The local rupture of the superconductivity and the curvature of the mesoscopic sample

In this article we revisit a well-known effect in superconductors, which is the penetration of the magnetic field by regions of greater radius of curvature (Tinkham, 2008; De Gennes, 1966). This is exposed in the literature but without a quantitative solution. Here we solve this problem by two distinct numerical simulations. We calculate the superconducting current density using numerical simulations via the London theory in the Meissner state and numerical simulations using the time-dependent Ginzburg–Landau (TDGL) theory for the vortex state. In both simulations, the results obtained are in agreement, as could not be otherwise. We show that in the Meissner state the current density increases much faster in the region where the radius of curvature is larger, thus reaching the critical value first in this location, and therefore local breakdown of superconductivity occurs. In the vortex state, our simulations, using TDGL, show that the vortices penetrate through exactly the same location pointed out by the previous simulation. For this study we worked with a superconducting needle with an ellipsoidal mesoscopic cross section.