Magnetic flux-line lattices and vortices in the copper oxide superconductors.

A variety of recent experiments on both the static and the dynamic properties of vortices and flux-line lattices in the mixed state of the copper oxide superconductors are discussed. The experiments are of two basic types: (i) experiments that image the magnetic flux patterns either with magnetic decoration or neutrons and give information about static structures, and (ii) experiments that explore the dynamics of vortices either through the resistivity or other electrodynamic responses of the material. Results of these experiments argue in favor of the existence of a true phase transition in the high-field vortex state from a low-temperature superconducting vortex glass phase into a disordered high-temperature vortex fluid phase. The vortex glass phase transition model does a good job of explaining high-precision measurements of the dynamics at the transition. At low fields and temperatures, very long range hexatic order in the flux-line lattice is observed.