Anomalous and normal dislocation modes in Floquet topological insulators

Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial insulator into a Floquet topological insulator (FTI) that accommodates nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe FTIs as well as unconventional π-trivial insulator in the bulk of driven quantum systems by supporting normal and anomalous modes, localized near the defect core. Respectively, normal and anomalous dislocation modes reside at the Floquet zone center and boundaries. We exemplify these outcomes specifically for two-dimensional (2D) Floquet Chern insulator and px + ipy superconductor, where the dislocation modes are respectively constituted by charged and neutral Majorana fermions. Our findings should be, therefore, instrumental in probing Floquet topological phases in the state-of-the-art experiments in driven quantum crystals, cold atomic setups, and photonic and phononic metamaterials through bulk topological lattice defects. Subject to a periodic drive, quantum materials can develop nontrivial bulk topological state, termed a Floquet topological insulator, which differs from its static counterpart due to the nontrivial role played by the time dimension. Here, the authors theoretically demonstrate that such dynamic topology can be probed by bulk dislocation lattice defects, realizable in state-of-the-art experiments in quantum crystals, cold atomic systems and various metamaterials.