Topological edge states in photonic Floquet insulator with unpaired Dirac cones

TL;DR

This paper introduces a photonic Floquet insulator with unpaired Dirac cones on a honeycomb lattice, demonstrating topologically protected unidirectional edge states that can bypass sharp corners without scattering, despite the absence of a full spectral gap.

Contribution

It presents a novel photonic system supporting unpaired Dirac cones and topological edge states without a full spectral gap, expanding understanding of topological phases in photonics.

Findings

Supports unidirectional edge states at sublattice detuning interfaces

Edge states circumvent corners without inter-valley scattering

Topological properties characterized by nonzero valley Chern number

Abstract

Topological insulators are most frequently constructed using lattices with specific degeneracies in their linear spectra, such as Dirac points. For a broad class of lattices, such as honeycomb ones, these points and associated Dirac cones generally appear in non-equivalent pairs. Simultaneous breakup of the time-reversal and inversion symmetry in systems based on such lattices may result in the formation of the unpaired Dirac cones in bulk spectrum, but the existence of topologically protected edge states in such structures remains an open problem. Here photonic Floquet insulator on honeycomb lattice with unpaired Dirac cones in its spectrum is introduced that can support unidirectional edge states appearing at the edge between two regions with opposite sublattice detuning. Topological properties of this system are characterized by the nonzero valley Chern number. Remarkably, edge states in this system can circumvent sharp corners without inter-valley scattering even though there is no total forbidden gap in the spectrum. Our results reveal unusual interplay between two different physical mechanisms of creation of topological edge states based on simultaneous breakup of different symmetries of the system.