Driven responses of periodically patterned superconducting films*

We have simulated the motion of a commensurate vortex lattice in a periodic lattice of circular artificial pinning sites having different diameters, pinning-strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density, J_c, the vortices de-pin, and the resulting steady-state motion then induces an oscillatory electric field, E(t), with a defect "hopping" frequency, f₀, that depends on the applied current density and the pinning landscape characteristics. Depending on the direction of the applied current (parallel to the edge and diagonal of the square lattice), the collective hopping in the super-cell can be synchronous and asynchronous. As a result, the macroscopic measurements, f₀,  and E(t), are different for asynchronous hopping compared to the single unit cell. Both collective hopping behaviors are studied as a function of the simulated super-cell size and the (asymptotic) synchronization threshold current densities were determined.