Influence of vortex-loop fluctuations on equilibrium properties of layered superconductors. I. Mean-field approach

In layered superconductors with weak interlayer coupling, fluctuations involving thermal excitation of vortex loops parallel to the layers occur over a wide range of temperatures below ${\mathit{T}}_{\mathit{c}}$. The problem of calculating the system’s equilibrium thermal and magnetic properties taking into account these fluctuations is considered. Describing the layered superconductor by a Villain-type lattice model, this problem is transformed into that of point vortices interacting through an effective Hamiltonian. An exact transformation allows this Hamiltonian to be related to the partition function of vortex loops interacting between themselves and with an external field produced by the point vortices. This partition function is evaluated in a mean-field approximation. The effect of parallel-loop fluctuations, in this approximation, is to renormalize the coupling constant that describes interlayer interactions between phase fluctuations by a temperature dependent factor. These results are applied to estimate the melting temperature, ${\mathit{T}}_{\mathit{m}}$, of a lattice of vortex lines perpendicular to the layers, using Lindemann’s criterion. The relationship between ${\mathit{T}}_{\mathit{m}}$ and the magnetic field is found to differ considerably from that obtained from anisotropic London theory.