Curvature-induced host-mediated polarization of active particles

Polar collective motion commonly arises from alignment interactions, particle anisotropy, or an imposed directional bias. Here we identify a distinct route to polar order that does not rely on alignment interactions between the active particles. We show that non-aligning active Brownian particles embedded in a dense passive medium can develop polar coherence when confined to a compact curved surface. Persistent active motion redistributes stress through the host and creates passive-depleted regions. When the stress-spreading length becomes comparable to the sphere radius, these regions merge into elongated scars that channel active motion and, through feedback with the active flux, promote a common direction of motion. Removing the passive host suppresses polar coherence even though the active particles continue to cluster on the same sphere. Our results establish an environment-mediated route to collective polarity in which symmetry breaking emerges from the coupling between active motion, passive stress redistribution, and compact geometry.