Odd elasticity in disordered chiral active materials

Chiral active materials are abundant in nature, including the cytoskeleton with attached motor proteins, rotary clusters of bacteria 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. Recently, it was found that chiral active materials may 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 still remains to explore how odd elasticity can emerge 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 this solid, when immersed in active self-spinning solvent (`odd fluid'), we discover both dynamically unstable regions and regions in which bulk waves can propagate even in an overdamped solid.