Dynamics of flux-line liquids in high-T_c superconductors

A hydrodynamic theory of the flux line lattice and the isotropic and hexatic flux line liquids in high-T_c superconductors is presented. Weak microscopic pinning centers are described within the flux flow model of Bardeen and Stephen, while strong macroscopic pinning centers set the boundary conditions for the flow. A large intervortex viscosity, which we attribute to entanglement, allows the effects of a few strong pins to propagate large distances in the fluid phases. In thin films, the diverging viscosity associated with a continuous freezing transition should produce similar effects. We propose a simple experiment to observe this pinning length scale and distinguish between various theories of the resistivity drop. The hydrodynamic modes of flux line solids, hexatics and liquids are discussed. Weak pinning shows up as an elastic peak in the dynamic correlation functions. The macroscopic flow of a flux liquid driven by a uniform external current in the presence of macroscopic obstacles of specified geometry is also described.