Study of an equation for Abrikosov vortex pinning on a linear defect in a superconducting slab

An equation for a bound state of an Abrikosov vortex on a pinning on linear defect in a thin superconducting slab in the presence of a transport current has been studied. An analytical analysis of the corresponding boundary problem has been performed, a critical current density resulting to vortex depinning is estimated. The form of an elastic vortex string is calculated, the instability threshold for a bound state with increasing current, which leads to the string depinning, is found using numerical simulation. The results agree qualitatively with experimental data for high temperature superconductors.