Superconducting boundary conditions for mesoscopic circular samples

Abstract

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 Hc3 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.

Surface Effects on the Dynamic Behavior of Vortices in Type II Superconducting Strips with Periodic and Conformal Pinning Arrays

“…In these cases, the size effects play an important role. With this purpose, several authors investigated theoretically finite and semi-finite size systems with diverse geometries, using the Ginzburg-Landau [64][65][66][67][68][69][70][71][72][73][74][75] and London approach [76][77][78][79][80]. However, there are still open questions about critical depinning currents and vortex behavior in such systems, specially under the influence of pinning arrays.…”

Superconducting properties of a parallelepiped mesoscopic superconductor: A comparative study between the 2D and 3D Ginzburg–Landau models

“…In all these theoretical studies, the Ginzburg-Landau model has been proven to give a good account of the superconducting properties in samples of several geometries, i.e., disks with finite height and spheres [12,13], shells [14], cone [15], prism with arbitrary base and a solid of revo-E-mail address: josejbarba@gmail.com (J. Barba-Ortega). lution with arbitrary profile [16], thin circular sectors and thin disks [17,18], among others. The local magnetic field profile of a mesoscopic superconductor in the so-called SQUID (superconducting quantum interference device) geometry was studied using the 3D approach [19].…”

Superconducting state in a circular SQUID shaped mesoscopic film

“…[5][6][7] The confinement on the superconducting condensate inside the samples can be controlled using the deGennes extrapolation length b in the boundary conditions described by Ginzburg-Landau theory (GL). 8,9 The GL theory has been proven to give a good account of the superconducting properties in samples of various geometries, e.g. disks with finite height and spheres, 10,11 shells 12 on cone.…”