Vortex physics in confined geometries

Patterned irradiation of cuprate superconductors with columnar defects allo ws a new generation of experiments which can probe the properties of vortex liquids by forcing them to flow in confined geometries. Such experiments c an be used to distinguish experimentally between continuous disorder-driven glass transitions of vortex matter, such as the vortex glass or the Bose g lass transition, and non-equilibrium polymer-like glass transitions driven by interaction and entanglement For continuous glass transitions, an analys is of such experiments that combines an inhomogeneous scaling theory with t he hydrodynamic description of viscous now of vortex liquids can be used to infer the critical behavior. After generalizing vortex hydrodynamics to in corporate currents and field gradients both longitudinal and transverse to the applied field, the critical exponents for all six vortex liquid viscosi ties are obtained. In particular, the shear viscosity is predicted to diver ge as \T - T-BG\(-nu z) at the Bose glass transition, with v similar or equ al to 1 and z similar or equal to 4.6 the dynamical critical exponent. The scaling behavior of the AC resistivity is also derived. As concrete example s of flux flow in confined geometries, now in a channel and in the Corbino disk geometry are discussed in detail. Finally, the implications of scaling for the hydrodynamic description of transport in the DC flux transformer g eometry are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.