Grain fission in odd crystals: A field-theoretical study

The intriguing properties of odd elastic crystals are studied using a continuum field theory which incorporates microscopic and mesoscopic length scales and diffusive timescales in the form of a new phase field crystal model incorporating transverse interactions (T-PFC). We derive the theory from microscopic dynamics of particles governed by both longitudinal and transverse interactions and show that the resulting T-PFC model exhibits 2D parity symmetry breaking and odd elasticity. It generates a variety of interesting phenomena that well agree with recent experiments and particle-based simulations of active and living odd crystals, such as self-rotation of crystallites, dislocation self-propulsion, unbinding of dislocation dipoles, and motion of circular grain boundaries. We identify a new type of surface cusp instability induced by self-generated surface odd stress that results in dislocation nucleation and proliferation, and importantly, the occurrence of fission and self-division of single-crystalline grains for strong enough transverse interaction. This behavior of grain fission leads to a transition from normal to reverse Ostwald ripening for self-rotating odd grains, and the spontaneous formation of a dynamical polycrystalline state resembling the polycrystal whorl state found in recent experiments of 2D colloidal odd crystals.