Study of the threshold line between macroscopic and bulk behaviors for homogeneous type II superconductors

In this work we solved the time dependent Ginzburg-Landau equations to simulate homogeneous superconducting samples with square geometry for several lateral sizes. As a result of such simulations we notice that in the Meissner state, when the vortices do not penetrate the superconductor, the response of small samples are not coincident with that expected for the bulk ones, i.e., $4πM=-H$. Thus, we focused our analyzes on the way which the $M(H)$ curves approximate from the characteristic curve of bulk superconductors. With such study, we built a diagram of the size of the sample as a function of the temperature which indicates a threshold line between macroscopic and bulk behaviors.

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