Topological defects in non-reciprocal solids*

Topological defects in crystals are responsible for phenomena ranging from plastic deformation to defect-mediated melting. A crucial assumption in the elastic theory of topological defects is a symmetry between deformation and stress known as Maxwell-Betti (MB) reciprocity. However, in active media, MB reciprocity need not hold. In this talk, I will discuss the theory of topological defects in two-dimensional crystals that violate MB reciprocity. Intriguingly when MB reciprocity is broken, we find that the Peach-Koehler forces between two dislocations need not be equal and opposite even when the medium is freestanding, homogeneous, and isotropic. Beyond active solids, our theory lends insights into systems with microscopic transverse interactions such as vortex lattices and gyroelastic media.