  The synchronization of self-propelled particles (SPPs) is a fascinating
instance of emergent behavior in living and man-made systems, such as colonies
of bacteria, flocks of birds, robot ensembles, and many others. The recent
discovery of chimera states in coupled oscillators opens up new perspectives
and indicates that other emergent behaviors may exist for SPPs. Indeed, for a
minimal extension of the classical Vicsek model we show the existence of
chimera states for SPPs, i.e., one group of particles synchronizes while others
wander around chaotically. Compared to chimeras in coupled oscillators where
the site position is fixed, SPPs give rise to new distinctive forms of chimeric
behavior. We emphasize that the found behavior is directly implied by the
structure of the deterministic equation of motion and is not caused by
exogenous stochastic excitation. In the scaling limit of infinitely many
particles, we show that the chimeric state persists. Our findings provide the
starting point for the search or elicitation of chimeric states in real world
SPP systems.
