Odd elasticity in disordered chiral active materials

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacterial flagella, and self-spinning starfish embryos. These materials break both time reversal and mirror-image (parity) symmetries due to injection of torques at the microscale. It was recently discovered that chiral active materials show a new type of elastic response termed `odd' elasticity. Currently, odd elasticity is understood microscopically only in ordered structures, e.g., lattice designs of metamaterials. It remains to explore how odd elasticity emerges in natural or biological systems, which are usually disordered. To address this, we propose a minimal generic model for disordered `odd solids', using micropolar (Cosserat) elasticity in the presence of local active torques. We find that odd elasticity naturally emerges as a nonlinear effect of internal particle rotations. Exploring the viscoelasticity of such a solid, when immersed in an odd fluid, we discover new dynamically unstable regions driven by the odd solid-fluid coupling, and, in the underdamped regime, also by inertia. Remarkably, in the overdamped limit, this odd solid-fluid coupling allows for bulk wave propagation near these unstable regions.