Odd elastic effects in a two-dimensional anisotropic fluid

There is a recent interest in studying odd viscosity and odd elasticity in soft and living matter. Current focus has been on simple liquids and solids. However, many complex fluids possess microstrures and can exhibit odd viscoelastity. How odd viscoelastic effects dictate its microstructure remains to be an open question. Here, we investigate odd elasticity in a particular complex fluid, namely nematic liquid crystal. Theoretically, we find that the elastic term in a two-dimensional nematic liquid crystal can exhibit oddness, which can give rise to nonreciprocal interactions between neighboring directors, in contrast to their reciprocal interactions due to elastic distortions. This odd elastic term can induce self propulsion of domain walls and self spinning of topological defects. In certain confinement, the odd nematic can rotate persistently and exert net torques on boundaries. By including the hydrodynamic effect of this odd elastic term, our hydrodynamic simulations demonstrate how an odd nematic liquid crystal can sustain dynamic motion of defects and spontaneous flows. As such, we have developed a theoretical model for odd nematic elasticity, which offers an alternative way to dynamically manipulate the microstructure of a nematic fluid.