Role of surface defects and material inhomogeneities for vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in 2 and 3 dimensions

TL;DR

This study uses time-dependent Ginzburg-Landau theory to analyze how surface defects and material inhomogeneities influence vortex nucleation and the superheating field in superconductors, with implications for accelerator cavity design.

Contribution

It introduces a finite element simulation approach combined with bifurcation analysis to evaluate the effects of inhomogeneities on vortex nucleation and superheating fields in 2D and 3D geometries.

Findings

Disorder localizes critical modes and reduces superheating fields.

Surface roughness and material variations can nucleate vortices.

3D surface divots can increase superheating fields under certain conditions.

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.