Emergent flocking in mixtures of antialigning self-propelled particles.

We observe a flocking mechanism, the emergence of a state with global polar order, in mixed systems of self-propelled particles with purely antialigning interactions, i.e., the ground state for any pair of particles is to be opposedly oriented. In binary mixtures, we find that flocking can be realized by cross-species antialigning that is dominant compared to intraspecies antialignment. While the key mechanism can be understood within a mean-field description, beyond mean-field we develop an asymptotically exact Boltzmann-scattering theory from first principles. This theory yields analytical predictions for the flocking transition and shows excellent quantitative agreement with simulations of dilute systems. For large systems, we find either microphase separation or static patterns with patches or stripes that carry different polarization orientations.