Dipolar colloids in three dimensions: non-equilibrium structure and re-entrant dynamics.

Understanding of collective behaviour in active systems is massively enhanced by minimal models which nevertheless capture its essence. Active colloids, whose interactions can be tuned and accurately quantified provide a valuable realisation of suitable basic models in an experimental setting and may even mimic certain biological systems. Experimental work on active colloids is dominated by (quasi) two-dimensional systems, but rather less is known of 3D systems. Here we investigate a 3D experimental system of active colloids up to volume fractions of 0.5. The particles in our system are self-propelled in the lateral plane under an AC electric field using induced-charge electrophoresis. The field in addition induces an electric dipole, and the competition between activity and both steric and dipolar interactions gives rise to phase behaviour ranging from an active gas to a dynamic labyrinthine phase as well as tetragonal and hexagonal crystals at a high volume fraction. Intermediate volume fractions are characterised by two-dimensional sheets with large fluctuations reminiscent of active membranes. These active sheets break symmetry in a direction perpendicular to the applied field. Moreover, the relationship between electric field and the particle dynamics depends in a complex and unexpected manner upon the position in the state diagram.