Optimal size of an insulating inclusion acting as a pinning center for magnetic flux in superconductors: calculation of pinning force

Abstract By numerically solving the two-dimensional Ginzburg-Landau equations, we have for the first time evaluated the optimal size of an insulating inclusion for pinning a single-quantum vortex in a superconductor. Although it has so far been believed that the optimal size of a pinning center is twice the coherence length, we found for the first time that, for the case of low magnetic fields and low pinning center density, a prismatic insulating inclusion with a square cross-section of the side length approximately equal to the penetration depth gives the strongest pinning force to the vortex.