Oscillations of a single Abrikosov vortex in hard type-II superconductors

During the last decade, detection and manipulation of single vortex lines in bulk superconductors have been achieved experimentally. Electrodynamic response of pinned vortices in the high-frequency range is instrumental in studying specific aspects of their behavior. The present paper reviews the state of the art in studies of the oscillations of a single Abrikosov vortex in type II superconductors. The equations for free and forced oscillations of a single elastic vortex line are analyzed taking into account different forces affecting its motion: pinning, elasticity, viscosity and the Lorenz force. The equations also account for the inertial properties of a vortex due to various mechanisms of massiveness. The nature and magnitude of the vortex effective mass caused by some of the mechanisms are discussed in the paper. The roles of each force and inertia in the free oscillation spectrum are thoroughly analyzed. For the De Gennes and Matricon mode (at about a megahertz) with parabolic dispersion and the pi...