Density-functional theory of flux-lattice melting in high-${\mathit{T}}_{\mathit{c}}$ superconductors

Flux-lattice melting in the mixed phase of anisotropic, layered superconductors is studied in the limit of infinite anisotropy. In this limit, if the external field is applied perpendicular to the layer plane, the problem reduces to that of the liquid-solid transition of an assembly of point vortices restricted to move on the superconducting layers and interacting through an anisotropic pair potential. We generalize approximate theories for correlations in the liquid-state to deal with the layering and study the melting of the vortex system using density-functional theory. Calculations of correlation functions measurable in neutron scattering are presented. The theory predicts a first-order melting transition. It has no adjustible parameters and the results are in good agreement with experiments on ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$. © 1996 The American Physical Society.