Floquet topological insulators with hybrid edges

TL;DR

This paper demonstrates the existence of unconventional topological edge states in Floquet insulators with hybrid edges, broadening the design possibilities for topological materials and their robustness against defects and nonlinearity.

Contribution

It introduces hybrid edge configurations in Floquet topological insulators, showing they support topological edge states even with complex lattice terminations.

Findings

Topological edge states exist in hybrid zigzag-armchair edges.

Edge states are robust through defects and nonlinear effects.

Hybrid edges expand the design space for topological insulators.

Abstract

Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet topological insulators unidirectional edge states appear upon breakup of the effective time-reversal symmetry due to dynamical modulations of the underlying lattice potential. However, such states are usually reported for certain simple lattice terminations, for example, at zigzag or bearded edges in honeycomb lattices. Here we show that unconventional topological edge states may exist in Floquet insulators based on arrays of helical waveguides with hybrid edges involving alternating zigzag and armchair segments, even if the latter are long. Such edge states appear in the largest part of the first Brillouin zone and show topological protection upon passage through the defects. Topological states at hybrid edges persist in the presence of focusing nonlinearity of the material. Our results can be extended to other lattice types and physical systems, they lift some of the constraints connected with lattice terminations that may not support edge states in the absence of effects breaking time-reversal symmetry of the system and expand the variety of geometrical shapes in which topological insulators can be constructed.