Real time dynamic of topological dislocation modes

Lattice defects, such as dislocations, play a pivotal role in identifying translationally active topological phases of matter, featuring band inversion at a finite momentum in the Brillouin zone, by hosting robust gapless modes in defect core. As such dislocation lattice defects are instrumental to probe this special class of topological states both in the static and driven or Floquet systems. Here we will show the real time dynamics of such dislocation modes by considering the following two distinct scenarios. First, we will discuss the long-time dynamics of dislocation modes after a sudden quench to either trivial or translationally inert topological phase, by computing their survival probability. We will argue that signature of dislocation modes appear periodically for a long time after the quench. Next, we will show the gradual formation of dislocation modes in the presence of a real time ramp to a translationally active phase, starting from a trivial phase. We will primarily focus on two dimensional Chern insulators and p+ip superconductors to demonstrate these outcomes. Finally, we will generalize these results to three-dimensional topological materials as well as to higher-order topological phases.