1
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Wu J, Zheng R, Liang J, Ke M, Lu J, Deng W, Huang X, Liu Z. Spin-Dependent Localization of Helical Edge States in a Non-Hermitian Phononic Crystal. PHYSICAL REVIEW LETTERS 2024; 133:126601. [PMID: 39373447 DOI: 10.1103/physrevlett.133.126601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Revised: 07/01/2024] [Accepted: 08/19/2024] [Indexed: 10/08/2024]
Abstract
As a distinctive feature unique to non-Hermitian systems, non-Hermitian skin effect displays fruitful exotic phenomena in one or higher dimensions, especially when conventional topological phases are involved. Among them, hybrid skin-topological effect is theoretically proposed recently, which exhibits anomalous localization of topological boundary states at lower-dimensional boundaries accompanied by extended bulk states. Here, we experimentally realize the hybrid skin-topological effect in a non-Hermitian phononic crystal. The phononic crystal, before tuning to be non-Hermitian, is an ideal acoustic realization of the Kane-Mele model, which hosts gapless helical edge states at the boundaries. By introducing a staggered distribution of loss, the spin-dependent edge modes pile up to opposite corners, leading to a direct observation of the spin-dependent hybrid skin-topological effect. Our Letter highlights the interplay between topology and non-Hermiticity and opens new routes to non-Hermitian wave manipulations.
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Affiliation(s)
| | | | | | - Manzhu Ke
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jiuyang Lu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Weiyin Deng
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | | | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
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2
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Zhang X, Wei Q, Peng M, Deng W, Lu J, Huang X, Jia S, Yan M, Liu Z, Chen G. Observation of 3D acoustic quantum Hall states. Sci Bull (Beijing) 2024; 69:2187-2193. [PMID: 38762435 DOI: 10.1016/j.scib.2024.04.055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Revised: 02/04/2024] [Accepted: 04/23/2024] [Indexed: 05/20/2024]
Abstract
Quantum Hall effect, the quantized transport phenomenon of electrons under strong magnetic fields, remains one of the hottest research topics in condensed matter physics since its discovery in 2D electronic systems. Recently, as a great advance in the research of quantum Hall effects, the quantum Hall effect in 3D systems, despite its big challenge, has been achieved in the bulk ZrTe5 and Cd3As2 materials. Interestingly, Cd3As2 is a Weyl semimetal, and quantum Hall effect is hosted by the Fermi arc states on opposite surfaces via the Weyl nodes of the bulk, and induced by the unique edge states on the boundaries of the opposite surfaces. However, such intriguing edge state distribution has not yet been experimentally observed. Here, we aim to reveal experimentally the unusual edge states of Fermi arcs in acoustic Weyl system with the aid of pseudo-magnetic field. Benefiting from the macroscopic nature of acoustic crystals, the pseudo-magnetic field is introduced by elaborately designed the gradient on-site energy, and the edge states of Fermi arcs on the boundaries of the opposite surfaces are unambiguously demonstrated in experiments. Our system serves as an ideal and highly tunable platform to explore the Hall physics in 3D system, and has the potential in the application of new acoustic devices.
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Affiliation(s)
- Xuewei Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Qiang Wei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Mian Peng
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Weiyin Deng
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Jiuyang Lu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Xueqin Huang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Mou Yan
- Key Laboratory of Materials Physics, Ministry of Education, School of Physics, Zhengzhou University, Zhengzhou 450001, China; Laboratory of Zhongyuan Light, School of Physics, Zhengzhou University, Zhengzhou 450001, China; Institute of Quantum Materials and Physics, Henan Academy of Sciences, Zhengzhou 450046, China.
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China; Institute for Advanced Studies, Wuhan University, Wuhan 430072, China.
| | - Gang Chen
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China; Key Laboratory of Materials Physics, Ministry of Education, School of Physics, Zhengzhou University, Zhengzhou 450001, China; Laboratory of Zhongyuan Light, School of Physics, Zhengzhou University, Zhengzhou 450001, China; Institute of Quantum Materials and Physics, Henan Academy of Sciences, Zhengzhou 450046, China.
