Title: Superconductors and Vortices at Radio Frequency Magnetic Fields
Author: Ernst Helmut Brandt
Institution: Max Planck Institute for Metals Research, D-70506 Stuttgart, Germany
Abstract: After an introduction to superconductivity and Abrikosov vortices, the statics and dynamics of pinned and unpinned vortices in bulk and thin film superconductors is presented. Particular interesting is the case of Niobium, which has a Ginzburg-Landau parameter near 0.71, the boundary between type-I and type-II superconductors. This causes the appearance of a so called type-II/1 state in which the vortex lattice forms round or lamellar domains that are surrounded by ideally superconducting Meissner state. This state has been observed by decoration experiments and by small-angle neutron scattering.
Also considered are the ac losses caused at the surface of clean superconductors, in particular Niobium, in the Meissner state, when no vortices have yet penetrated. The linear ac response is then xpressed by a complex resistivity or complex magnetic penetration depth, or by a surface impedance. At higher amplitudes, several effects can make the response nonlinear and increase the ac losses.
In particular, at sharp edges or scratches of a rough surface the magnetic field is strongly enhanced by demagnetization effects and the induced current may reach its depairing limit, leading to the nucleation of short vortex segments. Strong ac losses appear when such vortex segments oscillate. In high-quality microwave cavities the nucleation of vortices has thus to be avoided. Once nucleated, some vortices may remain in the superconductor even when the applied magnetic field goes through zero. This phenomenon of flux-trapping is caused by weak pinning in the bulk or by surface pinning.