Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions.

We numerically study the dynamics of two-dimensional blue phases in active chiral liquid crystals. We show that introducing contractile activity results in stabilised blue phases, while small extensile activity generates ordered but dynamic blue phases characterised by coherently moving half-skyrmions and disclinations. Increasing extensile activity above a threshold leads to the dissociation of the half-skyrmions and active turbulence. We further analyse isolated active half-skyrmions in an isotropic background and compare the activity-induced velocity fields in simulations to an analytical prediction of the flow. Finally, we show that confining an active blue phase can give rise to a system-wide circulation, in which half-skyrmions and disclinations rotate together.