Abstract: Merged, or giant, multi-quanta vortices (GVs) appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters/GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.

Abstract: We have revealed thermodynamically stable vortex-antivortex configurations in mesoscopic type I superconducting equilateral triangles. The revealed effect is explained by two factors: (i) vortex confinement in mesoscopic triangles and (ii) appearance of the vortex-antivortex repulsion in mesoscopic type I superconductor triangles in the vicinity of the dual point. The stability of the obtained solutions is examined as a function of material and external parameters – the Ginzburg-Landau parameter K and temperature – as well as a function of a distortion of the sample's shape. The vortex-antivortex. “molecule” turns out to be stable in a wide range of the parameters that makes it possible its experimental visualization.

Abstract: We study theoretically the simultaneous effect of regular and random pinning potentials on the vortex lattice structure at filling factor of 1. This structure is determined by a competition between the square symmetry of regular pinning array, by the intervortex interaction favoring a triangular symmetry, and by the randomness trying to depin vortices from their regular positions. Both analytical and molecular-dynamics approaches are used. We construct a phase diagram of the system in the plane of regular and random pinning strengths and determine typical vortex lattice defects appearing in the system due to the disorder. We find that the total disordering of the vortex lattice can occur either in one step or in two steps. For instance, in the limit of weak pinning, a square lattice of pinned vortices is destroyed in two steps. First, elastic chains of depinned vortices appear in the film; but the vortex lattice as a whole remains still pinned by the underlying square array of regular pinning sites. These chains are composed into fractal-like structures. In a second step, domains of totally depinned vortices are generated and the vortex lattice depins from regular array.

Abstract: We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e., a one-dimensional ring), we find a longitudinal acoustic mode and a transverse optical mode which show approximate agreement with the dispersion relation for a straight configuration for large radii of the ring. When the radius decreases, the dispersion relations modify: there appears an anticrossing of the modes near the crossing point resulting in a frequency gap between the lower and upper branches of the modified dispersion relations. For the double chain (i.e., a two-dimensional zigzag configuration), the dispersion relation has four branches: longitudinal acoustic and optical and transverse acoustic and optical.

Abstract: We consider magnetic flux moving in superconductors with periodic pinning arrays. We show that sample heating by moving vortices produces negative differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in the voltage-current characteristic (VI curve). The uniform flux flow state is unstable in the NDR region of the VI curve. Domain structures appear during the NDR part of the VI curve of an N type, while a filamentary instability is observed for the NDR of an S type. The simultaneous existence of the NDR of both types gives rise to the appearance of striking self-organized (both stationary and nonstationary) two-dimensional dynamical structures.

Abstract: We study the dynamics of vortex shells in mesoscopic superconducting Corbino disks, where vortices form shells as recently observed in micrometer-sized Nb disks. Due to the interplay between the vortex-vortex interaction, the gradient Lorentz force and the (in)commensurability between the numbers of vortices in shells, the process of angular melting of vortex-shell configurations becomes complex. Angular melting can start either from the center of the disk (where the shear stress is maximum) or from its boundary (where the shear stress is minimum) depending on the specific vortex configuration. Furthermore, we found that two kinds of defects can exist in such vortex-shell structures: intrashell and intershell defects. An intrashell defect may lead to an inverse dynamic behavior, i.e., one of the vortex shells under a stronger driving force can rotate slower than the adjacent shell that is driven by a weaker Lorentz force. An intershell defect always locks more than two shells until the gradient of the Lorentz force becomes large enough to break the rigid-body rotation of the locked shells. Such a lock-unlock process leads to hysteresis in the angular velocities of the shells.