Structural transitions and dynamical regimes for directional locking of vortices and colloids driven over periodic substrates

Abstract

Abstract. 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 as the drive rotates 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, some or all of the locking steps are destroyed due to the onset of chaotic plastic flow which produces pronounced changes in the transport characteristics. We show that similar effects occur for colloidal particles driven over square and triangular substrate arrays.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

“…4(f). Smectic type flows of particles in periodic pinning array structures have been observed in simulations of vortices and colloidal particles moving over quasiperiodic arrays [41,43] as well as for the incommensurate flow in periodic arrays [49].…”

Skyrmion dynamics and topological sorting on periodic obstacle arrays

“…In a square lattice of obstacles, these angles include φ = 0 • , 45 • and 90 • , and they are more generally described by the relation φ = arctan(n/m) where n and m are integers [1][2][3][4]. Dynamical directional locking effects have been studied for vortices interacting with square and triangular pinning arrays [1,5,6], electrons moving through antidot arrays [2,7] and colloidal assemblies moving on two dimensional periodic substrates [3,4,[8][9][10][11][12][13][14]. In these systems, as the angle of the drive is varied with respect to the symmetry direction of the substrate, the velocity vector or velocity-force curves show a series of steps corresponding to drive angle intervals over which the direction of the motion of the particles remains locked to the substrate instead of following the drive direction.…”

Experimental realization of smectic phase in vortex matter induced by symmetric potentials arranged in two-fold symmetry arrays

“…One promising system in which to look for smectic phases is vortices in layered superconductors. Vortex matter is a very well established field, making it an ideal playground to test different models and go deeper into relevant features associated with phase transitions and related topics such as vortex lattice dynamics [7][8][9][10][11][12]. Among layered systems, superconducting dichalcogenides [13][14][15], cuprates [16][17][18] and pnictides [19][20][21] have drawn the attention of many researchers.…”