circles), FMV to AFMV transition occurs at $\Delta/R\simeq\sqrt{2}$, while under CCW edge current (inverted black triangles) it occurs at a larger value of $\Delta/R\simeq1.9$.[]{data-label="fig5"}](figure5_8.jpg)

The edge current plays a crucial role in the ordering of interacting bacterial vortices. When two bacterial vortices interact with one another via near-field interaction, they have either the same rotational direction (defined as ferromagnetic vortices, FMV) or opposite rotational directions (anti-ferromagnetic vortices, AFMV) in a geometry-dependent manner[@wioland2; @beppu; @nishiguchi2]. To reveal how a chiral edge current affects the ordering of interacting bacterial vortices, we construct a theoretical model of interacting bacterial vortices in doublets of overlapping identical circular boundaries (Fig. \[fig5\](a))[@beppu].

Two identical overlapping circular microwells, with a radius $R$ and an inter-center $\Delta$, offer the means for a systematic investigation of the pairing order transition[@beppu]. The ratio $\Delta/R = 2\cos\Psi$ is an important geometric parameter characterizing the pairing order transition from FMV to AFMV: if $\Delta$/R is small enough, the two vortices align in co-rotational direction and pair into a FMV pattern. Transition from FMV to AFMV occurs at a predicted value $\Delta_c/R = 2 \cos \SI{45}{\degree} = \sqrt{2}$ because that is the only configuration at which the two pairing patterns are equiprobable[@beppu]. How 