Flux-lattice melting in layered superconductors

We describe a new representation to treat flux-lattice melting in an extreme type-II layered superconductor, generalizing an approach of Hu and MacDonald. The Ginzburg-Landau free-energy functional is expanded in eigenstates which are products of the lowest Landau levels in the xy plane, and tight-binding Bloch states in the z direction. The various correlation functions can be evaluated efficiently by Monte Carlo simulations. The melting temperature for a model of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$, as estimated from the apparently simultaneous disappearance of Bragg peaks in the density-density correlation function, and of long-range interlayer correlations, is estimated to be about 30 K at a field of 1 T, in reasonable agreement with the experimental value of 26 K.