Biot-Savart correlations in layered superconductors

TL;DR

This paper demonstrates that layered superconductors undergo a Kosterlitz--Thouless transition driven by pancake vortices, with three-dimensional correlations present in both phases, challenging previous assumptions about their phase transition nature.

Contribution

It provides an exact renormalization group analysis showing the superconductor-normal transition is a 2D Kosterlitz--Thouless transition in a 3D layered system, clarifying conflicting theories.

Findings

The phase transition is a Kosterlitz--Thouless transition despite the 3D nature.

Both phases exhibit three-dimensional correlations.

The superfluid stiffness jump has a small non-universal correction.

Abstract

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. We assume the dominant interaction between vortices in the same and in different layers is the electromagnetic interaction between the screening currents induced by these vortices. Our main result, obtained by exactly solving the leading order renormalization group 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 of this is that the jump in the measured in-plane superfluid stiffness, which is a universal quantity in 2d Kosterlitz-Thouless theory, will receive a small non--universal correction (of order 1% in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$). This overall picture places some claims expressed in the literature on a more secure analytical footing and also resolves some conflicting views.