Maximal persistent current in a type-II superconductor with an artificial pinning array at the matching magnetic field

The current carrying steady state of the pinned flux line lattice created by magnetic field is described. We calculate analytically the critical current for the case of the matching field (when the number of vortices is equal to that of the pinning centers) using a simple variational method in the framework of Ginzburg-Landau equations. The vortex cores are deformed and displaced in the current carrying state. Displacement of the centers of the vortices with respect to pinning centers and structure of these states are determined.