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Research Article

Spatiotemporal order and emergent edge currents in active spinner materials

Benjamin C. van Zuiden, Jayson Paulose, William T. M. Irvine, Denis Bartolo, and Vincenzo Vitelli
PNAS November 15, 2016 113 (46) 12919-12924; first published November 1, 2016 https://doi.org/10.1073/pnas.1609572113
Benjamin C. van Zuiden
aInstituut Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands;
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Jayson Paulose
aInstituut Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands;
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William T. M. Irvine
bJames Franck Institute, Department of Physics, The University of Chicago, Chicago, IL 60637;cEnrico Fermi Institute, Department of Physics, The University of Chicago, Chicago, IL 60637;
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Denis Bartolo
dLaboratoire de Physique, Ecole Normale Supérieure de Lyon, Université Claude Bernard, Université de Lyon, F-69342 Lyon, France
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Vincenzo Vitelli
aInstituut Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands;
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  • For correspondence: vitelli@lorentz.leidenuniv.nl
  1. Edited by Monica Olvera de la Cruz, Northwestern University, Evanston, IL, and approved September 29, 2016 (received for review June 15, 2016)

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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.

Abstract

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.

  • active matter
  • nonequilibrium steady states
  • edge currents
  • geometrical frustration

Footnotes

  • ↵1B.C.v.Z. and J.P. contributed equally to this work.

  • ↵2To whom correspondence should be addressed. Email: vitelli{at}lorentz.leidenuniv.nl.
  • Author contributions: B.C.v.Z., J.P., W.T.M.I., D.B., and V.V. designed research; B.C.v.Z., J.P., W.T.M.I., D.B., and V.V. performed research; B.C.v.Z. and J.P. analyzed data; and B.C.v.Z., J.P., W.T.M.I., D.B., and V.V. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1609572113/-/DCSupplemental.

Freely available online through the PNAS open access option.

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Spatiotemporal order and flow in active spinners
Benjamin C. van Zuiden, Jayson Paulose, William T. M. Irvine, Denis Bartolo, Vincenzo Vitelli
Proceedings of the National Academy of Sciences Nov 2016, 113 (46) 12919-12924; DOI: 10.1073/pnas.1609572113

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Spatiotemporal order and flow in active spinners
Benjamin C. van Zuiden, Jayson Paulose, William T. M. Irvine, Denis Bartolo, Vincenzo Vitelli
Proceedings of the National Academy of Sciences Nov 2016, 113 (46) 12919-12924; DOI: 10.1073/pnas.1609572113
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