Pinning of an Abrikosov vortex on a small cylindrical cavity: A   Ginzburg-Landau approach
  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 an extension of the electrostatic analogies method, which proved to be useful for calculations of the pinning force for large cavities, to the case of small defects. The pinning potential for an elliptic cavity is derived analytically. Also, we determine the depinning current for a circular defect. 
A. A. Bespalov and A. S. Mel'nikov
cond-mat.supr-con