Simulation studies for the vortex-depinning dynamics around a columnar defect in superconductors

Using the time-dependent Ginzburg-Landau equation with the complex relaxation rate and Maxwell equation, we perform the numerical simulation of vortex-pinning dynamics in two cases of metal-pinning and insulator-pinning. At the same time, the vortex-flow voltage induced by the vortex-motion and the Hall coefficient are calculated. Numerical simulations reveal that the trapped vortex at the pinning site disrupts the vortex-motion of non-trapped vortices and the Hall coefficient depends on that vortex-motion.