The distribution of vortices over different vortex shells in mesoscopic superconducting disks with sufficiently large sizes is investigated within the framework of the nonlinear Ginzburg-Landau theory. Keeping the total vorticity fixed, different vortex configurations can be found in which the vortices are distributed differently over the vortex shells. An overview is given of the different possible vortex configurations and the free energies of these states are compared. In general, the difference in the free energy between the possible vortex configurations with the same vorticity is much smaller than the difference in the free energy between vortex states with different vorticity. The transitions between different vortex states with the same and different vorticity are investigated. Contrary to small disks, the change in vorticity can be larger than one with increasing and decreasing magnetic field. Also a combination of a giant vortex state with a multivortex state can nucleate into a stable vortex state. The influence of the sample thickness is briefly studied. Our results are compared with those obtained from the London approximation which clearly shows the limited applicability of the latter.

Stable vortex states are studied in large superconducting thin disks (for numerical purposes we considered with radius R = 50ξ). Configurations containing more than 700 vortices were obtained using two different approaches: the nonlinear Ginzburg-Landau (GL) theory and the London approximation. To obtain better agreement with results from the GL theory we generalized the London theory by including the spatial variation of the order parameter following Clem's ansatz. We find that configurations calculated in the London limit are also stable within the Ginzburg-Landau theory for up to ∼ 230 vortices. For large values of the vorticity (typically, L 100), the vortices are arranged in an Abrikosov lattice in the center of the disk, which is surrounded by at least two circular shells of vortices. A Voronoi construction is used to identify the defects present in the ground state vortex configurations. Such defects cluster near the edge of the disk, but for large L also grain boundaries are found which extend up to the center of the disk.

The dynamics of the annihilation of a vortex-antivortex pair is investigated. The pair is activated magnetically during the run of a simulated hysteresis loop on a square mesoscopic superconducting cylinder with an antidot inserted at its center. We study the nucleation of vortices and antivortices by first increasing the magnetic field, applied parallel to the axis of the sample, from zero until the first vortex is created. A further increase in the field pulls the vortex in, until it reaches the antidot. As the polarity of the field is reversed, an antivortex enters the scene, travels toward the center of the sample, and eventually the pair is annihilated. Depending on the sample size, its temperature, and Ginzburg-Landau parameter, the vortex-antivortex encounter takes place at the antidot or at the superconducting sea around it. The position and velocity of the vortex and antivortex singularities were evaluated as a function of time. The current density, magnetization, and orderparameter topology were also calculated. Achieving a deep understanding of the nucleation and propagation of vortices in real superconductors is a truly complex task, since these entities interact with almost everything: first, with the surface of the specimen, to surpass it; upon entrance, with other vortices that might have already penetrated, and also with defects, which might attract them and even act as pinning centers. Additional difficulties to emulate the problem arise from the fact that vortices generate heat while propagating, what can be harmful to the robustness of the superconducting properties, if not catastrophic, as is the case of vortex avalanches observed in some superconducting films. [1][2][3][4][5][6] It is quite common, however, that the existence of pinning potentials represent a beneficial feature, since vortices can thus be prevented from undergoing dissipative motion. An interesting approach to the problem, which enables one to address most specificities without excessive complexity, is to work in the small universe of mesoscopic samples. In such an ambient, one can accommodate the essential ingredients: relatively important surface-tovolume ratio, only a few vortices on scene, and a number of defects-the so-called antidots-usually arranged in a regular pattern. Furthermore, one can study the interaction of an individual vortex-antivortex ͑V-AV͒ pair and, eventually, witness their mutual annihilation.Recently, there have been many studies about V-AV configurations in mesoscopic superconductors ͑see for instance Refs. 7-11͒. The authors of these references have found that vortices and antivortices may coexist in equilibrium in configurations which look like a V-AV molecule. A somewhat common approach is to assume an a priori configuration and minimize the free energy in terms of some relevant parameter for which the V-AV molecule is a stable configuration. Here, we will focus in a rather different approach concerning more with the dynamics of a V-AV encounter. The aim of the present work is to elucidate the de...

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Using scanning susceptibility microscopy, we shed light on the dynamics of individual superconducting vortices and examine the hypotheses of the phenomenological models traditionally used to explain the macroscopic ac electromagnetic properties of superconductors. The measurements, carried out on a 2H-NbSe 2 single crystal at relatively high temperature (T = 6.8 K), show a linear amplitude dependence of the global ac susceptibility for excitation amplitudes between 0.3 and 2.6 Oe. We observe that the low amplitude response, typically attributed to the oscillation of vortices in a potential well defined by a single, relaxing, Labusch constant, actually corresponds to strongly nonuniform vortex shaking. This is particularly pronounced in the field-cooled disordered phase, which undergoes a dynamic reorganization above 0.8 Oe as evidenced by the healing of lattice defects and a more uniform oscillation of vortices. These observations are corroborated by molecular dynamics simulations when choosing the microscopic input parameters from the experiments. The theoretical simulations allow us to reconstruct the vortex trajectories, providing deeper insight into the thermally induced hopping dynamics and the vortex lattice reordering.