Freezing of the Vortex Liquid in High-$T_c$ Superconductors: A Density-Functional Approach

The structure of the unpinned vortex fluid in layered oxide high-temperature superconductors is investigated numerically using appropriate classical liquid-state theory, for magnetic fields B perpendicular to the layer plane. The direct correlation function so obtained is used as input for a first-principles,parameter-free calculation of the discontinuous fluid-to-Abrikosov-lattice transition boundary $T_f(B)$.This transition boundary is found to have a shape and location similar to that observed in strongly anisotropic materials, e.g., Bi-Sr-Ca-Cu-O.