Direct Numerical Experiment on Two-Dimensional Pinning Dynamics of a Three-Dimensional Vortex Line in Layered Superconductors

We clarify structures and dynamics of tilted vortices in the ${T}_{c}$ modulated three-dimensional (3D) layered superconductor by performing a direct numerical simulation of the time-dependent Ginzburg-Landau equation coupled with Maxwell's equation. The change of vortex dynamics from a rigid and straight vortex line in the low temperature region to a stepwise vortex in the high temperature region is observed. We investigate vortex pinning for columnar and point defects, and find that a flexible deformation of vortex segments parallel to the layer in the 3D continuous stepwise vortex is reinforced in the presence of pinning centers and leads to 2D pinning dynamics. Also, this increased flexibility is shown to bring about more effective vortex pinning.