Prediction and Observation of Robust One-Way Bulk States in a Gyromagnetic Photonic Crystal

Jianfeng Chen and Zhi-Yuan Li

Phys. Rev. Lett. 128, 257401 – Published 21 June 2022

Abstract

We report a two-dimensional heterogeneous Haldane model composed of alternately stacking modified Haldane lattices with opposite next-nearest-neighbor hoppings, and predict the emergence of robust one-way bulk states by an ab initio theoretical calculation. These unique bulk states transport unidirectionally and are robust against backscattering from impurities in the strip bulk. By analogy with the heterogeneous Haldane model, we further confirm by numerical simulations and experimental measurements the existence of robust one-way bulk states in a two-dimensional microwave gyromagnetic photonic crystal, and demonstrate their robust one-way property over a long-distance even in the presence of metallic obstacles. Our study provides the strong support for the generalization and application of band theories to fermionic and bosonic systems, and paves a way for the implementation of high-throughput robust energy transmission materials and devices.

Received 1 March 2022
Accepted 26 May 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.257401

Physics Subject Headings (PhySH)

Magneto-optical effect Photonic crystals Topological insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jianfeng Chen ¹ and Zhi-Yuan Li^1,2,*

¹School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
²State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, China

^*Corresponding author. phzyli@scut.edu.cn

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 128, Iss. 25 — 24 June 2022

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic of three correlated Haldane models and corresponding topological states. (a)–(c) Haldane model. (d)–(f) Modified Haldane model. (g)–(i) Heterogeneous Haldane model. (a),(d),(g) Lattice schematics. The lattice constant $a$ is the distance between $A A$ or $B B$ pairs. (b),(e),(h) Band structures of zigzag strip are calculated by Haldane Hamiltonians. $t_{1}$ is taken as the unit of energy, $t_{2} = 0.1 5$ . There are no trivial bidirectional bulk states in the green regions. (c),(f),(i) Schematic diagrams of topological states.
Reuse & Permissions
Figure 2
Experimental sample, projected band structure and eigenmodal field of heterogeneous gyromagnetic photonic crystal strip. (a) Top view of the sample with the top metallic plate and magnet array is removed. The outline of whole strip is marked with a blue dashed line. The gyromagnetic cylinders in the middle of strip bulk are replaced with metallic cylinders of the same size that are used to verify the transport robustness of one-way bulk states. The inset is the illustration of the experimental system. (b) Projected band structure. The frequency range of the green region is $5.2 5 \sim 5.4 0 GHz$ and the gray regions are light cone. (c) Eigenmodal field profiles of states 1–4.
Reuse & Permissions
Figure 3
Measured electric field intensity distributions and transmission spectra of robust one-way bulk states. Electric field distributions excited by (a) left-incident plane wave, (b) right-incident plane wave, and (c) right-incident plane wave when the gyromagnetic cylinders of five honeycomb lattices in the strip bulk are replaced by the metallic cylinders of the same size [blue circles, see also Fig. 2]. Measured transmission spectra with (d) no metallic obstacle and (e) metallic obstacles in the strip bulk. The frequency range of yellow regions is $5.2 5 \sim 5.4 0 GHz$ . S21 and S12 represent the transmission coefficients of leftward and rightward propagation, respectively. (f) Measured electric intensity profiles along the white dotted lines 1–3 in (a)–(c). The gray region indicates the strip bulk and the two black dotted lines represent the strip edge.
Reuse & Permissions
Figure 4
Simulated electric field intensity distributions of robust one-way bulk states in a strip with a length of $100 a$ . (a) There are no metallic obstacles. (b) The gyromagnetic cylinders of five honeycomb lattices are replaced by metallic cylinders of the same size in the strip bulk. (c) An “X” shape array of gyromagnetic cylinders in the strip bulk is replaced by metallic cylinders of the same size. (d) Simulated electric intensity profiles along the white dotted lines 1–3 in (a)–(c). (e) Simulated electric intensity profiles along the white dotted lines a–f in (a)–(c). The gray region indicates the strip bulk and the black dotted lines represent the strip edges.
Reuse & Permissions

Physical Review Letters