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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...

In the present paper we solve the time dependent Ginzburg–Landau (TDGL) equations by using the link variables technique for two shapes of circular geometry, a circular sector and a disc. The implemented algorithm is applied to a circular geometry surrounded by different kinds of material and immersed in an external magnetic field applied perpendicular to its plane. The properties of these materials are accounted for in the de Gennes boundary conditions with the de Gennes extrapolation length (the so called b parameter). We evaluate the magnetization, the superconducting electron density, the superconducting–normal magnetic field transition, and the applied magnetic field/b-parameter phase diagram. For the circular sector, our results point out that, under an appropriate choice of the b parameter, the third critical field Hc3 can be greatly increased. For the disc, we determine the b-limit for the occurrence of the Meissner, single and multi-vortex states in a type-II superconductor. In addition, we show that under an appropriate construction of the boundary, a type-II superconducting disc may behave like a type-I.

We obtain the vortex configurations, the matching fields, and the magnetization of a superconducting film with a finite cross section. The applied magnetic field is normal to this cross section, and we use the London theory to calculate many of its properties, such as the local magnetic field, the free energy, and the induction for the mixed state. Thus previous similar theoretical works, done for an infinitely long superconducting film, are recovered here, in the special limit of a very long cross section. ͓S0163-1829͑99͒00242-8͔

In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the magnetization, and the number of vortices. This algorithm is applied to a circular sector. We evaluate the superconduting-normal magnetic field transition, the magnetization, and the superconducting density. Our results point out that, as we reduce the superconducting area, the nucleation field increases. Nevertheless, as the angular width of the circular sector goes to small values the asymptotic behavior is independent of the sample area. We also show that the value of the first nucleation field is approximately the same independently of the form of the circular sector. Furthermore, we study the nucleation of giant and multivortex states for the different shapes of the present geometry.

In this work we investigate the dynamics of vortices in a square mesoscopic superconductor. As time evolves we show how the vortices are nucleated into the sample to form a multivortex, single vortex, and giant vortex states. We illustrate how the vortices move around at the transition fields before they accommodate into an equilibrium configuration. We also calculate the magnetization and the free energy as functions of the applied magnetic field for several values of temperature. In addition, we evaluate the upper critical field.

We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner states, with boundary conditions appropriate for this geometry. Using the Monte Carlo simulated annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for Nϭ3 up to 18 vortices. The free energy of the Meissner and mixed states provides expressions for the matching fields. We find that, as in the case of samples of different geometry, the finite-size effect provokes a delay on the vortex penetration and a vortex accumulation in the center of the sample. The vortex patterns obtained are in good agreement with experimental results. ͓S0163-1829͑98͒03430-4͔

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