Disorder-induced unbinding of a flux line from an extended defect

We study the competition, for a single flux line, between pinning by bulk point randomness and an extended defect, such as an ion track, dislocation line, or twin plane. In three dimensions, there is an unbinding transition for a linear (but not a planar) defect. This transition is analyzed using Flory, Migdal-Kadanoff, functional renormalization-group, and numerical methods. The localization length, describing the typical transverse separation between the vortex line and defect, diverges like ${\mathit{l}}_{\mathrm{\perp }}$∼‖T-${\mathit{T}}_{\mathit{c}}$ ${\mathrm{\Vert }}_{\mathrm{\perp }}^{\mathrm{-}\nu }$, with ${\nu }_{\mathrm{\perp }}$≊1.4. We predict the effects of this localization length on the I-V characteristics of the superconductor, and suggest experiments to observe the transition.