-
ing a Gorkov universal function of the impurity pa-
rameter l/�0 (�0 is the BCS coherence length). The
subscripts «Wl» and «el» denote the weak-link region
and electrode regions, respectively. It was shown that
the critical current density of the weak link exceeds its
intrinsic value due to the proximity effect, especially
278 Fizika Nizkikh Temperatur, 2004, v. 30, No. 3
Z.G. Ivanov, N.Ya. Fogel, O.I. Yuzephovich, E.A. Stepantsov, and A.Ya. Tzalenchuk
0,7 0,8 0,9 1,0
0
10
20
T/T c
b
j c
(1
0
6
A
/c
m
2
)
0
10
20
aTc = 86 K
j c
(1
0
6
A
/c
m
2
)2
2
2
2
/
/
/
/
3
3
3
3
Fig. 2. jc
2/3 vs T/Tc dependences for a microbridge with
a 4� grain boundary junction (a) and for a uniform micro-
bridge (b). The microbridges were 500 nm wide 120 nm
thick and 10 µm long.
0 20 40 60 80 100 120
38
39
40
41
42
43
44
T = 79.1 K
I,
m
A
V, � V
Fig. 3. I–V curve plotted for currents larger than the crit-
ical value in a 500 nm wide microbridge crossing a 4�
grain boundary. T = 79.1 K. Note the periodic structure
(�I � 0.5 mA) and that the slope (resistance) in the inter-
mediate regions is proportional to the step number.
in close vicinity to Tc (the coherence length diverges
as (1 – T/Tc)
–1/2). If the condition L/2�Wl < �1/2
is met (L is the geometrical length of the weak link
and L/2�Wl is its normalized length) the critical cur-
rent density of the weak region is only slightly below
the value in the electrodes, i.e., it can be close to the
pair-breaking density jcp(T). Nevertheless, since the
order parameter in such a contact is depressed in the
middle of the weak link, the current–phase relation is
close to the Josephson one, and one can expect a
Josephson-like behavior [6]. This assumption explains
the (Tc – T)3/2 dependence of jc and its large value
near Tc. Now let us try to understand the Ic(T) de-
pendence of the microbridges with GBJ obtained in
the range T < T*. Near T*, the jc of the junction at-
tains values exceeding 107 A/cm2. At such current
densities and small cross sections of the microbridge,
the self-magnetic field of the critical current, HIc, at
the outer edge of the microbridge, with thickness d, is
given by the expression:
H
Ic
= 2�j
c
d/c. (2)
The HIc is quite large and may play an essential
role in determining the GBJ behavior. As long as this
field is lower than HV determined by formula (1),
there are no vortices inside the sample, and the critical
current is determined by pair-breaking. Estimates us-
ing (1) and (2) show that HIc equals to HV at T =
= 81 K for the microbridge in Fig. 1.
Penetration of vortices begins at the weakest spot,
i.e., in the Josephson contact. We believe that the in-
stability that appears at T � T* is connected to the
penetration of vortices into the weak link. The critical
magnetic field Hc1J for penetration of a single vortex
into a tunnel junction is [7]:
H
c1J = 2
o/(�2�
J
Leff). (3)
Here � �J c / j Lc
/� ( )
� 8 2 1 2
eff is the Josephson pen-
etration length, and L LLeff � �2� . Formula (3) is
obtained for a tunnel junction, but one can assume
that it is valid for an S– �S –S junction as well since
the area occupied by a flux quantum is about �JLeff.
Assuming L<< �L and substituting for �J in (3) we
obtain the following expression:
H
c1J= (4/�)(
ojc/c�
L
)1/2. (4)
Near Tc, where HIc < Hc1J, the critical current of the
weak link is close to the pair-breaking critical current
jcp(T) for the bulk material. As the two fields become
equal, the mechanism leading to disappearance of su-
perconductivity changes. Starting with the assump-
tion that at T < T* the critical current density may be
defined by the condition HIc=Hc1J, one can find the
critical current density connected to the vortex mech-
anism. Using formulas (2) and (4), we obtain
j T c / d Tc L( ) ( )� 4 4 2
� � � . (5)
Relation (5), with the temperature dependence
�L(T) � (1 – T/T*)–1/2 near T* taken into account,
is shown in Fig. 1 as a dotted line (T* is assumed to
be the transition temperature of the �S superconduc-
tor). The agreement of this approximation with the
experimental data is good. �L(0) in the GBJ region
was the only fitting parameter. The value obtained,
62 nm, is less than the values of �L(0) for YBCO
known from the literature (�L(0) = 100–140 nm; see
Ref. 8 and references therein). In view of the ap-
proximateness of our approach the agreement is quite
reasonable. In particular, a numerical coefficient may
appear in (5) to take into account the nonuniform
distribution of the self-magnetic field of the transport
current.