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3
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Long Y, Wang Z, Zhang C, Xue H, Zhao YX, Zhang B. Non-Abelian Braiding of Topological Edge Bands. PHYSICAL REVIEW LETTERS 2024; 132:236401. [PMID: 38905662 DOI: 10.1103/physrevlett.132.236401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/10/2024] [Revised: 04/08/2024] [Accepted: 05/06/2024] [Indexed: 06/23/2024]
Abstract
Braiding is a geometric concept that manifests itself in a variety of scientific contexts from biology to physics, and has been employed to classify bulk band topology in topological materials. Topological edge states can also form braiding structures, as demonstrated recently in a type of topological insulators known as Möbius insulators, whose topological edge states form two braided bands exhibiting a Möbius twist. While the formation of Möbius twist is inspiring, it belongs to the simple Abelian braid group B_{2}. The most fascinating features about topological braids rely on the non-Abelianness in the higher-order braid group B_{N} (N≥3), which necessitates multiple edge bands, but so far it has not been discussed. Here, based on the gauge enriched symmetry, we develop a scheme to realize non-Abelian braiding of multiple topological edge bands. We propose tight-binding models of topological insulators that are able to generate topological edge states forming non-Abelian braiding structures. Experimental demonstrations are conducted in two acoustic crystals, which carry three and four braided acoustic edge bands, respectively. The observed braiding structure can correspond to the topological winding in the complex eigenvalue space of projective translation operator, akin to the previously established point-gap winding topology in the bulk of the Hatano-Nelson model. Our Letter also constitutes the realization of non-Abelian braiding topology on an actual crystal platform, but not based on the "virtual" synthetic dimensions.
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Affiliation(s)
- Yang Long
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Zihao Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Chen Zhang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Haoran Xue
- Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China
| | - Y X Zhao
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
- HK Institute of Quantum Science and Technology, The University of Hong Kong, Hong Kong, China
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
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4
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Hu J, Zhuang S, Yang Y. Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries. PHYSICAL REVIEW LETTERS 2024; 132:213801. [PMID: 38856291 DOI: 10.1103/physrevlett.132.213801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 04/19/2024] [Indexed: 06/11/2024]
Abstract
We theoretically construct a higher-order topological insulator (HOTI) on a Brillouin real projective plane enabled by momentum-space nonsymmorphic (k-NS) symmetries from synthetic gauge fields. Two anicommutative k-NS glide reflections appear in a checkerboard Z_{2} flux model, impose nonsymmorphic constraints on Berry curvature, and quantize bulk and Wannier-sector polarization nonlocally across different momenta. The model's bulk exhibits an isotropic quadrupole phase diagram, where the transition appears intrinsically from bulk gap closure. The model hosts the simultaneous presence of intrinsic and extrinsic HOTI features: in a ribbon geometry where one pair of boundaries gets open, the edge termination can induce boundary-obstructed topological phase within the symmetry-protected topological phase due to the breaking of k-NS symmetry. At last, we present a concrete design for the real projective plane quadrupole insulator and show how to measure the momentum glide reflection based on acoustic resonator arrays. Our results shed light on HOTIs on deformed Brillouin manifolds via k-NS symmetries.
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Affiliation(s)
- Jinbing Hu
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
- College of Optical-Electrical Information and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Songlin Zhuang
- College of Optical-Electrical Information and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
| | - Yi Yang
- Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China
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5
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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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6
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Qiu H, Li Y, Zhang Q, Qiu C. Discovery of Higher-Order Nodal Surface Semimetals. PHYSICAL REVIEW LETTERS 2024; 132:186601. [PMID: 38759197 DOI: 10.1103/physrevlett.132.186601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Accepted: 03/29/2024] [Indexed: 05/19/2024]
Abstract
The emergent higher-order topological insulators significantly deepen our understanding of topological physics. Recently, the study has been extended to topological semimetals featuring gapless bulk band nodes. To date, higher-order nodal point and line semimetals have been successfully realized in different physical platforms. However, for the conceptually expected higher-order nodal surface semimetals, a concrete model has yet to be proposed, let alone experimentally observed. Here, we report an ingenious design route for constructing this unprecedented higher-order topological phase. The three-dimensional model, layer-stacked with a two-dimensional anisotropic Su-Schrieffer-Heeger lattice, exhibits appealing hinge arcs connecting the projected nodal surfaces. Experimentally, we realize this new topological phase in an acoustic metamaterial, and present unambiguous evidence for both the bulk nodal structure and hinge arc states, the two key manifestations of the higher-order nodal surface semimetal. Our findings can be extended to other classical systems such as photonic, elastic, and electric circuit systems, and open new possibilities for controlling waves.
