Flux-line entanglement in high-Tcsuperconductors

In anisotropic high-${\mathit{T}}_{\mathit{c}}$ superconductors an isolated vortex line can wander or diffuse significant distances in a plane normal to the applied field as it traverses the sample. In order to assess whether this effect persists in a dense vortex-line liquid and an entangled flux-liquid phase can arise, a phenomenological mode-coupling calculation of the diffusion constant of a tagged vortex in a dense vortex liquid is presented. The calculation exploits the analogy with the diffusion in real time of a tagged particle in a dense fluid. The renormalized diffusion constant is found to depend only weakly on its bare value for a wide range of magnetic fields. In Y-Ba-Cu-O the diffusion constant of a tagged vortex in a dense vortex liquid is at most ten times smaller than that of an isolated vortex line. It is still large enough that flux-line entanglement will occur in bulk samples.