We study the interaction of vortices in a type-II superconductor with a regular cubic array of pinning centers. The pinning centers are normal spheres of radius $R=2\mathrm{}{\xi }_0$ and the lattice size is $L=12\mathrm{}{\xi }_0,$ where ${\xi }_0$ is the zero-temperature coherence length. A modified version of the Ginzburg-Landau theory, which effectively incorporates appropriate boundary conditions at normal-metal–superconductor interfaces into the free energy functional, is used to numerically solve the problem for $\kappa =5.\mathrm{}$ Assuming one pinning center per unit cell, we find the number of vortices trapped inside a single defect as a function of the magnetic induction. We show also that for large enough vortex densities, the defect-bearing superconductor has lower energy than the defect-free one.

• Received 25 March 2002

DOI:https://doi.org/10.1103/PhysRevB.66.064519