Active cholesterics and smectics are hydrodynamically distinct*

The cholesteric is the archetypal chiral liquid crystal, in which the molecular orientation displays a spontaneous, static, periodic twist about a pitch axis. At thermal equilibrium, this chirality is undetectable in the long-wavelength elasticity and hydrodynamics of a cholesteric, which are identical to that of a smectic. We show theoretically that active cholesterics, by contrast, display striking signatures of chirality, and are thus qualitatively distinct from smectics, even in their asymptotic long-wavelength dynamics. Our predictions include arrays of alternating vortical flow in the layers when active stresses create an undulational instability; an on-off switch for such flow using imposed uniaxial stress; and a disruption of the layers in 2D chiral striped phases. We elucidate the relation and crucial differences between these effects and "odd elasticity". We discuss possible experimental realizations.