Two-dimensional vortices in a stack of thin superconducting films: A model for high-temperature superconducting multilayers

Abstract

The structure of vortices within an infinite stack of thin superconducting layers is considered and examined in detail in the limit of zero interlayer Josephson coupling. The basic building block for the description of three-dimensional (3D) vortex lines is shown to be the 2D pancake vortex, which is a vortex located in only one of the layers; the other layers contain no vortices, but have an important effect in screening the magnetic field generated by currents in the first layer. It is shown that 3D vortex lines can be built up by superposing the contributions of stacks of 2D pancake vortices. Thermal excitation is shown to break up a single 3D vortex line at a temperature corresponding to the Kosterlitz-Thouless temperature of a single superconducting layer. The effect of thermally induced decoupling of the 2D vortex solids in different layers, corresponding to melting only in the direction perpendicular to the layers, is also considered. It is shown that Josephson coupling can be neglected in the high-temperature superconductors only under very stringent conditions. Although these conditions evidently are not met in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ and ${\mathrm{Tl}}_2$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_1$ ${\mathrm{Cu}}_2$ ${\mathrm{O}}_8$, they should be satisfied in superconducting-insulating multilayer systems, such as ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$/${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$.