Phase Locking, Devil's Staircases, Farey Trees, and Arnold Tongues in Driven Vortex Lattices with Periodic Pinning

Using numerical simulations, we observe phase locking, Arnold tongues, and devil's staircases for vortex lattices driven at varying angles with respect to an underlying superconducting periodic pinning array. This rich structure should be observable in transport measurements. The transverse $V\left(I\right)$ curves have a devil's staircase structure, with plateaus occurring near the driving angles along symmetry directions of the pinning array. Each of the plateaus corresponds to a different dynamical phase with a distinctive vortex structure and flow pattern.