Vector potential gauge for superconducting regular polygons

Chibotaru, Liviu F.; Ceulemans, Arnout; Teniers, Gerd; Bruyndoncx, V.; Moshchalkov, Victor

doi:10.1140/epjb/e2002-00164-3

Cited by 16 publications

(13 citation statements)

References 19 publications

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“…Chibotaru et al [19][20][21][22][23] investigated, using the LGL equation, the N/S phase boundary and vortex states in regular polygons (square, equilateral triangle, and rectangle, etc.) having discrete rotational symmetry.…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

Kim¹,

Gunzburger²,

Peterson³

et al. 2009

CiCP

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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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Section: Introductionmentioning

confidence: 99%

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

Kim¹,

Gunzburger²,

Peterson³

et al. 2009

CiCP

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“…The results of theoretical calculations in the framework of the linearized Ginzburg-Landau equation 12,13 are presented in fig. 1 and 2 for a superconducting triangle and square.…”

Section: Theorymentioning

confidence: 99%

Confinement and quantization effects in nanosuperconductors

et al. 2005

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A systematic study of the geometry dependent nucleation of superconductivity in nanoscaled superconductors is presented in this paper. The experimental T c (H) phase boundary is compared to theoretical calculations obtained in the framework of the linearized Ginzburg-Landau theory for different geometries (square, triangle, disk). The influence of the transformation of a square into a rectangle on the T c (H) phase boundary is analyzed. In elongated rectangles, a crossover from a linear to a parabolic field dependence of T c has been observed. The evolution of the superconducting state is studied in a perforated disk by varying the size of the hole. A transition from a one-dimensional to a two-dimensional regime is seen when increasing the magnetic field for disks with small holes.

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“…Most of the newly accessible bounded geometries by semianalytical methods were solved by a superconducting gauge method [21,22]. In this method, the boundary condition of the LGL problem, Eq.…”

mentioning

confidence: 99%

“…= 0. This is called the superconducting gauge [21]. In the superconducting gauge approach, the gauge function, S( r), is found from the condition…”

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confidence: 99%

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Method for the solution of the nucleation problem in arbitrary mesoscopic superconductors: Theory and application

2012

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We present a method for finding the condensate distribution at the nucleation of superconductivity for arbitrary polygons. The method is based on conformal mapping of the analytical solution of the linearized Ginzburg-Landau problem for the disk and uses the superconducting gauge for the magnetic potential proposed earlier. As a demonstration of the method's accuracy, we calculate the distribution of the order parameter in regular polygons and compare the obtained solutions with available numerical results. As an example of an irregular polygon, we consider a deformed hexagon and prove that its calculation with the proposed method requires the same level of computational efforts as the regular ones. Finally, we extend the method over samples with arbitrary smooth boundaries. With this, we have made simulations for an experimental sample. They have shown perfect agreement with experimental data.

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Vector potential gauge for superconducting regular polygons

Cited by 16 publications

References 19 publications

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

Confinement and quantization effects in nanosuperconductors

Method for the solution of the nucleation problem in arbitrary mesoscopic superconductors: Theory and application

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