Vortex Phases

These lecture notes are meant to provide a pedagogical introduction, and present the latest theoretical and experimental developments on the physics of vortices in type II superconductors. 1 Why and what in vortices The discovery of high Tc superconductors has shattered the comforting sense of understanding that we had of the phase diagram and physical properties of type II superconductors, and in particular of the mixed (vortex) phase in such systems. Indeed, it was well known since Abrikosov [1] that above H c1 the magnetic field penetrates under the form a vortex, made of a filament of radius ξ (the coherence length) surrounded by supercurrent screening the external field running over a radius λ (the penetration length). Because of the repulsion between vortices due to supercurrents (see Fig. 1), the naive idea is that vortex will form a perfect triangular crystal (the Abrikosov lattice). This has led to the phase diagram shown in Fig. 1, that has been the cornerstone of our understanding of all type II superconductors for more than three decades [2,3]. However in high Tc, one could reach much higher temperatures, and it was soon apparent that some of the physics linked to the existence of the thermal fluctuations and disorder was overlooked. This led to a burst of investigations, both theoretical and experimental, to understand the physical properties of such vortex matter. Of course, high Tc were not the only field of investigations and low Tc supercon-ductors were reexamined as well, now that we knew what to look for in them. Indeed the vortex phase provides an excellent system for both the fundamental researcher and one in search of physics with useful applications. From the fundamental point of view, vortex matter provides a unique system where one can study a crystal, in which one can vary the density (the lattice spacing) at the turn of a knob (simply by varying the magnetic field). In addition, because this crystal is embedded in a " space " with a much finer lattice constant (the real atomic crystal), it can be submitted to various perturbations such as disorder, difficult to investigate in normal crystals. This provides thus a unique opportunity to study the combined effect of disorder and thermal fluctuations on a crystal. From a more practical point of view, if one has vortices in a su-perconductor and passes a current J in them, the current will act as …