Evaporation of a single vortex line in a weakly coupled multilayered superconductor

A single Abrikosov line is considered in a field perpendicular to the layers in superconductors with Josephson coupling of the layers. It is shown that the vortex line evaporates above some critical temperature {ital T}{sup *} in compounds with perpendicular superconducting correlation length {xi}{sub {ital z}}(0){much lt}{ital d}/{kappa} where {kappa} is the Ginzburg parameter and {ital d} is the interlayer distance. In a system with identical layers, {ital T}{sup *} coincides with the critical temperature of the Kosterlitz-Thouless transition.