Hysteresis, Laning, and Negative Drag in Binary Systems with Opposite and Perpendicular Driving

We consider a binary system of particles with repulsive interactions that move in opposite or perpendicular directions to each other under an applied external drive. For opposite driving, at higher drives a phase-separated laned state forms that has strong hysteresis in the velocity-force curve and the fraction of topological defects as the drive is cycled up and down from zero. The amount of hysteresis depends on the drive value at which the drive changes from increasing to decreasing. For perpendicular driving, we find a jammed state that transitions into a disordered state or a tilted lane state, both of which also show strong hysteresis effects. Additionally, a negative drag effect can appear in which one species moves in the direction opposite to the other species due to a tilting of the lanes by the perpendicular drive. When a constant drive is applied along one direction while the drive in the perpendicular direction is increased, we observe a series of drops and jumps in the velocity as the system forms locked and tilted laned states. For weakly interacting particles, the jammed system can show co-tilted stripe-forming states.

💡 Research Summary

The authors investigate a two‑dimensional binary system of repulsively interacting particles in which the two species are driven in opposite directions (± x) or in perpendicular directions (+ x for species A and + y for species B). Using overdamped molecular‑dynamics simulations with a Coulomb pair potential, they sweep the drive magnitude from zero to a maximum and back, measuring species‑resolved average velocities and the fraction of six‑fold coordinated particles (P₆) obtained from Voronoi tessellation.

For opposite driving, three dynamical regimes appear as the drive increases: (i) a jammed state with zero velocity and perfect triangular order (P₆≈1); (ii) a fluctuating, disordered flow where particles interpenetrate and P₆ drops to ~0.5; (iii) a phase‑separated laned state in which like‑species form narrow streams, collisions are reduced, the velocity jumps up, and P₆ rises to ~0.8. When the drive is decreased, the laned state persists down to a much lower drive than on the up‑sweep, producing a pronounced hysteresis loop in both the velocity–force curves and the defect fraction. The width of the hysteresis and the drive values at which transitions occur depend strongly on particle density: at low density the jammed window shrinks and laning appears at smaller drives, whereas at high density the jammed region expands and laning requires larger forces.

For perpendicular driving, the system initially forms a jammed configuration that attempts to move along the 45° diagonal. Increasing the drive triggers a decoupling transition to a disordered flow, followed by the emergence of tilted lanes. These lanes are inclined relative to the drive axes, and because of the tilt one species can move opposite to the direction of the other species’ drive, giving rise to a negative‑drag effect. When the x‑drive is held fixed and the y‑drive is ramped up, a series of lock–unlock events occurs, each accompanied by jumps in velocity and abrupt changes in P₆. The tilted‑lane states can be either positively or negatively hysteretic depending on the tilt angle.

Overall, the work demonstrates that merely changing the relative orientation of external drives in a binary repulsive system generates a rich set of nonequilibrium phases—jammed, disordered, laned, and tilted‑laned—and that the transitions between them are first‑order‑like with strong hysteresis. The discovery of negative drag via lane tilting provides a novel mechanism for controlling transport in mixed‑species assemblies, with potential relevance to skyrmion‑skyrmionium mixtures, pedestrian cross‑flows, and electrically or gravitionally driven colloids.