Biot-Savart correlations in layered superconductors

We discuss the superconductor-to-normal phase transition in an infinite-layered, type-II superconductor in the limit where the Josephson coupling between layers is negligible. We model each layer as a neutral gas of thermally excited pancake vortices and assume that the dominant interlayer coupling is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group (RG) flow, is that the phase transition in this model is a Kosterlitz-Thouless transition despite being a three-dimensional system. While the transition itself is driven by the unbinding of two-dimensional pancake vortices, an RG analysis of the low temperature phase and a mean-field theory of the high temperature phase reveal that both phases possess three-dimensional correlations. An experimental consequence is that the jump in the measured in-plane superfluid stiffness, a universal quantity in 2d Kosterlitz-Thouless theory, receives a small nonuniversal correction (of order 1% in Bi2Sr2CaCu2O8+x). This overall picture places some claims expressed in the literature on a more secure analytical footing and resolves some conflicting views.