  We report on the emergence of spontaneously rotating clusters in active
emulsions. Ensembles of self-propelling 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.
