Phase-locking of vortex lattices interacting with periodic pinning

We examine Shapiro steps for vortex lattices interacting with periodic pinning arrays driven by ac and dc currents. The vortex flow occurs by the motion of the interstitial vortices through the periodic potential generated by the vortices that remain pinned at the pinning sites. Shapiro steps are observed for fields $B_{\phi }<B<\mathrm{}{2.25B}_{\phi }$ with the most pronounced steps occurring for fields where the interstitial vortex lattice has a high degree of symmetry. The widths of the phase-locked current steps as a function of the magnitude of the ac driving are found to follow a Bessel function in agreement with theory.