Chiral active materials are composed of complex molecules that break both parity and time-reversal symmetry (TRS) at the microscale. This is generally a result of continuous injection of energy and angular momentum through local torques, fueled by local energy consumption. These materials are abundant, from living matter such as the cytoskeleton twisted by motor proteins and self-spinning starfish embryos, to synthesized materials such as a fluid of rotating magnetic active colloids. A striking phenomenon of breaking TRS is the possible appearance of odd viscosity, as first predicted by Onsager. Such odd viscosity is non-dissipative and should thus be derivable from a Hamiltonian theory.

In the first part of this talk I will show how odd viscosity emerges from any distribution of active torques, and that the mere existence of spin angular momentum density due to the local torques also breaks Onsager’s reciprocity relations and leads to non-Hermitian dynamical matrix. When interactions are included phenomenologically, we find regions in in the parameter space in which novel 3D mechanical waves propagate in the bulk, and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting of a non-reciprocal phase transition.

In the second part of the talk, I will show that active torques together with non-linear elasticity generically lead to the appearance of odd elasticity, even in disordered materials, as is ubiquitous in nature. This odd elasticity couples in a nonreciprocal way shear strains with shear stresses, and has been shown to give rise to remarkable mechanics. We further study the viscoelasticity of such chiral active material and discover new type of propagating waves and new unreported instability regions in the dynamic phase diagram.