Superconducting boundary conditions for mesoscopic circular samples
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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 H(c3) 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.