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1199
Physics of the Solid State, Vol. 43, No. 7, 2001, pp. 1199–1206. Translated from Fizika Tverdogo Tela, Vol. 43, No. 7, 2001, pp. 1157–1164.
Original Russian Text Copyright © 2001 by Kuzmin.
1. INTRODUCTION
An important property of clusters of a normal phase
located in a superconducting medium is their ability to
trap magnetic flux. While preventing vortices from
moving under the action of the Lorentz force, these
clusters can act as effective pinning centers [1–4]. This
property is widely used in creating composite super-
conducting materials with high critical current values
[5, 6]. The morphologic characteristics of clusters of a
normal phase essentially influences the dynamics of
trapped magnetic flux, especially in the case when the
clusters have fractal boundaries [7–9]. In the present
work, we consider in detail the geometric and probabil-
ity properties of these fractal clusters and their influ-
ence on the critical current and dynamics of trapped
magnetic flux upon transition of the superconductor
into a resistive state.
2. FRACTAL GEOMETRY OF THE CLUSTERS
OF NORMAL PHASE
AND THE DISTRIBUTION
OF CRITICAL CURRENTS
We consider a superconductor which contains frag-
ments of a normal phase. Let the dimension of these
fragments along one direction significantly exceed the
other dimensions. Similar columnar defects are of great
interest in creating artificial pinning centers [5, 10–12].
If this superconducting structure is cooled in a mag-
netic field directed along the axis of alignment of these
defects below the critical temperature, then the distri-
bution of trapped magnetic flux in clusters of the nor-
mal phase will be two-dimensional. This can be espe-
cially easily done with a superconducting film, in
which such clusters are formed near defects at the
boundary with the substrate during the growing process
and are normal to the film plane [5, 12]. Let the relative
filling of the film surface with the normal phase be less
than the percolation threshold for the transfer of mag-
netic flux (i.e., less than 50% for 2
D
percolation [13]).
In this case, the fraction of the superconducting phase
exceeds the percolation threshold and, in the film plane,
there is a superconducting percolation cluster capable
of conducting a transport current. This kind of structure
provides for the effective pinning, thereby raising the
critical current, as the magnetic flux is trapped in iso-
lated clusters of the normal phase and vortices cannot
leave them without crossing the surrounding supercon-
ducting space. As the current increases, the trapped flux
will remain unchanged until the vortices begin to break
away from those clusters for which the pinning force is
less than the Lorentz force caused by the transport cur-
rent. When the magnetic flux is breaking away from the
pinning centers, each vortex must cross the infinite
superconducting cluster. In this case, the vortices will
move primarily along the weak links that connect the
clusters of the normal phase to each other [3, 14–17].
These weak links are especially easily formed in high-
temperature superconductors (HTSCs), which are char-
acterized by a small coherence length [5, 16]. Struc-
tural defects, which could serve simply as scattering
centers at a large coherence length, create weak links in
HTSCs. There is a large variety of weak links in a wide
range of spatial scales in HTSCs [5, 14–18]. On the
atomic level, weak links are created by structural point
defects, primarily by oxygen vacancies [16, 19]. On a
Resistive State of Superconducting Structures
with Fractal Clusters of a Normal Phase
Yu. I. Kuzmin
Ioffe Physicotechnical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia
e-mail: yurk@shuv.ioffe.rssi.ru
e-mail: iourk@usa.net
Received October 10, 2000; in final form, November 13, 2000
Abstract
—The effect of morphologic factors on magnetic flux trapping and critical currents in a superconduct-
ing structure, which presents a type II percolation superconductor with pinning centers, is considered. The role
of pinning centers is played by fractal clusters of the normal phase. The properties of these clusters are analyzed
in detail: their statistics is studied, the distribution of critical currents of depinning is found, and the depen-
dences of the main statistical parameters on the fractal dimension are obtained. The effect of fractal clusters of
the normal phase on the electric field caused by the motion of the magnetic flux after the vortices have been
broken away from pinning centers is considered. The current–voltage characteristics of superconducting struc-
tures in a resistive state are obtained for an arbitrary fractal dimension. It is found that the fractality of
the boundaries of normal-phase clusters forces magnetic flux trapping, thereby increasing the critical current.
© 2001 MAIK “Nauka/Interperiodica”.
METALS
AND SUPERCONDUCTORS