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Affiliation(s)
- Huahui Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Yuzeng Li
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Qicheng Zhang
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
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7
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Yang YB, Wang JH, Li K, Xu Y. Higher-order topological phases in crystalline and non-crystalline systems: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:283002. [PMID: 38574683 DOI: 10.1088/1361-648x/ad3abd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 04/04/2024] [Indexed: 04/06/2024]
Abstract
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.
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Affiliation(s)
- Yan-Bin Yang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region of China, People's Republic of China
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiong-Hao Wang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Kai Li
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yong Xu
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
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8
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Cerjan A, Loring TA, Schulz-Baldes H. Local Markers for Crystalline Topology. PHYSICAL REVIEW LETTERS 2024; 132:073803. [PMID: 38427858 DOI: 10.1103/physrevlett.132.073803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2023] [Accepted: 01/19/2024] [Indexed: 03/03/2024]
Abstract
Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches currently used to classify bulk topological crystalline phases cannot predict the existence, localization, or spectral isolation of any resulting boundary-localized modes. While interfaces between materials in different crystalline phases must have topological states at some energy, these states need not appear within the band gap, and thus may not be useful for applications. Here, we derive a class of local markers for identifying material topology due to crystalline symmetries, as well as a corresponding measure of topological protection. As our real-space-based approach is inherently local, it immediately reveals the existence and robustness of topological boundary-localized states, yielding a predictive framework for designing topological crystalline heterostructures. Beyond enabling the optimization of device geometries, we anticipate that our framework will also provide a route forward to deriving local markers for other classes of topology that are reliant upon spatial symmetries.
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Affiliation(s)
- Alexander Cerjan
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Terry A Loring
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Hermann Schulz-Baldes
- FAU Erlangen-Nürnberg, Department Mathematik, Cauerstr. 11, D-91058 Erlangen, Germany
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9
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Chen Z, Li Z, Weng J, Liang B, Lu Y, Cheng J, Alù A. Sound non-reciprocity based on synthetic magnetism. Sci Bull (Beijing) 2023; 68:2164-2169. [PMID: 37604721 DOI: 10.1016/j.scib.2023.08.013] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 04/22/2023] [Accepted: 07/17/2023] [Indexed: 08/23/2023]
Abstract
Synthetic magnetism has been recently realized using spatiotemporal modulation patterns, producing non-reciprocal steering of charge-neutral particles such as photons and phonons. Here, we design and experimentally demonstrate a non-reciprocal acoustic system composed of three compact cavities interlinked with both dynamic and static couplings, in which phase-correlated modulations induce a synthetic magnetic flux that breaks time-reversal symmetry. Within the rotating wave approximation, the transport properties of the system are controlled to efficiently realize large non-reciprocal acoustic transport. By optimizing the coupling strengths and modulation phases, we achieve frequency-preserved unidirectional transport with 45-dB isolation ratio and 0.85 forward transmission. Our results open to the realization of acoustic non-reciprocal technologies with high efficiency and large isolation, and offer a route towards Floquet topological insulators for sound.
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Affiliation(s)
- Zhaoxian Chen
- Collaborative Innovation Center of Advanced Microstructures, Key Laboratory of Modern Acoustics of Ministry of Education, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, China; College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Zhengwei Li
- Collaborative Innovation Center of Advanced Microstructures, Key Laboratory of Modern Acoustics of Ministry of Education, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, China
| | - Jingkai Weng
- Collaborative Innovation Center of Advanced Microstructures, Key Laboratory of Modern Acoustics of Ministry of Education, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, China
| | - Bin Liang
- Collaborative Innovation Center of Advanced Microstructures, Key Laboratory of Modern Acoustics of Ministry of Education, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, China.
| | - Yanqing Lu
- College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China.
| | - Jianchun Cheng
- Collaborative Innovation Center of Advanced Microstructures, Key Laboratory of Modern Acoustics of Ministry of Education, Institute of Acoustics, Department of Physics, Nanjing University, Nanjing 210093, China.
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York NY 10031, USA; Physics Program, Graduate Center, City University of New York, New York NY 10016, USA.
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10
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Xue H, Chen ZY, Cheng Z, Dai JX, Long Y, Zhao YX, Zhang B. Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal. Nat Commun 2023; 14:4563. [PMID: 37507388 PMCID: PMC10382567 DOI: 10.1038/s41467-023-40252-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 07/19/2023] [Indexed: 07/30/2023] Open
Abstract
Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence-while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system.
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Affiliation(s)
- Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Z Y Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, China
| | - Zheyu Cheng
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - J X Dai
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, China
| | - Yang Long
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Y X Zhao
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China.