There is additional confirmation that crossover in
the jc temperature dependence is associated with the
beginning of self-field vortex penetration into the
microbridge. The crossover takes place at practically
the same critical current density on different mic-
robridges with equal widths (see Fig. 2).
As always, the critical current connected with vor-
tex motion should be smaller than the pair-breaking
one. Indeed, we found not only a drastically changed
temperature dependence of jc below T*, but relatively
small values of jc in comparison with values extrapo-
lated from the (1–T/Tc)
3/2 dependence. The sup-
pression of jc may also be considered as evidence for
the validity of our model.
The data for an uniform microbridge cut in the
body of a single grain (see Fig. 2,b) also demonstrate
a jc � (1 – T/Tc)
3/2 dependence near Tc. For a uni-
form microbridge with W = 0.8 �m, the deviation
of the experimental points from a (1 – T/Tc)
3/2 de-
pendence takes place at a lower T/Tc than for a
microbridge with a GBJ, but the phenomenon deter-
mining this deviation from the jcp(T) dependence is of
the same type as in the case of the microbridge with a
GBJ, although it is less pronounced. In the uniform
microbridge, features similar to those of the GBJ have
been observed: instability of jc around T*, steps, in
the I–V curves (although irregular), and a change of
the jc(T) dependence below T*. These data can be rea-
sonably explained with the assumption that the uni-
form microbridge contains some random, uncontrolled
S– �S –S weak links which are not as clearly defined as
the specially introduced GBJ, but which influence the
jc and I–V curves in a similar way. One may conclude
that only if such weak links are not present, can the
Depairing critical currents and self-magnetic field effects in submicron YBa2Cu3O7–� microbridges
Fizika Nizkikh Temperatur, 2004, v. 30, No. 3 279
depairing critical current be observed to low tempe-
ratures.
It is also easy to estimate the temperature T* below
which the inequality HIc < Hc1J is violated. Using
the experimental jc temperature dependence obtained
near Tc one can rewrite this condition as follows:
1 4 0 04 2� �T / T c / d jc c L* ( ) ( ) .
� � � (6)
Here jc(0) is the coefficient in the experimental de-
pendence j T j T/Tc c c
/( ) ( )( – )� 0 1 3 2. The resulting
value T*=79.4 K is rather close to that observed in
the experiment (see Fig. 1), when the value �L(0) =
= 62 nm obtained above is used.
A comparison of the experimental jc(T) depend-
ence at T > T* with the formula for the depairing crit-
ical current, [9]
j c / T Tcp L�
0
212 3 2[ ( ) ( )]� � � , (7)
may also be used to estimate the value of �L(0). It
should be pointed out that there is some uncertainty
in such an estimate because of the essential discrep-
ancy in values of �(0) obtained by different authors
(�ab(0) = 1–3 nm, see Ref. 8 and references therein).
Another source of error is connected with a coefficient
jcWl/jcel < 1 which should be introduced in (7) to
take into account the reduced value of the junction jc
in comparison with that of the «bulk». Using formula
(7) with �L(0) = 62 nm defined in the range T < T*,
one obtains �(0) = 3.3 nm. This value is in the range
of those from other measurements. Therefore, the pa-
rameter � = jcWl/jcel is close to unity. This is ex-
pected due to the proximity effect between S and �S .
Thus all the experimental numerical values and the
temperature dependence of jc in the whole tempera-
ture range may be described self-consistently in terms
of an S– �S –S weak-link model using only one fitting
parameter, �L(0) = 62 nm. The distinction of this pa-
rameter from the values of �L(0) known from the lit-
erature may be explained by the uncertainty in the
numerical factors in formulas (5) and (7). This im-
plies that the measurements of jc(T) in microbridges
cannot be used for precise �L(0) determination.
