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Proliferation of topological defects like vortices and dislocations plays a key role in the physics of systems with long-range order, particularly, superconductivity and superfluidity in thin films, plasticity of solids, and melting of atomic monolayers. Topological defects are characterized by their topological charge reflecting fundamental symmetries and conservation laws of the system. Conservation of topological charge manifests itself in extreme stability of static topological defects because destruction of a single defect requires overcoming a huge energy barrier proportional to the system size. However, the stability of driven topological defects remains largely unexplored. Here we address this issue and investigate numerically a dynamic instability of moving vortices in planar arrays of Josephson junctions. We show that a single vortex driven by sufficiently strong current becomes unstable and destroys superconductivity by triggering a chain reaction of self-replicating vortex-antivortex pairs forming linear of branching expanding patterns. This process can be described in terms of propagating phase cracks in long-range order with far-reaching implications for dynamic systems of interacting spins and atoms hosting magnetic vortices and dislocations.

Current-driven production of vortex-antivortex pairs in planar Josephson junction arrays and phase cracks in long-range order