Chiral active particles on a sphere

Interesting dynamics are observed from the class of particles which can self-propel and self-rotate on their own. Using numerical simulations, we study a model of self-propelled chiral particles with polar alignment and soft repulsion confined to move on the surface of a sphere. The incompatibility between order and curvature leads to frustration in the motion as a direct consequence of Poincaré's "Hairy ball theorem". This coupling to curvature, in addition to chirality, nontrivially affects collective motion in active systems, resulting in motion patterns. A source-whirlpool-sink state is observed for low activity and chirality, leading to a shifted band when activity is increased, but not in flat geometry. One of the interesting dynamics observed at higher activity and chirality is the formation of a macroflock in the polar region. The circulating equatorial band state obtained for non-chiral particles is regained in the presence of low chirality but at higher activity. The average angular momentum of the active particles oscillates at a fixed frequency, depending on the strength of activity and chirality. The frequency of revolution of the macroflocks and the length scales of these macroflocks, plotted as a function of chirality, exhibit a power-law relationship. These findings highlight the rich variety of collective behaviours and provide a deeper understanding of how curvature and chirality influence the dynamics of particles in active matter systems.