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Bulk dislocation lattice defects are instrumental in identifyingtranslationally active topological insulators (TATIs), featuring band inversionat a finite momentum (${\bf K}_{\rm inv}$). As such, TATIs host robust gaplessmodes around the dislocation core, when the associated Burgers vector ${\bf b}$satisfies ${\bf K}_{\rm inv} \cdot {\bf b}=\pi$ (modulo $2 \pi$). From the timeevolution of appropriate density matrices, we show that when a TATI via a realtime ramp enters into a trivial or translationally inert topological insulatingphase, devoid of gapless dislocation modes, the signatures of the prerampdefect modes survive for a long time. More intriguingly, as the system rampsinto a TATI phase from any translationally inert insulator, signature of thedislocation mode dynamically builds up near its core, which is prominent forslow ramps. We exemplify these generic outcomes for two-dimensionaltime-reversal symmetry breaking insulators. Proposed dynamic responses at thedislocation core can be experimentally observed in quantum crystals, opticallattices and metamaterials with time a tunable band gap.

Dynamic melting and condensation of topological dislocation modes