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

TLDR

The basic building block for three‑dimensional vortex lines is the 2D pancake vortex, which resides in a single layer while the other layers screen its magnetic field. The authors analyze vortex structures in an infinite stack of thin superconducting layers with zero interlayer Josephson coupling, including thermally induced decoupling that melts the vortex solid only perpendicular to the layers. The study shows that 3D vortex lines arise from superposed stacks of 2D pancake vortices, that thermal excitation destroys a single 3D line at the Kosterlitz–Thouless temperature of a layer, and that Josephson coupling can be ignored only under stringent conditions not met in Bi‑2212 or Tl‑2201 but likely satisfied in YBCO/PrBCO 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}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$/${\mathrm{PrBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$.