Dynamic melting and condensation of topological dislocation modes

TL;DR

This paper investigates the dynamic behavior of topological dislocation modes during phase transitions in topological insulators, revealing how defect signatures evolve and can be observed in various physical systems.

Contribution

It introduces a real-time analysis of dislocation mode evolution during topological phase transitions, highlighting the dynamic buildup and persistence of defect signatures.

Findings

Dislocation modes persist long after entering trivial phases.

Signature of dislocation modes dynamically develops during phase ramps.

Results are applicable to quantum crystals, optical lattices, and metamaterials.

Abstract

Bulk dislocation lattice defects are instrumental in identifying translationally active topological insulators (TATIs), featuring band inversion at a finite momentum (${\bf K}_{\rm inv}$). As such, TATIs host robust gapless modes 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 time evolution of appropriate density matrices, we show that when a TATI via a real time ramp enters into a trivial or translationally inert topological insulating phase, devoid of gapless dislocation modes, the signatures of the preramp defect modes survive for a long time. More intriguingly, as the system ramps into a TATI phase from any translationally inert insulator, signature of the dislocation mode dynamically builds up near its core, which is prominent for slow ramps. We exemplify these generic outcomes for two-dimensional time-reversal symmetry breaking insulators. Proposed dynamic responses at the dislocation core can be experimentally observed in quantum crystals, optical lattices and metamaterials with time a tunable band gap.