Dirichlet boundary condition for the Ginzburg-Landau equations

摘要

As is well known, the Ginzburg Landau phenomenological theory described with a good accuracy the thermodynamic properties of a superconducting material. The system of two coupled nonlinear differential equations is completed with the usual Neumann boundary condition as long as is considered a superconductor insulator interface. In this paper, we solve the Ginzburg Landau equations for a circular geometry containing a half-circular pillar defect and considering the unusual superconducting Dirichlet boundary condition. This choice, leading to take the extrapolation de Gennes length equal to zero. Our results point that, the thermodynamic critical fields, magnetization, free energy and vorticity, depend on the chosen boundary condition.