VORTEX LINES IN LAYERED SUPERCONDUCTORS .1. FROM 3D TO 2D BEHAVIOR

The fundamental aspects of vortices in layered superconductors (natura l or artificial multilayered materials) are reviewed, focusing on the role of anisotropy and very short coherence lengths. These materials d ivide into three classes, with increasing T(c)'s : chalcogenides, orga nic superconductors and high-T(c) copper oxides. The first part of the paper summarizes the quantitative features of the vortex lattice, due to the incorporation of anisotropy in the 3D Ginzburg-Landau or Londo n descriptions : anisotropy of critical fields and vortex lattice, ela stic coefficients and melting. This kind of model describes most of th e properties of moderately anisotropic compounds as Y : 123. The secon d part concerns the Josephson-coupled layered systems and identifies i n which regimes vortices exhibit a quasi-2D character. Qualitatively n ew features as Josephson vortices. 2D vortices. Kosterlitz-Thouless tr ansition and lock-in of vortices are reviewed. This analysis is adapte d to compounds as Bi : 2212 or multilayers, but also to Y : 123 for so me aspects.