Simulations of Critical Currents in Polycrystalline Superconductors Using Time-Dependent Ginzburg–Landau Theory

Abstract

In this thesis, we investigate the in-field critical current density of polycrystalline
superconducting systems with grain boundaries modelled as Josephson-type planar defects, both
analytically and through computational time-dependent Ginzburg--Landau (TDGL) simulations in 2D
and 3D.
For very narrow SNS Josephson junctions (JJs), with widths smaller than the superconducting
coherence length, we derive what to our knowledge are the first analytic expressions for across a JJ over the entire applied magnetic field range.
We extend the validity of our analytic expressions to describe wider junctions and confirm them
using TDGL simulations. We model superconducting systems containing grain boundaries as a
network of JJs by using large-scale 3D TDGL simulations applying state-of-the-art solvers
implemented on GPU architectures.
These simulations of have similar magnitudes and dependencies on applied
magnetic field to those observed experimentally in optimised commercial superconductors.
They provide an explanation for the dependence found for in high
temperature superconductors and are the first to correctly provide the inverse power-law grain size
behaviour as well as the Kramer field dependence, widely found in many low temperature
superconductors.