The Critical Current Density of SNS Josephson Junctions and Polycrystalline Superconductors in High Magnetic Fields

We investigate the in-field critical current density Jc(B) of SNS Josephson Junctions (JJs) and polycrystalline superconductors 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 JJs, we derive analytic expressions for Jc(B) that to our knowledge are the first high field solutions for Jc(B) for JJs across the entire field range up to the effective upper critical field. They generalise the well-known (low-field) exponential junction thickness dependence for Jc from de Gennes, often used in the Josephson relation. We extend the new analytic expressions to describe wider junctions and confirm their validity using TDGL optimised for high field applications. They provide an explanation for the B^{-0.6} field dependence found for Jc(B) in high temperature superconductors, and the Kramer dependence and inverse power-law grain size widely found in many low temperature superconductors.