Fig. 4: Local order inside of collective chiral rollers states.

a Uncorrelated gas of chiral rollers. E = 1.60 V μm⁻¹. b α- (‘heads-out’) vortices. E = 1.76 V μm⁻¹. c β-vortices. E = 1.92 V μm⁻¹. d γ- (‘heads-in’) vortices. E = 2.08 V μm⁻¹. e Rotating flocks. E = 2.40 V μm⁻¹. In a–e particle orientations are shown as arrow-heads and also color coded to better visualize rotating flocks and vortex patterns in the system. Area fractions correspond to ϕ = 0.108. The inserts demonstrate the local order and are representative zoomed-in areas from the corresponding panels. Scale bars are 0.5 mm for the main panels and 0.1 mm for the inserts. f Probability distribution functions of the local orientational polar order parameters, ∣Ψ₁∣ (solid lines), and nematic order parameters, ∣Ψ₂∣ (dashed lines), calculated for emergent collective patterns shown in (a)–(e). α-, γ-Vortices and Rotating flocks exhibit a polar local ordering, while β-vortices show tendency toward a local nematic ordering.