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

We numerically investigate collective ordering and disordering effects for vortices in type-II superconductors interacting with square and triangular substrate arrays under a dc drive that is slowly rotated with respect to the fixed substrate. A series of directional locking transitions occur when the particle motion locks to symmetry directions of the substrate, producing a series of steps in the velocity-force curves. The locking transitions coincide with structural transitions between triangular, square, smectic, or disordered particle arrangements, which can be identified using the structure factor. We show that the widths of the locking steps pass through local minima and maxima as a function of the ratio of the number of particles to the number of substrate minima. Unlike a static system, where matching effects occur for simple integer commensuration ratios, our system exhibits dynamical commensuration effects where an integer number of particle chains flow between one-dimensional lines of substrate minima. As the system enters and exits the locking steps, order-disorder transitions in the structure of the moving particle assembly occur. We identify two distinct symmetry locking regimes as a function of substrate strength which produce different locking step characteristics. For weak substrates, all the particles are in motion and a portion of the particles flow through the substrate minima, leading to structural transitions at certain driving angles. For strong substrates, some particles are permanently pinned while the remaining particles flow around them. At the crossover between these two regimes of substrate strength, the locking steps are destroyed due to the onset of chaotic plastic flow which produces pronounced changes in the transport characteristics. Similar effects occur for colloidal particles driven over square and triangular substrate arrays.