The behavior of the critical current density below and above the first matching field in superconductors with periodic square arrays of pinning sites

We have studied the effect of the applied magnetic field on critical depinning force at zero and finite temperatures and for several values of pinning strength. This was achieved by conducting extensive series of molecular dynamic simulations on driven vortex lattices interacting with periodic square arrays of pinning sites. We have found that the critical depinning force decreases as the applied magnetic field is increased. We have also observed two distinct behaviors of dependence of the critical depinning force on the applied magnetic field below and above the first matching filed.