- HK Institute of Quantum Science & Technology, The University of Hong Kong, Hong Kong, China.
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, Singapore.
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11
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Zhang C, Chen ZY, Zhang Z, Zhao YX. General Theory of Momentum-Space Nonsymmorphic Symmetry. PHYSICAL REVIEW LETTERS 2023; 130:256601. [PMID: 37418718 DOI: 10.1103/physrevlett.130.256601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 02/20/2023] [Accepted: 05/23/2023] [Indexed: 07/09/2023]
Abstract
As a fundamental concept of all crystals, space groups are partitioned into symmorphic groups and nonsymmorphic groups. Each nonsymmorphic group contains glide reflections or screw rotations with fractional lattice translations, which are absent in symmorphic groups. Although nonsymmorphic groups ubiquitously exist on real-space lattices, on the reciprocal lattices in momentum space, the ordinary theory only allows symmorphic groups. In this work, we develop a novel theory for momentum-space nonsymmorphic space groups (k-NSGs), utilizing the projective representations of space groups. The theory is quite general: Given any k-NSGs in any dimensions, it can identify the real-space symmorphic space groups (r-SSGs) and construct the corresponding projective representation of the r-SSG that leads to the k-NSG. To demonstrate the broad applicability of our theory, we show these projective representations and therefore all k-NSGs can be realized by gauge fluxes over real-space lattices. Our work fundamentally extends the framework of crystal symmetry, and therefore can accordingly extend any theory based on crystal symmetry, for instance, the classification crystalline topological phases.
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Affiliation(s)
- Chen Zhang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- The University of Hong Kong Shenzhen Institute of Research and Innovation, Shenzhen 518057, China
| | - Z Y Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- The University of Hong Kong Shenzhen Institute of Research and Innovation, Shenzhen 518057, China
| | - Zheng Zhang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- The University of Hong Kong Shenzhen Institute of Research and Innovation, Shenzhen 518057, China
| | - Y X Zhao
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Pokfulam Road, Hong Kong, China
- HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam Road, Hong Kong, China
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12
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Li Y, Xu S, Zhang Z, Yang Y, Xie X, Ye W, Liu F, Xue H, Jing L, Wang Z, Chen QD, Sun HB, Li E, Chen H, Gao F. Polarization-Orthogonal Nondegenerate Plasmonic Higher-Order Topological States. PHYSICAL REVIEW LETTERS 2023; 130:213603. [PMID: 37295078 DOI: 10.1103/physrevlett.130.213603] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Accepted: 04/19/2023] [Indexed: 06/12/2023]
Abstract
Photonic topological states, providing light-manipulation approaches in robust manners, have attracted intense attention. Connecting photonic topological states with far-field degrees of freedom (d.o.f.) has given rise to fruitful phenomena. Recently emerged higher-order topological insulators (HOTIs), hosting boundary states two or more dimensions lower than those of bulk, offer new paradigms to localize or transport light topologically in extended dimensionalities. However, photonic HOTIs have not been related to d.o.f. of radiation fields yet. Here, we report the observation of polarization-orthogonal second-order topological corner states at different frequencies on a designer-plasmonic kagome metasurface in the far field. Such phenomenon stands on two mechanisms, i.e., projecting the far-field polarizations to the intrinsic parity d.o.f. of lattice modes and the parity splitting of the plasmonic corner states in spectra. We theoretically and numerically show that the parity splitting originates from the underlying interorbital coupling. Both near-field and far-field experiments verify the polarization-orthogonal nondegenerate second-order topological corner states. These results promise applications in robust optical single photon emitters and multiplexed photonic devices.
