Volume 6, Issue 4
Computational Investigation of the Effects of Sample Geometry on the Superconducting-normal Phase Boundary and Vortex-antivortex States in Mesoscopic Superconductors

Sangbum Kim, Max Gunzburger, Janet Peterson & Chia-Ren Hu

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Commun. Comput. Phys., 6 (2009), pp. 673-698.

Published online: 2009-06

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  • Abstract

A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented. The computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes, aspect ratios, and crosssectional shapes, i.e., squares, triangles, circles, pentagons, and four star shapes. The vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s) of the sample. The eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each sample. Vortex-antivortex (V-AV) configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational approach. These V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase diagram. Comparisons are made between the results obtained for the different sample shapes.

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@Article{CiCP-6-673, author = {}, title = {Computational Investigation of the Effects of Sample Geometry on the Superconducting-normal Phase Boundary and Vortex-antivortex States in Mesoscopic Superconductors}, journal = {Communications in Computational Physics}, year = {2009}, volume = {6}, number = {4}, pages = {673--698}, abstract = {

A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented. The computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes, aspect ratios, and crosssectional shapes, i.e., squares, triangles, circles, pentagons, and four star shapes. The vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s) of the sample. The eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each sample. Vortex-antivortex (V-AV) configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational approach. These V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase diagram. Comparisons are made between the results obtained for the different sample shapes.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7700.html} }
TY - JOUR T1 - Computational Investigation of the Effects of Sample Geometry on the Superconducting-normal Phase Boundary and Vortex-antivortex States in Mesoscopic Superconductors JO - Communications in Computational Physics VL - 4 SP - 673 EP - 698 PY - 2009 DA - 2009/06 SN - 6 DO - http://dor.org/ UR - https://global-sci.org/intro/cicp/7700.html KW - AB -

A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented. The computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes, aspect ratios, and crosssectional shapes, i.e., squares, triangles, circles, pentagons, and four star shapes. The vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s) of the sample. The eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each sample. Vortex-antivortex (V-AV) configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational approach. These V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase diagram. Comparisons are made between the results obtained for the different sample shapes.

Sangbum Kim, Max Gunzburger, Janet Peterson & Chia-Ren Hu. (1970). 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. 6 (4). 673-698. doi:
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