Emergent odd viscoelasticity in chiral soft glassy materials

Rheological properties of chiral active materials have been an important area of research in the recent past, in particular regarding odd terms in their mechanical response. While much progress has been made in the study of odd viscous fluids and odd elastic solids, there is still a lack of understanding of odd viscoelastic responses. We introduce a chiral soft glassy rheology model to understand the emergence and nature of such odd viscoelastic responses in a class of amorphous solids. We use this model, which effectively considers an ensemble of actively rotating inclusions in a glassy matrix, to study the linear stress response to steady and oscillatory shear flows. For steady shear we find an odd viscosity that, non-trivially, grows as the active rotation frequency Ω decreases. In oscillatory shear we find an odd viscoelastic spectrum with a non-trivial dependence on the driving frequency ω, combining resonance effects around ω = 2Ω with glassy power laws at larger ω.