Lattice-dependent orientational order in active crystals

TL;DR

This paper investigates how active particles in crystalline arrangements develop orientational order influenced by the lattice structure, revealing strong coupling between positional and orientational order.

Contribution

It introduces a model linking active particle orientation dynamics to lattice-dependent interactions, highlighting how crystalline lattice influences orientational alignment.

Findings

Particles align along lattice directions based on interaction variation with distance.

The orientational dynamics map onto a spin lattice with (anti-)ferromagnetic and nematic interactions.

Orientational and positional order are strongly coupled in active crystals.

Abstract

Via mechanisms not accessible at equilibrium, self-propelled particles can form phases with positional order, such as crystals, and with orientational order, such as polar flocks. However, the interplay between these two types of order remains relatively unexplored. Here, we address this point by studying crystals of active particles that turn either towards or away from each other, which can be experimentally realised with phoretic or Janus colloids or with elastically-coupled walker robots. We show that, depending on how these interactions vary with interparticle distance, the particles align along directions determined by the underlying crystalline lattice. To explain the results, we map the orientational dynamics of the active crystal onto a lattice of spins that interact via (anti-)ferromagnetic alignment with each other plus nematic alignment with the lattice directions. Our findings indicate that orientational and positional order can be strongly coupled in active crystals, thus suggesting strategies to control orientational order by engineering the underlying crystalline lattice.