Effect of Pinning Size on the Critical Current Density in Superconducting Films with Slightly Distorted Square Arrays of Pinning Sites

In this study, we examine the effects of pinning forces and pinning center radius on critical current density using a square pinning array and the application of dual conformal transformations. This transformation slightly distorts the square pinning array. We study vortex dynamics by considering the interaction between vortices and pinning centers, as well as the impact of thermal fluctuations. Initially, by determining the mentioned forces that affect vortex dynamics, the corresponding Langevin equation for the vortices is solved. By solving this equation, the position of the vortices over time is determined, and using these positions along with boundary conditions, the critical current density as a function of the magnetic field is calculated. Our studies show that the critical current density increases with the enhancement of pinning force and pinning center radius under conformal transformation.