When soft crystals defy Newton's third law: Non-reciprocal mechanics and dislocation motility*

The effective interactions between the constituents of driven and active soft matter are able to bypass the constraints imposed by Newton's third law. This phenomenon is exemplified by the hydrodynamic interactions between units moving in a fluid medium: sedimenting particles, driven emulsions in shallow channels, spinning particles and microswimmers all interact by pairwise forces that are not equal and opposite and/or feature a transverse component.

I will first show that such non-reciprocal forces cannot stabilize crystalline order on their own. Then, I will explain how non-reciprocal forces in 2D crystals define six classes of mechanical responses with no counterparts in equilibrium solids. This includes odd elasticity, but also unconventional strain-stress relations (such as couplings between dilation deformations and shear stresses), and unanticipated net forces arising from local deformations. Finally, I will show that, when competing with conventional stabilizing interactions, all classes of non-reciprocal forces are able to set otherwise quiescent dislocations into motion.

These theoretical predictions will be illustrated by recent experimental realizations.