Dependence of the critical current density on the first matching field density

Molecular dynamic simulations were carried out to investigate the properties of the critical depinning force in high temperature superconductors at several vortex densities at the first matching field. The study was conducted on samples with periodic square arrays of vortices and pinning sites. The variables in the simulations were the vortex density, the pinning sites density, the temperature, the pinning strength, the size of pinning sites. The critical depinning force is found to decrease with temperature for all first matching field densities. The rate of this decrease was found to be slower as the pinning strength and size of pinning site gets larger. At low temperatures and for large pinning strengths, the critical depinning force was found to decrease with increasing the first matching field density. But very interesting results were obtained at moderate temperatures where the critical depinning force was found to increase as the first matching field density increases. The same behavior of the critical depinning force was found at low temperatures, for small pinning strengths. These unexpected results were attributed to a vortex structural phase transition from a disordered state to an ordered state.