Observation of unconventional edge states in ‘photonic graphene’

Abstract

Graphene, a two-dimensional honeycomb lattice of carbon atoms, has been attracting much interest in recent years. Electrons therein behave as massless relativistic particles, giving rise to strikingly unconventional phenomena. Graphene edge states are essential for understanding the electronic properties of this material. However, the coarse or impure nature of the graphene edges hampers the ability to directly probe the edge states. Perhaps the best example is given by the edge states on the bearded edge that have never been observed-because such an edge is unstable in graphene. Here, we use the optical equivalent of graphene-a photonic honeycomb lattice-to study the edge states and their properties. We directly image the edge states on both the zigzag and bearded edges of this photonic graphene, measure their dispersion properties, and most importantly, find a new type of edge state: one residing on the bearded edge that has never been predicted or observed. This edge state lies near the Van Hove singularity in the edge band structure and can be classified as a Tamm-like state lacking any surface defect. The mechanism underlying its formation may counterintuitively appear in other crystalline systems.

Ultrafast-laser-inscribed 3D integrated photonics: challenges and emerging applications

“…Using hexagonal waveguide arrays, the structure of graphene has been extensively studied, such as the influence of strain resulting in Landau levels [182], compression of the lattice [183], the influence of disorder on the edge states [184] as well as the band collapse under the influence of an external field [185]. Furthermore, a previously unknown edge state of graphene has been discovered using a honeycomb photonic lattice [186]. The Floquet topological insulator has been realised using a hexagonal array of helical waveguides that exhibits light propagation along the edges which is free of scattering because of topological protection [187].…”

Topological Quantum Optics in Two-Dimensional Atomic Arrays

“…To explore the spectrum of edge modes in the gap, we calculated the band structure for periodic stripes of atoms in a honeycomb lattice. The stripes may have bearded, armchair, or zig-zag edges [41,42]. Figure 3 shows the edge geometries and the corresponding band structures of stripes with bearded and armchair edges.…”

Optical properties of honeycomb photonic structures

“…A new research hotspot becomes a Dirac point that was first investigated in the electronic energy band structure of graphene [3]. Importantly, this concept penetrated into the field of optics where the so-called photonic graphene, a twodimensional photonic crystal structure that is analogous to graphene, has been studied theoretically and extensively [4][5][6][7][8] The conical diffraction and the dynamics of optical waves in photonic graphene was studied experimentally [4,9]. In particular, it was demonstrated that an incident narrow light beam at 488 nm wavelength, with momentum at the vicinity of a diabolic point, diffracts in the honeycomb lattice in a characteristic conical form, obtaining the shape of a ring whose thickness does not broaden, whereas its radius grows linearly with distance [4].…”