Non-Reciprocal Interactions Reshape Topological Defect Annihilation

We show how non-reciprocal ferromagnetic interactions between neighbouring planar spins in two dimensions, affect the behaviour of topological defects. Non-reciprocity is introduced by weighting the coupling strength of the two-dimensional XY model by an anisotropic kernel. As a consequence, in addition to the topological charge $q$, the actual shape of the defects becomes crucial to faithfully describe their dynamics. Non-reciprocal coupling twists the spin field, selecting specific defect shapes, dramatically altering the pair annihilation process. Defect annihilation can either be enhanced or hindered, depending on the shape of the defects concerned and the degree of non-reciprocity in the system. We introduce a continuous description -- for which the phenomenological coefficients can be explicitly written in terms of the microscopic ones -- that captures the behaviour of the lattice model.