Dynamics of the magnetic flux trapped in fractal clusters of normal phase in a superconductor

Abstract

The effect of the fractal clusters of a normal phase, which act as pinning centers, on the dynamics of magnetic flux in percolative type-II superconductor is considered. The main features of these clusters are studied in detail: the cluster statistics is analyzed; the fractal dimension of their boundary is estimated; the distribution of critical currents is obtained, and its peculiarities are explored. It is found that there is the range of fractal dimension where this distribution has anomalous statistical properties, specifically, its dispersion becomes infinite. It is examined how the finite resolution capacity of the cluster geometric size measurement affects the estimated value of fractal dimension. The effect of fractal properties of the normal phase clusters on the electric field arisen from magnetic flux motion is investigated for the cluster area distribution of different kinds. The voltage-current characteristics of fractal superconducting structures in the resistive state are obtained for an arbitrary fractal dimension. It is revealed that the fractality of the boundaries of the normal phase clusters intensifies the magnetic flux trapping and thereby raises the critical current of a superconductor.

Investigation of Gd Addition Added on Magnetic and Structural Properties of Bi1.8Pb0.35Sr1.9Ca2.1Cu3Gd x O y Superconductors by ac Susceptibility

“…The results show that the superconducting properties of the samples were found to decrease with increasing Gd addition. Moreover, using a self-field approximation together with J c dependence on temperature [34,35], the characteristic length (L c ) associated with the pinning force in relation to the average grain size (R g ) of the samples is estimated. Surface morphology and grain connectivity of the samples were also interpreted by SEM investigations.…”

Magnetic-flux creep at the initial stage of resistive transition in superconductors with fractal clusters of normal phase

“…The statement of the problem is described in detail in [5,6,8]. The superconductor is considered, which contains isolated clusters of normal phase.…”

Depinning at the initial stage of the resistive transition in superconductors with a fractal cluster structure

“…The reason of this effect is an increase in the density of free vortices broken away from the pinning centers by the Lorentz force. Dependencies of the free vortex density on the fractal dimension of the normal phase cluster boundaries are obtained.The dynamics of vortices in superconductors with fractal boundaries between the normal and superconducting phases has recently received much attention [1] - [3]. The study of their U-I characteristics enable to get new information on the electromagnetic properties as well as on the nature of a vortex state in such materials.…”

“…Thus, the number of weak links involved in the superconducting cluster is randomly reduced so the transition of a superconductor into a resistive state corresponds to breaking of the percolation through a superconducting cluster. The transport current acts as a random generator that changes the relative fractions of conducting components in classical percolative medium [24], hence the resistive transition can be treated as a current-induced critical phenomenon [8].The depinning current of each cluster is related to the cluster size, because the larger cluster has more weak links over its boundary with the surrounding superconducting space, and thus the smaller current of depinning [3]. As a measure of the cluster size we will take the area of its cross-section, and in the subsequent text we will call this value simply "the cluster area".…”

“…The fractal regime in the initial stage of dissipation has been observed in BSCCO-2223, YBa 2 Cu 3 O 7−x (YBCO), and GdBa 2 Cu 3 O 7−x [8]. The fractal nature of the normal phase clusters in YBCO thin films has been found [2] and the effect of such clusters on vortex dynamics has been analyzed [3] - [5], [7].…”