It is worthwhile also to mention here that a the-
ory [10] considering the critical current of wide
HTS epitaxial films with small-angle misorientation
between grains predicts that the jc (T) dependence
is governed by the temperature dependence (1–
– T/Tc)
3/2 of the depairing current if the distance
between edge dislocations rd on the bicrystal grain
boundary is less than coherence length � (T). For a 4�
grain boundary the value of rd is equal to 5.7 nm. This
means that such a dependence should be observed to
temperatures very close to Tc (T/Tc = 0.997).
The most remarkable feature of Fig. 1 is the cross-
over in the temperature dependence of Ic and the large
spread in the values of the critical current around the
crossover temperature. This Ic instability is not under-
stood in detail, but most probably such a behavior is
connected with the dynamics of vortex nucleation,
and the motion in the conditions, when magnetic field
of the transport current attains the threshold for the
vortex pair penetration in the GBJ.
Besides the nontrivial jc(T) dependence, another
remarkable feature that is characteristic for a
small-angle GBJ is the presence of steps in the I–V
curves. The steps are periodic with current and they
appear within a limited temperature interval. At first
sight, the origin of regular periodic steps in I–V, ap-
pearing in the temperature range where the critical
current is governed by the penetration of Josephson
vortices in the weak link can be connected with the os-
cillation behavior predicted in Ref. 11. It would then
reflect the entrance of the second, third and further
vortex–antivortex pairs into the Josephson junction.
However, the periodicity of the steps in terms of the
self-field of the current is found to be several Oe,
while the expected periodicity for the entrance of the
next vortices [11], �H =
0/2W�L(T), is more than
an order of magnitude larger than the values obtained
experimentally.
The interaction of moving vortices with the peri-
odic inhomogeneities in the bicrystal boundary (regu-
lar misfit dislocation grid) may be considered as possi-
ble explanation of the step structure in the I–V curve
[12]. The commensurability of the dislocation grid
and the vortex spacing, which is determined by the
magnetic field (i.e., transport current), may play the
key role in this scenario.
In the case of the «uniform» microbridge, the steps
are not periodic with current. This may be explained
by the presence of a number of low-angle grain bound-
aries in the microbridge due to YBCO island growth.
The question of the origin of the step-like behavior re-
quires a closer investigation. The transition at lower
temperatures to the usual flux flow behavior may be
explained by a penetration of Abrikosov vortices along
the whole length of the microbridge and their motion.
In summary, we have shown that near Tc the criti-
cal current density of a submicron microbridge is gov-
erned by the pair-breaking mechanism. This is also
true for a microbridge containing a controlled weak
link of the grain boundary type if the misorientation
angle is small. The possibility of carrying a critical
current close to the depairing limit is due, in particu-
lar, to the absence of vortices in the microbridge. This
is caused by the high vortex entrance field for nar-
row superconducting channels. The properties of such
280 Fizika Nizkikh Temperatur, 2004, v. 30, No. 3
Z.G. Ivanov, N.Ya. Fogel, O.I. Yuzephovich, E.A. Stepantsov, and A.Ya. Tzalenchuk
small–angle junctions may be described in a model of
an S– �S –S high current density Josephson contact.
The value of jc in such a contact differs only slightly
from jcp in the electrodes due to the influence of the
proximity effect. At lower temperatures, when jc be-
comes controlled by Josephson vortex penetration into
the weak link, the jc(T) dependence changes radically
and the jc values become lower. The same is true for
«uniform» microbridges that often contain low angle
grain boundaries. The crossover to the vortex motion
mechanism of dissipation is accompanied by the ap-
pearance of steps in the I–V curves. These disappear
again when the whole microbridge enters the vortex
state. The steps may be connected with the dynamics
of vortex pair motion and annihilation.
Discussions with R.I. Shekhter and L.Yu. Gorelik
are gratefully acknowledged. The project utilized the
Swedish Nanometer Laboratory and was supported by
the Materials consortium on superconductivity.
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