Evolution of the edge states and corner states in a multilayer honeycomb valley-Hall topological metamaterial

Abstract

The valley-Hall effect provides topological protection to a broad class of defects in valley-Hall photonic topological metamaterials. Unveiling precisely how such protection is achieved and its implications in practical implementations is paramount to move from fundamental science to applications. To this end, we investigate a honeycomb valley-Hall topological metamaterial and monitor the evolution of the topological valley-Hall edge states and higher-order corner states under different perturbation δR. The evolutions of the edge states of the armchair and zigzag interfaces are demonstrated, respectively. By adjusting the geometric parameters and introducing disturbances to break the inversion symmetry, we achieve the edge states with different modes including the conventional crossed edge state and the specific gapped edge state. It is found that the edge states of topological valley kinking will gradually separate with the increase of δR, and finally a complete gap between the edge states appears. The gap has rarely been reported previously in topological materials fabricated by printed circuit board technology. In addition, the higher-order topological corner states can also be observed in the proposed topological metamaterial. The higher-order topological phase is theoretically characterized by nontrivial bulk polarization and the Wannier centers. Our results show that the corner state localization becomes stronger with the increase of δR. It is expected that our results will provide a platform for the realization of optical topological insulators.

Topological phononic metamaterials

“…In particular, the eigenfield concentrates dominantly in either the upper layer or the lower layer, that is a layer-pseudospin polarized transport. Therefore, assisted with the additional layer information, the valley edge modes can be either layer mixed or layer polarized, based on which even an interlayer converter has been conceived for possible application [220,[255][256][257][258][259][260][261][262]. The bilayer design late stimulates related research in square lattice [263], and van der Waals metamaterials [264].…”

Multi‐Type Topological States in Higher‐Order Photonic Insulators Based on Kagome Metal Lattices

“…Topological photonics provide a convenient platform to manipulate the propagation of electromagnetic waves, offering an unprecedented degree of control and robustness. [1][2][3][4] 1D topological edge state, [5][6][7][8][9][10]19] higher-order 0D topological corner state, [11][12][13][14][15][16][17][18][19] as well as a new higher-order corner state caused by longrange interactions, [11,20] show rich topological photonic properties and play an important role in revealing topological physics theory. Topological photonic structures have been extensively DOI: 10.1002/adom.202300986 demonstrated in various platforms such as coupled waveguide arrays, [21,22] photonic crystals, [7][8]11,14] metamaterials [19,23,24] and coupled ring resonators.…”

“…[1][2][3][4] 1D topological edge state, [5][6][7][8][9][10]19] higher-order 0D topological corner state, [11][12][13][14][15][16][17][18][19] as well as a new higher-order corner state caused by longrange interactions, [11,20] show rich topological photonic properties and play an important role in revealing topological physics theory. Topological photonic structures have been extensively DOI: 10.1002/adom.202300986 demonstrated in various platforms such as coupled waveguide arrays, [21,22] photonic crystals, [7][8]11,14] metamaterials [19,23,24] and coupled ring resonators. [25,26] Introducing new degrees of freedom to break the timereversal symmetry (TRS) and inversion symmetry, topological phase transition is obtained, leading to a kind of optical topological insulator.…”

“…[29][30][31] Valley as a new degree of freedom has also been widely demonstrated to obtain quantum valley-Hall effect (QVHE). [19,[32][33][34][35] Recently, there is an emerging type of topological systems, where orbital degree of freedoms (DOF) is introduced into for multiplexing. [36,37] Most of the previously reported topological insulators focus on designing a single structure to obtain one type of topological insulator.…”