Observation of Photonic Antichiral Edge States

Peiheng Zhou, Gui-Geng Liu, Yihao Yang, Yuan-Hang Hu, Sulin Ma, Haoran Xue, Qiang Wang, Longjiang Deng, and Baile Zhang

Phys. Rev. Lett. 125, 263603 – Published 29 December 2020

Abstract

Chiral edge states are a hallmark feature of two-dimensional topological materials. Such states must propagate along the edges of the bulk either clockwise or counterclockwise, and thus produce oppositely propagating edge states along the two parallel edges of a strip sample. However, recent theories have predicted a counterintuitive picture, where the two edge states at the two parallel strip edges can propagate in the same direction; these anomalous topological edge states are named as antichiral edge states. Here, we report the experimental observation of antichiral edge states in a gyromagnetic photonic crystal. The crystal consists of gyromagnetic cylinders in a honeycomb lattice, with the two triangular sublattices magnetically biased in opposite directions. With microwave measurement, unique properties of antichiral edge states have been observed directly, which include tilted dispersion, chiral-like robust propagation in samples with certain shapes, and 100% scattering into backward bulk states at certain terminations. These results extend and supplement the current understanding of chiral edge states.

Received 1 September 2020
Accepted 28 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.263603

Physics Subject Headings (PhySH)

Topological materials

Atomic, Molecular & Optical

Authors & Affiliations

Peiheng Zhou ¹, Gui-Geng Liu ^2,3,*, Yihao Yang^2,3, Yuan-Hang Hu¹, Sulin Ma ¹, Haoran Xue², Qiang Wang ², Longjiang Deng^1,†, and Baile Zhang ^2,3,‡

¹National Engineering Research Center of Electromagnetic Radiation Control Materials, State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, China
²Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
³Centre for Disruptive Photonic Technologies, The Photonics Institute, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

^*guigeng001@e.ntu.edu.sg
^†denglj@uestc.edu.cn
^‡blzhang@ntu.edu.sg

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Issue

Vol. 125, Iss. 26 — 31 December 2020

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Images

Figure 1
Buildup of antichiral edge states in a gyromagnetic photonic crystal. (a) Conceptual illustration of antichiral edge states that propagate in the same direction, while the bulk states propagate in the opposite direction. (b) The modified Haldane model. The next-nearest-neighbor coupling $t_{2} e^{i φ}$ directs inversely in sublattices $A$ and $B$ . (c) A photonic honeycomb lattice consisting of gyromagnetic cylinders with identical diameter $d = 4.4 mm$ . The lattice constant is $a = 12 mm$ . The sublattice $A$ ( $B$ ) indicated in red (blue) is magnetically biased along the $+$ ( $-$ ) $z$ direction. (d),(e) Design (d) and implementation (e) of the gyromagnetic photonic crystal. The crystal is placed in a parallel-plate copper waveguide with height $h_{1} = 5 mm$ . The thickness of the waveguide plates is $h_{2} = 1 mm$ . Permanent magnets of diameter $d = 4.4 mm$ and height $h_{3} = 2 mm$ are embedded in copper plates of the same height and vertically aligned with the YIG cylinders. In (e), the compositional layers are glided two to three lattices away from their edges for photographing.
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Figure 2
Observation of antichiral edge states in a strip sample. (a) Numerically calculated band structure for a strip with 15 unit cells in the $y$ direction. The black dots belong to bulk states. (b) Photograph of a strip sample that consists of $5 \times 23$ unit cells placed on a copper plate. Copper bars are placed at the upper and lower edges as PEC boundaries. Left and right edges are covered by microwave absorbers (blue). (c),(d) Measured field distribution ( $| E |^{2}$ ) at 7.3 GHz. The blue star shows the position of the source antenna. (e),(f) Band structure obtained from Fourier transform of the edge states mapped in (c) and (d), respectively.
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Figure 3
Robustness of antichiral edge states. (a) Clockwise propagation of antichiral edge states in a downward triangular sample consists of 91 unit cells. All edges are $A$ -type zigzag edges. (b) Photograph of the sample in (a). The sample is wrapped by copper bars and microwave absorber (blue) and placed on a copper plate. (c) Measured transmission. The $S_{12}$ ( $S_{21}$ ) parameter is measured by placing the source antenna at port 2 (port 1) and detector antenna at port 1 (port 2), as indicated by pink stars in (b). (d) Mapped field distribution ( $| E |^{2}$ ) for the sample at 7.3 GHz. The blue star shows the position of the source antenna, as the green arrow marks the wave propagation direction. (e) Counterclockwise propagation of antichiral edge states in an upward triangular sample. All edges are $B$ -type zigzag edges. (f) Photograph of the sample in (e). (g),(h) Measured results for the sample in (f), with similar labeling to (c) and (d).
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Figure 4
Conversion of antichiral edge states into bulk states at a termination. (a) Schematic of a strip sample with a trapezoid termination consists of 153 unit cells. (b) Photograph of the sample in (a). The sample is wrapped by copper bars except for the left open edge and placed on a copper plate. (b) Measured field distributions ( $| E |^{2}$ ) at 7.3 GHz. The blue star shows the position of the source antenna, as the green arrows mark the wave propagation direction.
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