Minimum size for the occurrence of vortex matter in a square mesoscopic superconductor

The study of superconducting samples in mesoscopic scale presented a remarkable improvement during the last years. Certainly, such interest is based on the fact that when the size of the samples is close to the order of the temperature dependent coherence length ξ(T) and/or the size of the penetration depth λ(T), there are some significant modifications on the physical properties of the superconducting state. This contribution tests the square cross-section size limit for the occurrence (or not) of vortices in mesoscopic samples of area L2, where L varies discretely from 1ξ(0) to 8ξ(0). The time dependent Ginzburg–Landau (TDGL) equations approach is used upon taking the order parameter and the local magnetic field invariant along the z-direction. The vortex configurations at the equilibrium can be obtained from the TDGL equations for superconductivity as the system relaxes to the stationary state. The obtained results show that the limit of vortex penetration is for the square sample of size 3ξ(0)×3ξ(0) in which only a single vortex are allowed into the sample. For smaller specimens, no vortex can be formed and the field entrance into the sample is continuous and the total flux penetration occurs at higher values of H/Hc2(0), where Hc2(T) is the upper critical field. Otherwise, for larger samples different vortices patterns can be observed depending on the sample size.