Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal

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Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal

Jing-jing Liu, Zheng-wei Li, Ze-Guo Chen, Weiyuan Tang, An Chen, Bin Liang, Guancong Ma, and Jian-Chun Cheng

Phys. Rev. Lett. 129, 084301 – Published 17 August 2022

Abstract

Weyl points—topological monopoles of quantized Berry flux—are predicted to spread to Weyl exceptional rings in the presence of non-Hermiticity. Here, we use a one-dimensional Aubry-Andre-Harper model to construct a Weyl semimetal in a three-dimensional parameter space comprising one reciprocal dimension and two synthetic dimensions. The inclusion of non-Hermiticity in the form of gain and loss produces a synthetic Weyl exceptional ring (SWER). The topology of the SWER is characterized by both its topological charge and non-Hermitian winding numbers. We experimentally observe the SWER and synthetic Fermi arc in a one-dimensional phononic crystal with the non-Hermiticity introduced by active acoustic components. Our findings pave the way for studying the high-dimensional non-Hermitian topological physics in acoustics.

Received 19 February 2022
Accepted 20 July 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.084301

Physics Subject Headings (PhySH)

Phononic crystals

Topological materials

General PhysicsCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Jing-jing Liu¹, Zheng-wei Li¹, Ze-Guo Chen², Weiyuan Tang², An Chen ¹, Bin Liang^1,*, Guancong Ma ^2,†, and Jian-Chun Cheng^1,‡

¹Collaborative Innovation Center of Advanced Microstructures and Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, People’s Republic of China
²Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China

^*Corresponding author. liangbin@nju.edu.cn
^†Corresponding author. phgcma@hkbu.edu.hk
^‡Corresponding author. jccheng@nju.edu.cn

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Issue

Vol. 129, Iss. 8 — 19 August 2022

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Images

Figure 1
(a) SWPs in the synthetic-reciprocal space. (b) Schematic of the SWP located at $(π / a, π / 2, π / 2)$ . (c), (d) Band structures in the Hermitian limit in the $k_{x} ξ_{y}$ plane at $ξ_{z} = 0.5 π$ and $k_{x} ξ_{z}$ plane at $ξ_{y} = 0.5 π$ , respectively. The SWP is marked by the red dot. (e) Schematic of the SWER located at $(π / a, π / 2, π / 2)$ . (f), (g) Real part and imaginary part of the spectrum in the $k_{x} ξ_{y}$ plane at $ξ_{z} = 0.5 π$ in the non-Hermitian system. A SWER is identified and marked by the red circles. (h), (i) The same system viewed on $k_{x} ξ_{z}$ plane for $ξ_{y} = 0.5 π$ .
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Figure 2
The gray surfaces enclose (a) the SWP and (b) the SWER for calculating topological charge. And the yellow plane represents the $k_{x} ξ_{y}$ plane at $ξ_{z} = 0.5 π$ . (c),(d) The distribution of the Berry curvature of Hermiticity and non-Hermiticity in the $k_{x} ξ_{y}$ plane at $ξ_{z} = 0.5 π$ , respectively. The color scale indicates the magnitude of the Berry curvature. (e) Schematics of eigenfrequency trajectories for looping around the EP in the $k_{x} ξ_{z}$ plane at $ξ_{y} = 0.5 π$ , which are used to calculate a quantized Berry phase characterizing the EP. The encircled EP is at $(k_{x}, ξ_{z}) = (43 π / 50 a, π / 2)$ . The bottom is a projection of the loop on the $k_{x} ξ_{z}$ plane.
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Figure 3
(a) The 1D non-Hermitian model. The dotted box indicates the unit cell. (b) Loss and gain are introduced to on-site terms and modulated by functions $ω_{\pm} (ξ_{z})$ . The couplings are modulated by functions $- κ_{\pm} (ξ_{y})$ . (c) The experimental system. The circuits connecting the loudspeakers and microphones at the top of cavities achieve active control of gain and loss in each cavity. The left inset is an enlarged view of a unit cell ( $a = 210 mm$ ). The pressure profile of the cavity’s mode is at the right.
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Figure 4
(a) Schematic of using different planes to cut two band structures. (b) Measured dispersions of the 1D PC. After we add additional loss and gain in the cavities, the point evolves into a nodal line at eigenfrequency $ω_{0}$ at $ξ_{y} = ξ_{z} = 0.5 π$ . The dashed lines correspond to the numerically calculated band structures of the designed Hamiltonian. (c) For different values of $ξ_{y}$ at $ξ_{z} = 0.5 π$ , the images show the evolution of band structures. (d) is similar to (c), but it is for different values of $ξ_{z}$ at $ξ_{y} = 0.5 π$ . The SWP becomes a SWER and exists in the $k_{x} ξ_{y}$ plane at $ξ_{z} = 0.5 π$ in the synthetic momentum space.
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Figure 5
The real spectra of a 24-site lattice with an open boundary and $ξ_{z} = 0.5 π$ of the Hermitian (a) and non-Hermitian case (b). The blue dots are measured results of the Fermi arcs. The measured pressure fields of edge states at $ξ_{y} = 0$ for Hermitian (c) and non-Hermitian case (d).
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