J Supercond Nov Magn DOI 10.1007/s10948-013-2390-2 ORIGINAL PAPER Magnetic Flux Penetration in a Mesoscopic Superconductor with a Slit Isaias G. de Oliveira Received: 2 July 2013 / Accepted: 13 August 2013 © Springer Science+Business Media New York 2013 Abstract In this work, the vortex nucleation process in a mesoscopic squared superconductor with a slit is numer- ically investigated in terms of time dependent Ginzburg– Landau theory. We have calculated, simultaneously, the Gibbs free energy and the vortex configuration in function of time, it allows to identify the correspondence between special points in the Gibbs free energy and the configuration of the vortex system. Keywords Ginzburg–Landau theory · Mesoscopic superconductor · Vortex 1 Introduction In the last two decades, the theoretical and experimen- tal studies of mesoscopic system have been drastically in- creased. The expertise acquired in the measurements tech- niques and the progress in microfabrications of these sys- tems allowed to confront several theoretical predictions and discovery of new effects. On the other hand, the expertise in new numerical technics had permitted to solve complex sets of equations for specified geometry and considering the appropriated boundary conditions. These two expertises allow to understand mesoscopic effect generated by these small systems, and also make new predictions. The new fea- tures of vortex states in mesoscopic samples are due to the competition between the intervortex interaction, which is modified due to the presence of boundaries, and the con- finement of the system [1]. The Ginzburg–Landau theory is I.G. de Oliveira (B ) Departamento de Física, Universidade Federal Rural do Rio de Janeiro, cep 23890-000, Seropédica, RJ, Brazil e-mail: isaias@ufrrj.br one of the most powerful theory in order to understand the mesoscopic superconducting system. Many mesoscopic su- perconducting systems have been studied in the last years, for instance, thin disk [2–6]; mesoscopic cylinder [6–8]; mesoscopic ring [9–11]; mesoscopic sphere [12]. Having also studied nucleation of superconductivity and vortex mat- ter in superconductor-ferromagnet hybrids, in this last case, a good review can be found in the paper of Moshchalkov et al. [13]. In this work, we solved the couple of the time de- pendence Ginzburg–Landau equations for a mesoscopic su- perconducting squared with a slit. A uniform magnetic field is applied orthogonally to this. The size of this mesoscopic system is L = 5λ 0 , where λ 0 is the penetration length at T = 0. In the present simulations, the GL parameter is kept constant, κ = 4, and we study, numerically, the dynamic of entrance of vortex in this sample and also its accommoda- tion. We have calculated the Gibbs-free energy of the sys- tem as a function of time. The condition of stability of the system is found at the moment this energy presents a satu- ration. Before this energy reaches this state, some structures appear in this curve. All these structures are related to vor- tex nucleations, and their accommodations. In this paper, it is possible to show the chronology of the entrancing of vor- tices into the sample. We have calculated the number of vor- tices as a function of the applied magnetic field, determined the lower critical magnetic field of this mesoscopic system, and also the upper critical field, when the superconducting into the sample disappears. We have analyzed the influence of the temperature, in this case, the applied magnetic field was kept constant with the temperature changes. And finally, we have calculated the Gibbs-free energy of this system for different values of magnetic field. The first case is the first critical field (one vortex nucleation), and in the second case, the magnetic field nucleates four vortices into the sample. The simultaneous analysis of the Gibbs-free energy as func-