OPTIMAL SIZE OF A CYLINDRICAL INSULATING INCLUSION ACTING AS A PINNING CENTER FOR MAGNETIC-FLUX IN SUPERCONDUCTORS

We examined the effectiveness of an insulating inclusion in a superconductor as a pinning center. With regard to a single-quantum vortex, the dependence of the minimum pinning potential U(p) on a radius R of a cylindrical insulating inclusion was investigated by solving the Ginzburg-Landau equations numerically. Here, U(p) is defined by the free energy difference between the vortex being inside the inclusion and that being infinitely distant from the inclusion. U(p) is negative for all Rs and is very shallow for R smaller than the coherence length xi(T). The depth of U(p) increases rapidly with increasing R up to the penetration depth lambda(T), and there U(p) is found to saturate. U(p) for R greater than or similar to lambda(T) is much deeper than that for R less than or similar to xi(T). In other words, even for a single vortex, the insulating inclusion with R greater than or similar to lambda(T) gives a stronger attractive interaction with the vortex and works as a more effective pinning center than that with R less than or similar to xi(T).