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We numerically investigate collective ordering and disordering effects forvortices in type-II superconductors interacting with square and triangularsubstrate arrays under a dc drive that is slowly rotated with respect to thefixed substrate. A series of directional locking transitions occur when theparticle motion locks to symmetry directions of the substrate, producing aseries of steps in the velocity-force curves. The locking transitions coincidewith structural transitions between triangular, square, smectic, or disorderedparticle arrangements, which can be identified using the structure factor. Weshow that the widths of the locking steps pass through local minima and maximaas a function of the ratio of the number of particles to the number ofsubstrate minima. Unlike a static system, where matching effects occur forsimple integer commensuration ratios, our system exhibits dynamicalcommensuration effects where an integer number of particle chains flow betweenone-dimensional lines of substrate minima. As the system enters and exits thelocking steps, order-disorder transitions in the structure of the movingparticle assembly occur. We identify two distinct symmetry locking regimes as afunction of substrate strength which produce different locking stepcharacteristics. For weak substrates, all the particles are in motion and aportion of the particles flow through the substrate minima, leading tostructural transitions at certain driving angles. For strong substrates, someparticles are permanently pinned while the remaining particles flow aroundthem. At the crossover between these two regimes of substrate strength, thelocking steps are destroyed due to the onset of chaotic plastic flow whichproduces pronounced changes in the transport characteristics. Similar effectsoccur for colloidal particles driven over square and triangular substratearrays.

Structural Transitions and Dynamical Regimes for Directional Locking of Particles Driven over Periodic Substrates