Breakdown of Volterra's Elasticity Theory of Dislocations in Polar Skyrmion Lattices.

Emerging polar skyrmion crystals (SkX) have raised much interest for technological applications owing to their nontrivial topologies of electric dipoles, quasiparticle-like behaviors, and unique electrical responses. Understanding SkX defects, especially dislocations, is crucial for their unique lattice dynamics and responses; however, it still remains elusive. Here, we have not only demonstrated that a SkX dislocation exhibits an anomalously deformed core structure with over 50% elongation of skyrmions but also discovered that Volterra's elasticity theory of dislocation is broken down in SkX. Our phase-field simulation reveals that these distinct features of SkX dislocation arise from a rigid to soft quasiparticle transition of skyrmions depending on the electric field and temperature. In SkX, there exist inherent mechanics that mitigate the mismatch by both migration and deformation of skyrmions. This work provides novel insights into a new class of lattice mechanics and related functionality arising from the unique properties of quasi-particle SkX.