Dynamic melting and condensation of topological dislocation modes

Bulk dislocation lattice defects are instrumental to identify translationally active topological insulators (TATIs), featuring band inversion at a finite momentum (K_inv). They harbor robust gapless modes around the dislocation core, when the associated Burgers vector (b) satisfies K_inv · b = π (modulo 2π). From the time evolution of the appropriate density matrix, here we show that when a TATI via a ramp enters into a trivial or topological insulating phase, devoid of any gapless dislocation mode, at least weak signatures of the original defect modes survive for a long time. More intriguingly, as the system ramps into a TATI phase, signature of the dislocation mode dynamically builds up. Such evolutions of dislocation modes are more prominent for slow ramps. We exemplify these generic outcomes for two-dimensional time-reversal symmetry breaking insulators. Proposed dynamic responses at the core of dislocation lattice defects can be experimentally observed on quantum crystals, optical lattices and various metamaterials with time tunable band gap.