Vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in two and three dimensions: Role of surface defects and material inhomogeneities

Abstract

We use Time-Dependent Ginzburg-Landau theory to study the nucleation of vortices in type II superconductors in the presence of both geometric and material inhomogeneities. The superconducting Meissner state is meta-stable up to a critical magnetic field, known as the superheating field. For a uniform surface and homogenous material, the superheating transition is driven by a non-local critical mode in which an array of vortices simultaneously penetrate the surface. In contrast, we show that even a small amount of disorder localizes the critical mode and can have a significant reduction in the effective superheating field for a particular sample. Vortices can be nucleated by either surface roughness or local variations in material parameters, such as Tc. Our approach uses a finite element method to simulate a cylindrical geometry in 2 dimensions and a film geometry in 2 and 3 dimensions. We combine saddle node bifurcation analysis along with a novel fitting procedure to evaluate the superheating field and identify the unstable mode. We demonstrate agreement with previous results for homogenous geometries and surface roughness and extend the analysis to include variations in material properties. Finally, we show that in three dimensions, suface divots not aligned with the applied field can increase the super heating field. We discuss implications for fabrication and performance of superconducting resonant frequency cavities in particle accelerators.

Vortex control in superconducting Corbino geometry networks

“…[77] In the case of the numerical simulation, we observe that even a slight modification of the meshing configuration required for the finite element method changes the nucleation points and the number of trapped vortices, when the system starts to develop vortices, which is also reported in Ref. [87].…”

Моделирование Критического Состояния Слоистых Сверхпроводящих Структур С Неоднородными Слоями

“…Исследования свойств реальных структур из сверхпроводящих материалов не теряют своей актуальности [1][2][3][4]. Одним из основных методов моделирования таких структур является теория Гинзбурга-Ландау (ГЛ) [1][2][3].…”

“…Исследования свойств реальных структур из сверхпроводящих материалов не теряют своей актуальности [1][2][3][4]. Одним из основных методов моделирования таких структур является теория Гинзбурга-Ландау (ГЛ) [1][2][3]. Интерес представляют моделирование критического тока в структурах с пиннингом [5][6][7], зарождение вихрей Абрикосова в сверхпроводниках второго рода и структурах из этих сверхпроводников [3,8,9].…”

Vortex nucleation barriers and stable fractional vortices near boundaries in multicomponent superconductors

“…While many works, both analytical and numerical, focused on the calculation of the nucleation fields, that is the magnetic field needed to suppress the barrier [20][21][22][23][24], the calculation of the barrier height and the sphaleron configuration is very complicated and, until recently, there has been no analytical nor numerical fullycontrollable approach to address this problem in gauge theories such as Ginzburg-Landau models. One of the many methods to compute the minimum energy path for other models is the string method [25; 26], originally designed to compute saddle points in molecular dynamics problems.…”