Vortex-antivortex interaction in high-${\mathit{T}}_{\mathit{c}}$ superconductors

The free energy of a vortex-antivortex pair in a Josephson-coupled layered superconductor is derived within the framework of the Lawrence-Doniach theory. We find that the free energy of large pairs depends linearly on the pair separation and that there is no logarithmic term in the free energy for large pairs. We also derive the free energy of a pair of vortex lines, i.e., a vortex-antivortex pair in every layer. It is found that the free energy of this system corresponds to the usual result for conventional superconductors. In conclusion we discuss that the vortex-antivortex interaction cannot be described by a simple modification of the Kosterlitz-Thouless theory.