Anomalous and normal dislocation modes in Floquet topological insulators

TL;DR

This paper reveals how lattice dislocations can serve as probes for Floquet topological insulators, supporting unique localized modes that help identify and distinguish different driven topological phases.

Contribution

It demonstrates that dislocations support both normal and anomalous modes in Floquet topological insulators, providing a new method to probe these phases in experiments.

Findings

Dislocations support localized modes in Floquet topological phases.

Normal and anomalous modes reside at different Floquet zone regions.

Majorana fermions can be hosted at dislocation sites in specific models.

Abstract

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 $\pi$-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 $p_x+ip_y$ 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.