Chiral active matter is both `odd’ and non-reciprocal

Active materials are composed of many components that convert energy from the environment into directed mechanical motion, thus locally breaking time reversal symmetry (TRS). Examples of active materials are abundant, from living systems such as bacteria to colloidal rollers. A striking phenomenon of breaking TRS is the possible appearance of odd viscosity. Onsager reciprocal relations require that when TRS holds the viscosity tensor is symmetric for exchanging its first and last pair of indices. However, when TRS is broken, Onsager relations predict an odd viscosity that is both odd under TRS and under the change of indices. Such odd viscosity is non-dissipative and should thus be derivable from a Hamiltonian theory. In this talk I will discuss chiral active materials in which both parity and TRS are broken at the microscale. This is usually a result of continuous injection of energy and angular momentum through local torques, which are abundant in living systems, and generically result in odd viscosity, even when the constituents are non-interacting. I will show 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.