Abrikosov vortex pinning on a cylindrical cavity inside the vortex core: formation of a bound state and depinning

Within the Ginzburg-Landau theory we consider Abrikosov vortex pinning on a columnar defect with the characteristic size of the cross-section much smaller than the coherence length. We present a simple analytical approach to the problem of pinning potential calculation suitable for cases of the defect situated inside as well as outside the vortex core. We determine the depinning current for a cavity in the form of a circular cylinder and the pinning potential for a defect with a general elliptical cross-section. For a range of applied currents below the depinning threshold we predict the possibility to observe a stable bound state where the vortex center is located outside the cavity.