The effect of temperature and pinning density on the critical current of a superconductor with a square periodic array of pinning sites

We have studied the effect of temperature and pinning density on the critical depinning force for several values of pinning strength through an extensive series of molecular dynamic simulations on driven vortex lattices interacting with square periodic arrays of pinning sites. We have solved the overdamped equation of vortex motion taking into account the vortex-vortex repulsion interaction, the attractive vortex pinning interaction, the thermal force, and the driving Lorentz force. We have found that the critical depinning force, as a function of the pinning density, may decrease, increase, or even remain constant, depending on the temperature and pinning strength values