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Spatiotemporal order and emergent edge currents in active spinner materials

Benjamin C. van Zuiden,J. Paulose,W. Irvine,D. Bartolo,V. Vitelli

Published 2016 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance Active materials are composed of building blocks individually powered by internal energy or external fields. Here, we explore the collective behavior of interacting particles with active rotations but no self-propulsion (i.e., active spinning without walking). When many such spinners are brought together, they form unique nonequilibrium steady states reminiscent of crystals, liquids, and glasses. Unlike equilibrium phases of matter, which stem from the balance between entropy and internal energy, the spinner states arise from the competition between active torques and interactions. Active spinner crystals have distinctive features: they vary periodically in time as well as space and melt under increasing pressure. Emergent unidirectional edge currents are the nonequilibrium probes of the transition between crystalline and liquid-like states in active spinner materials. Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion (i.e., spinning without walking) remains less explored. Here, we numerically and theoretically investigate the behavior of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-assemble into a triangular lattice with their orientations phase-locked into spatially periodic phases. The phase-locked patterns form dynamical analogs of the ground states of various spin models, transitioning from the three-state Potts antiferromagnet at low densities to the striped herringbone phase of planar quadrupoles at higher densities. As the density is raised further, the competition between active rotations and interactions leads to melting of the active spinner crystal. Emergent edge currents, whose direction is set by the chirality of the active spinning, arise as a nonequilibrium signature of the transition to the active spinner liquid and vanish when the system eventually undergoes kinetic arrest at very high densities. Our findings may be realized in systems ranging from liquid crystal and colloidal experiments to tabletop realizations using macroscopic chiral grains.

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