Symmetry-controlled edge states in graphene-like topological sonic crystal

doi:10.1088/1674-1056/ab9c0e

Abstract

Unique topological states emerged in various topological insulators (TI) have been proved with great application value for robust wave regulation. In this work, we demonstrate the parity inversion related to the definition of the primitive cell in one common lattice, and realize a type of symmetry-controlled edge states confined on the zigzag interfaces of the graphene-like sonic topological crystal. By simply sliding the selected ‘layer’ near the interface, the coupling of the pseudospin states induced by the multiple scattering for the C_6v lattice results in the adjustment of the edge states. Based on the physics of the states, we experimentally propose a prototype of acoustic topological filter hosting multiple channels with independent adjustable edge states and realize the selective high transmission. Our work diversifies the prospects for the applications of the gapped edge states in the robust wave regulation, and proposes a frame to design new topological devices.

Keywords: acoustic higher-order topological insulator acoustic filter controllable edge states

Received: 11 April 2020
Revised: 23 May 2020
Accepted manuscript online: 12 June 2020

PACS:	43.20.+g	(General linear acoustics)
	43.35.+d	(Ultrasonics, quantum acoustics, and physical effects of sound)
	52.35.Dm	(Sound waves)

Corresponding Authors: ^†Corresponding author. E-mail: xyzou@nju.edu.cn

About author:

†Corresponding author. E-mail: xyzou@nju.edu.cn

* Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303700), the National Natural Science Foundation of China (Grant Nos. 11634006, 11934009, and 11690030), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20191245), the Fundamental Research Funds for the Central Universities, China (Grant No. 020414380131), and the State Key Laboratory of Acoustics, Chinese Academy of Sciences.

Cite this article:

Zhang-Zhao Yang(杨彰昭), Jin-Heng Chen(陈晋恒), Yao-Yin Peng(彭尧吟), and Xin-Ye Zou(邹欣晔)† Symmetry-controlled edge states in graphene-like topological sonic crystal 2020 Chin. Phys. B 29 104302

Fig. 1.

(a) Schematic of two selected supercells (red dashed lines) based on one common graphene-like lattice, the corners and the edges of the supercells represent the pseudo-atoms and the corresponding hoppings, respectively. The corresponding energy band structures labeled with parities are presented in (b) and (c). (d) and (e) The pressure field distributions of the first two double-degenerate bands from bottom to top at M point of the two supercells, respectively. The opposite parities indicate the parity inversion.

Fig. 2.

Band structures of the ribbons composed of (a) 30 trivial supercells and (b) 15 trivial and 15 nontrivial supercells, being finite along y direction and periodic along x direction.

Fig. 3.

(a) Schematic of the structure divided into independent layers. Inset: Details of the configuration near the interface. (b) β_A-dependent band-edge frequencies for the supercells with k = 0 within a translation period. g₁ and g₂ represent the ranges between the two topological bands. Energy band structures with distinct edge states for (c) β_A = 0.125, (d) 0.25, and (e) 0.375, respectively.

Fig. 4.

(a) Energy band structure of the ribbon with two independent interfaces, the two pairs of the edge states are independently emerging on the specific interface. (b) Pressure field distributions and intensity flows of the pseudo-spin-dependent edge states for k = ± 0.05 × 2 π / a_x on the interfaces of the ribbon.

Fig. 5.

(a) Experimental setup of the two-dimensional acoustic topological filter. (b) Measured bulk (green) and port 3 (red) transmission spectra for β_P₁ = β_P₃ = 0.25. (c) Measured bulk (green) and port 3 (red) transmission spectra for β_P₁ = β_P₃ = 0.5. The gray regions in both (b) and (c) represent the theoretic range of the edge states.

Fig. 6.

(a) Measured transmission spectra for port 2 (red), port 3 (green), and port 4 (blue) when β_{P_i} = 0. (b) Measured transmission spectra for port 2 (red), port 3 (green), port 4 (blue) and the sum of the three ports for β_P₁ = β_P₃ = 0.5 and β_P₂ = β_P₄ = 0.25. The green dashed curve representing the total transmission loss exhibits lossless transmission in the two theoretical frequency ranges marked with grey. (c) and (d) The simulated acoustic energy transmission distributions for 6400 Hz and 7125 Hz, respectively.

Fig. A1.

Pseudo-spin states at (a) Γ and (b) M. In (a), d_{mod 1,2} represents the double-degenerate modes below the upper gap at Γ, and p_{mod 1,2} represents the modes upon the upper gap. In (b), the labels of the four dotted boxes represent the count of the double-degenerate bands from bottom to top. The (±) represents the parity of each mode, and circulation arrow of energy flow demonstrates the certain pseudo-spin state. The relative band structure is shown in Fig. 3(b).

Fig. A2.

Schematic diagrams of the two conditions: (a) the upper and the lower materials are the same and (b) the upper and the lower materials are different. The structure in (a) appears to be insulating, and the structure in (b) appears to be conductive.

Fig. B1.

Comparison of the simulated acoustic field distribution at 6.84 kHz for topological interface and ordinary defects, corresponding to (a) a cavity and (b) a disturbance in the waveguide. The red and black arrows represent propagation of the topological states and ordinary sound, respectively. (c) Simulated transmission spectra for perfect topological interface (red curve), topological interface with a cavity (green curve), topological interface with a disturbance (black curve) and ordinary defects (blue dashed curve). The white region represents the predicted range of edge states.

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Symmetry-controlled edge states in graphene-like topological sonic crystal

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