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Sun XC, Wang JB, He C, Chen YF. Non-Abelian Topological Phases and Their Quotient Relations in Acoustic Systems. PHYSICAL REVIEW LETTERS 2024; 132:216602. [PMID: 38856262 DOI: 10.1103/physrevlett.132.216602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 04/09/2024] [Indexed: 06/11/2024]
Abstract
Non-Abelian topological phases (NATPs) exhibit enigmatic intrinsic physics distinct from well-established Abelian topological phases, while lacking straightforward configuration and manipulation, especially for classical waves. In this Letter, we exploit novel braiding-type couplings among a pair of triple-component acoustic dipoles, which act as functional elements with effective imaginary couplings. Sequencing them in one dimension allows us to generate acoustic NATPs in a compact yet time-reversal invariant Hermitian system. We further provide the whole phase diagram that encompasses all i, j, and k non-Abelian phases, and directly demonstrate their unique quotient relations via different end point states. Our NATPs based on real-space braiding may inspire the exploration of acoustic devices with non-commutative characters.
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Affiliation(s)
- Xiao-Chen Sun
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Jia-Bao Wang
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Cheng He
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing 210093, China
| | - Yan-Feng Chen
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
- Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing 210093, China
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Yang Y, Yang B, Ma G, Li J, Zhang S, Chan CT. Non-Abelian physics in light and sound. Science 2024; 383:eadf9621. [PMID: 38386745 DOI: 10.1126/science.adf9621] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 01/17/2024] [Indexed: 02/24/2024]
Abstract
Non-Abelian phenomena arise when the sequence of operations on physical systems influences their behaviors. By possessing internal degrees of freedom such as polarization, light and sound can be subjected to various manipulations, including constituent materials, structured environments, and tailored source conditions. These manipulations enable the creation of a great variety of Hamiltonians, through which rich non-Abelian phenomena can be explored and observed. Recent developments have constituted a versatile testbed for exploring non-Abelian physics at the intersection of atomic, molecular, and optical physics; condensed matter physics; and mathematical physics. These fundamental endeavors could enable photonic and acoustic devices with multiplexing functionalities. Our review aims to provide a timely and comprehensive account of this emerging topic. Starting from the foundation of matrix-valued geometric phases, we address non-Abelian topological charges, non-Abelian gauge fields, non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their realizations with photonics and acoustics and conclude with future prospects.
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Affiliation(s)
- Yi Yang
- Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong, China
- HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - Biao Yang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
- Nanhu Laser Laboratory, National University of Defense Technology, Changsha, China
| | - Guancong Ma
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Jensen Li
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - Shuang Zhang
- Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong, China
- HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong, China
- New Cornerstone Science Laboratory, The University of Hong Kong, Pokfulam, Hong Kong, China
| | - C T Chan
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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Wang D, Jia H, Yang Q, Hu J, Zhang ZQ, Chan CT. Intrinsic Triple Degeneracy Point Bounded by Nodal Surfaces in Chiral Photonic Crystal. PHYSICAL REVIEW LETTERS 2023; 130:203802. [PMID: 37267572 DOI: 10.1103/physrevlett.130.203802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2022] [Accepted: 04/24/2023] [Indexed: 06/04/2023]
Abstract
In periodic systems, band degeneracies are typically protected and classified by spatial symmetries. However, in photonic systems, the Γ point at zero frequency is an intrinsic degeneracy due to the polarization degree of freedom of electromagnetic waves. For chiral photonic crystals, such an intrinsic degeneracy carries ±2 chiral topological charge while having linear band dispersions, different from the general perception of charge-2 nodes being associated with quadratic dispersions. Here, we show that these topological characters originate from the spin-1 Weyl point at zero frequency node of triple degeneracy, due to the existence of an electrostatic flat band. Such a topological charge at zero frequency is usually buried in bulk band projections and has never been experimentally observed. To address this challenge, we introduce space-group screw symmetries in the design of chiral photonic crystal, which makes the Brillouin zone boundary an oppositely charged nodal surface enclosing the Γ point. As a result, the emergent Fermi arcs are forced to connect the projections of these topological singularities, enabling their experimental observation. The number of Fermi arcs then directly reveals the embedded topological charge at zero frequency.
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Affiliation(s)
- Dongyang Wang
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Hongwei Jia
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
- Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, China
| | - Quanlong Yang
- School of Physics and Electronics, Central South University, Changsha 410083, Hunan, China
| | - Jing Hu
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - Z Q Zhang
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
| | - C T Chan
- Department of Physics, Hong Kong University of Science and Technology, Hong Kong, China
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