Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors (Communications in Computational Physics, 2009)
A computational study of superconducting states near the superconducting-normalphase boundary in mesoscopic finite cylinders is presented. The computationalapproach uses a finite element method to find numerical solutions of the linearizedGinzburg-Landau equation for samples with various sizes, aspect ratios, and cross-sectionalshapes, i.e., squares, triangles, circles, pentagons, and four star shapes. Thevector potential is determined using a finite element method with two penalty termsto enforce the gauge conditions that the vector potential is solenoidal and its normalcomponent vanishes at the surface(s) of the sample. The eigenvalue problem for thelinearized Ginzburg-Landau equations with homogeneous Neumann boundary conditionsis solved and used to construct the superconducting-normal phase boundaryfor each sample. Vortex-antivortex (V-AV) configurations for each sample that accuratelyreflect the discrete symmetry of each sample boundary were found through thecomputational approach. These V-AV configurations are realized just within the phaseboundary in the magnetic field-temperature phase diagram. Comparisons are madebetween the results obtained for the different sample shapes.