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 ${\mathit{T}}^{\mathrm{*}}$ in compounds with perpendicular superconducting correlation length ${\xi }_{\mathit{z}}$(0)≪d/κ where κ is the Ginzburg parameter and d is the interlayer distance. In a system with identical layers, ${\mathit{T}}^{\mathrm{*}}$ coincides with the critical temperature of the Kosterlitz-Thouless transition.