Critical Current Densities Through Josephson Junctions in Low Magnetic Fields

Understanding the properties of grain boundaries in polycrystalline superconductors is essential for optimizing their critical current density. Here, we provide computational simulations of 2D Josephson junctions (JJs) in low magnetic fields using time-dependent Ginzburg-Landau theory, since they can he considered a proxy for a grain boundary between two grains. We present data for junctions with a wide range of superconducting electrodes of different Ginzburg-Landau parameter (kappa) values and geometries, as well as normal harriers with different strengths of pair-breaking- characterized by the thickness of the junction and the junction condensation parameter ((alpha) over bar (n)). We describe our results using analytic solutions, and hence provide a detailed description of Josephson junctions in low fields up to that required for a single fluxon to penetrate the junction.