Active crystals on a sphere

TL;DR

This paper introduces a phase-field-crystal-type model for active crystals composed of self-propelled colloidal particles on a sphere, revealing three distinct states—static, vortex-vortex, and source-sink—based on propulsion strength.

Contribution

It presents a novel theoretical model for active crystals on curved surfaces, characterizing their defect structures and dynamic states depending on activity levels.

Findings

Identifies three types of active crystal states: static, vortex-vortex, and source-sink.

Describes defect structures associated with each crystalline state.

Provides theoretical predictions that can be tested experimentally.

Abstract

Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here, we consider "active crystals" on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a new phase-field-crystal-type model that involves a density and a polarization field on the sphere. Depending on the strength of the self-propulsion, three different types of crystals are found: a static crystal, a self-spinning "vortex-vortex" crystal containing two vortical poles of the local velocity, and a self-translating "source-sink" crystal with a source pole where crystallization occurs and a sink pole where the active crystal melts. These different crystalline states as well as their defects are studied theoretically here and can in principle be confirmed in experiments.