The vortex pinning on the cylindrical defects and the electronic structure of the vortex core

The model of the Abrikosov vortex pinning on a cylindrical defect is proposed. It is shown that in the limit $\varkappa \gg 1$ the potential for the vortex core excitations can be treated in terms of the zero-range potentials method. Using the variational method the estimates for the energy of pinning, the pinning force and the density of critical current defect are obtained.