Vortex wandering among splayed columnar defects

Abstract

We investigate the scaling properties of single flux lines in a random pinning landscape consisting of splayed columnar defects. Such correlated defects can be injected into type II superconductors by inducing nuclear fission or via direct heavy ion irradiation. The result is often very efficient pinning of the vortices which gives, e.g., a strongly enhanced critical current. The wandering exponent and the free energy exponent of a single flux line in such a disordered environment are obtained analytically from scaling arguments combined with extreme-value statistics. In contrast to the case of point disorder, where these exponents are universal, we find a dependence of the exponents on details in the probability distribution of the low lying energies of the columnar defects. The analytical results show excellent agreement with numerical transfer matrix calculations in two and three dimensions.

Elastic lines on splayed columnar defects studied numerically

“…The only difference is that u is drawn independently for each bond which destroys the correlations along the columns. For point disorder we use uniformly distributed u and for splay disorder the following distribution in order to make comparisons to single line results by Lidmar et al [10]:…”

“…The lines enter the system at the bottom plane (z = 0) and they exit at the top plane (z = H), and we use both fixed and free entrance points, and free exit points. The case of a fixed entry point and a free exit point is that considered by Lidmar et al for a single line [10], who discuss an experimental scenario for the same. Also rough enough surface could pin the end points of flux lines.…”

“…Here z is the distance along the height direction, and r the transverse displacement. According to Lidmar et al the roughness exponent ζ is sensitive to the shape of the distribution of the tilt angle and the energy distributions of the defects [10]. For instance with an opening angle of 90 • and for a uniform energy distribution the roughness exponent in 2d is ζ = 3/4, in contrast to the point-disorder result 2/3 [11].…”

“…The ground state properties of an ensemble of flux lines in such disordered environments has never been investigated before. Single flux line properties in the presence of tilted columnar defects at zero temperature were studied by Lidmar et al [10]. They show that the behavior of the lines depends on the energy distribution of the lines.…”

“…It occupies a splay defect until a jump to a energetically more favorable one takes place. The lines undergo jumps from splay defect to splay defect so that the average distance between two successive jumps grows as ∆z ∼ z [10]. Thus though the jump density decreases with growing z the roughening exhibits a non-trivial scaling.…”