Anisotropy and two-dimensional behaviour in the high-temperature superconductors

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Abstract
The electrodynamic behaviour of the high-temperature cuprate superconductors is strongly affected by the anisotropy of these layered materials. Their transport, magnetic and pinning properties are determined by the properties of vortices, which can be regarded as stacks of two-dimensional (2D) pancake vortices (with cores localized in the layers, bilayers or trilayers) connected by Josephson vortices (with cores localized in the nonsuperconducting charge-reservoir layers). When the Josephson coupling between the superconducting layers is strong, as in YBCO, the line energy associated with the Josephson vortices is large, the 2D pancake vortices in adjacent layers are strongly coupled and the magnetic anisotropy of the superconductor is relatively weak. When the Josephson coupling is weak, as in BSCCO, the line energy associated with the Josephson vortices is small, the 2D pancake vortices in adjacent layers are weakly coupled and the magnetic properties are highly anisotropic and nearly 2D. The transport properties for currents flowing parallel to the layers are dominated by 2D pancake vortex motion, while those for currents flowing perpendicular to the layers are dominated by Josephson vortex motion. In this paper, I review these effects and discuss a number of consequences for vortex-lattice melting, flux pinning, flux creep and the critical current density.