Vortex pinning by meandering line defects in planar superconductors

Abstract

To better understand vortex pinning in thin superconducting slabs, we study the interaction of a single fluctuating vortex filament with a curved line defect in (1+1) dimensions. This problem is also relevant to the interaction of scratches with wandering step edges in vicinal surfaces. The equilibrium probability density for a fluctuating line attracted to a particular fixed defect trajectory is derived analytically by mapping the problem to a straight line defect in the presence of a space and time-varying external tilt field. The consequences of both rapid and slow changes in the frozen defect trajectory, as well as finite size effects are discussed. A sudden change in the defect direction leads to a delocalization transition, accompanied by a divergence in the trapping length, near a critical angle.

Effects of kinked linear defects on planar flux line arrays

“…9. This effect was also present in the single vortex-meandering defect system, and disappears when h ′ → h [18].…”

“…The trapping displacement does not depend on the tilt h ′ , as similarly defined quantities for single vortex systems, i.e. the trapping length in [19] and the vortex shift m(h) in [18], do. This contradicts the intuitive expectation, derived from the single pinned flux lines that l tr should decrease as h ′ increases.…”

“…In a spirit similar to Ref. [18], where the interaction of a single flux line with a meandering linear defect with trajectory x o (τ ) was discussed, in this Section we derive an expression for the probability density of an array of flux lines interacting with an attractive delta function potential whose direction changes suddenly along the superconducting slab. To allow for a simple analytical treatment, we consider only piece-wise constant defect trajectories, and focus in particular on a defect consisting of two straight segments joined at an angle.…”

“…The mapping of the classical flux line system to imaginary bosons (or fermions) is explained in many publications, see for example Refs. [18,19]. However for completeness, we briefly review it here.…”

“…The case of a single flux line interacting with a meandering linear defect has been studied in Ref. [18]. In this paper, we study the more experimentally relevant case of many flux lines interacting with a single kinked or terminating defect, confined to a thin superconducting slab.…”