The role of 2D pancake vortices in high-temperature superconductors

To describe vortices in the high-temperature superconductors, a multilayer model consisting of alternating superconducting and nonsuperconducting layers is useful. Superconductivity within the layers is strong, while that between superconducting layers is weak. The Lawrence-Doniach model provides a helpful starting point, in treating the in-plane superconductivity via the Ginzburg-Landau theory and the out-of-plane superconductivity via the Josephson effect. With the help of this model, one may represent a vortex line threading through the layers as a stack of 2D pancake vortices connected by Josephson strings, whose axes are confined within the nonsuperconducting layers. The magnetic fields and currents generated by a single pancake vortex can be calculated analytically in the limit of extreme anisotropy or vanishing Josephson coupling. Here, we review the results of this calculation and discuss how pancake vortices magnetically interact with each other in the absence of Josephson coupling. In this limit, pancake vortices at zero temperature strongly prefer to align themselves perpendicular to the superconducting layers. We review recent results showing that a tilted stack of 2D pancake vortices in an infinite set of Josephson-decoupled superconducting layers is unstable when the angle of tilt is greater than 52°. We also discuss the behavior of pancake vortices in a finite set of N superconducting layers. The magnetic-field and current-density distributions generated throughout the multilayer structure by a single pancake vortex in an arbitrary layer can be calculated and used to examine the stability of tilted stacks of pancake vortices, where the tilt is maintained by application of transport currents in the top or bottom superconducting layers. At a sufficiently high transport current in the top layer, we find that the pancake vortex array in this layer shears off.