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Abstract

We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of selfpropelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which
hover over the container bottom while spinning around the plane normal. This effect exists for
symmetric and asymmetric arrangements of isotropic droplets and is therefore not caused by torques
due to geometric asymmetries. We found, however, that individual droplets exhibit a helical swimming
mode in a small window of intermediate activity in a force-free bulk medium. We show that by forming
an ordered cluster, the droplets cooperatively suppress their chaotic dynamics and turn the transient
instability into a steady rotational state. We analyse the collective rotational dynamics as a function of
droplet activity and cluster size and further propose that the stable collective rotation in the cluster is
caused by a cooperative coupling between the rotational modes of individual droplets in the cluster.