Vortices in anisotropic type-II superconductors

We present a generalized variational model of an isolated vortex, valid in the anisotropic case when the external magnetic field is along one of the symmetry directions. We discuss the effects of the field anisotropy on the core and magnetic pinning of individual vortices.     

The Bardeen-Stephen theory

The experimental situation that prompted the theory is reviewed, the essentials of the Bardeen-Stephen theory are sketched, and several extensions are mentioned, particularly those that are needed to understand the high-temperature copper-oxide superconductors.     

Flux-line cutting in type II superconductors

Experimental evidence for flux-line cutting in superconductors (intersection and cross-joining of singly quantized vortices) is briefly reviewed. The interaction energy between two straight vortices tilted at an angle ( 0)is then shown to be finite in the London model, i.e., in the limit of vanishing core radius. Next, the activation energy and maximum interaction force are calculated for the vortices in an analytic approximation to the Ginzburg-Landau theory. Here two competing interactions determine the behavior. Electromagnetic repulsion (0 < < /2) varies as cos and decays over distances scaled by the penetration depth , while core attraction is independent of and varies over distances scaled by the coherence length . The force is always repulsive at large flux-line separation (0 < < /2) and its maximum decreases rapidly as decreases, so that flux-line cutting isexpected to be more probable in low- materials. The calculations provide a basis for explaining longitudinal flux-flow resistance as well as some intriguing magnetization behavior in the same configuration.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division, and by the Deutsche Forschungsgemeinschaft.On leave from Max-Planck-Institut für Metallforschung, Institut für Physik, Stuttgart, West Germany.On leave from New University of Ulster, Coleraine, Northern Ireland.     

Pancake Vortices

I describe the magnetic-field and current-density distributions generated by two-dimensional (2D) pancake vortices in infinite, semi-infinite, and finite-thickness stacks of Josephson-decoupled superconducting layers. Arrays of such vortices have been used to model the magnetic structure in highly anisotropic layered cuprate high-temperature superconductors. I show how the electromagnetic forces between pancake vortices can be calculatated, and I briefly discuss the effects of interlayer Josephson coupling.     

The Bardeen-Stephen theory

The experimental situation that prompted the theory is reviewed, the essentials of the Bardeen-Stephen theory are sketched, and several extensions are mentioned, particularly those that are needed to understand the high-temperature copper-oxide superconductors.