Josephson Coupling, Phase Correlations, and Josephson Plasma Resonance in Vortex Liquid Phase

Josephson plasma resonance has been introduced recently as a powerful tool to probe interlayer Josephson coupling in different regions of the vortex phase diagram in layered superconductors. In the liquid phase, the high temperature expansion with respect to the Josephson coupling connects the Josephson plasma frequency with the phase correlation function. This function, in turn, is directly related to the pair distribution function of the liquid. We develop a recipe to extract the phase and density correlation functions from the dependencies of the plasma resonance frequency $\omega_p({\bf B})$ and the $c$ axis conductivity $\sigma_c({\bf B})$ on the {\it ab}-component of the magnetic field at fixed {\it c} -component. Using Langevin dynamic simulations of two-dimensional vortex arrays we calculate density and phase correlation functions at different temperatures. Calculated phase correlations describe very well the experimental angular dependence of the plasma resonance field. We also demonstrate that in the case of weak damping in the liquid phase, broadening of the JPR line is caused mainly by random Josephson coupling arising from the density fluctuations of pancake vortices. In this case the JPR line has a universal shape, which is determined only by parameters of the superconductors and temperature.