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Affiliation(s)
- Yuanzhen Li
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
| | - Su Xu
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China
| | - Zijian Zhang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
| | - Yumeng Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
| | - Xinrong Xie
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
| | - Wenzheng Ye
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
| | - Feng Liu
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
| | - Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Liqiao Jing
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
| | - Zuojia Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
| | - Qi-Dai Chen
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China
| | - Hong-Bo Sun
- State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China
- State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Haidian, Beijing 100084, China
| | - Erping Li
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Fei Gao
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China
- Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China
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13
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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14
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Wu H, Hu H, Wang X, Xu Z, Zhang B, Wang QJ, Zheng Y, Zhang J, Cui TJ, Luo Y. Higher-Order Topological States in Thermal Diffusion. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2210825. [PMID: 36730361 DOI: 10.1002/adma.202210825] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 01/28/2023] [Indexed: 06/18/2023]
Abstract
Unlike conventional topological materials that carry topological states at their boundaries, higher-order topological materials are able to support topological states at boundaries of boundaries, such as corners and hinges. While band topology has been recently extended into thermal diffusion for thermal metamaterials, its realization is limited to a 1D thermal lattice, lacking access to the higher-order topology. In this work, the experimental realization is reported of a higher-order thermal topological insulator in a generalized 2D diffusion lattice. The topological corner states for thermal diffusion are observed in the bandgap of diffusion rate of the bulk, as a consequence of the anti-Hermitian nature of the diffusion Hamiltonian. The topological protection of these thermal corner states is demonstrated with the stability of their diffusion profile in the presence of amorphous deformation. This work constitutes the first realization of higher-order topology in purely diffusive systems and opens the door for future thermal management with topological protection beyond 1D geometries.
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Affiliation(s)
- Haotian Wu
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Hao Hu
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Xixi Wang
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Zhixia Xu
- State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China
- School of Information Science and Technology, Dalian Maritime University, Dalian, 116026, China
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Qi Jie Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore
| | - Yuanjin Zheng
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
| | - Jingjing Zhang
- State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China
| | - Tie Jun Cui
- State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China
| | - Yu Luo
- School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
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15
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Zhang P, Jia H, Lu J, Yang X, Wang S, Yang Y, Liu Z, Yang J. Observations of acoustic Wannier configurations revealing topological corner anomaly. Sci Bull (Beijing) 2023; 68:679-683. [PMID: 36931914 DOI: 10.1016/j.scib.2023.03.015] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Revised: 02/13/2023] [Accepted: 03/07/2023] [Indexed: 03/13/2023]
Affiliation(s)
- Peng Zhang
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China
| | - Han Jia
- University of Chinese Academy of Sciences, Beijing 100049, China; State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China.
| | - Jiuyang Lu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510641, China; Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China.
| | - Xinghang Yang
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China
| | - Suhao Wang
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yuzhen Yang
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China; Institute for Advanced Studies, Wuhan University, Wuhan 430072, China.
| | - Jun Yang
- Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China.
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16
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Liu L, Li T, Zhang Q, Xiao M, Qiu C. Universal Mirror-Stacking Approach for Constructing Topological Bound States in the Continuum. PHYSICAL REVIEW LETTERS 2023; 130:106301. [PMID: 36962038 DOI: 10.1103/physrevlett.130.106301] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Accepted: 02/17/2023] [Indexed: 06/18/2023]
Abstract
Bound states in the continuum (BICs) are counterintuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulting in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of which directly inherits the energy spectrum information and band topology of the original monolayer. By tuning the interlayer couplings, the topological bound state of one subspace can move into and out of the continuum of the other subspace continuously without hybridization. As representative examples, we construct one-dimensional first-order and two-dimensional higher-order TBICs, and demonstrate them unambiguously by acoustic experiments. Our findings will expand the research implications of both topological materials and BICs.
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Affiliation(s)
- Luohong Liu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Tianzi Li
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Qicheng Zhang
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Meng Xiao
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Wuhan Institute of Quantum Technology, Wuhan 430206, China
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
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17
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Wang Q, Qian J, Jiang L. Non-Hermitian kagome photonic crystal with a totally topological spatial mode selection. OPTICS EXPRESS 2023; 31:5363-5377. [PMID: 36823818 DOI: 10.1364/oe.482836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
Recently, the study of non-Hermitian topological edge and corner states in sonic crystals (SCs) and photonic crystals (PCs) has drawn much attention. In this paper, we propose a Wannier-type higher-order topological insulator (HOTI) model based on the kagome PC containing dimer units and study its non-Hermitian topological corner states. When balanced gain and loss are introduced into the dimer units with a proper parity-time symmetric setting, the system will show asymmetric Wannier bands and can support two Hermitian corner states and two pairs of complex-conjugate or pseudo complex-conjugate non-Hermitian corner states. These topological corner states are solely confined at three corners of the triangular supercell constructed by the trivial and non-trivial kagome PCs, corresponding to a topological spatial mode selection effect. As compared to the non-Hermitian quadrupole-type HOTIs, the non-Hermitian Wannier-type HOTIs can realize totally topological spatial mode selection by using much lower coefficients of gain and loss. Our results pave the way for the development of novel non-Hermitian photonic topological devices based on Wannier-type HOTIs.
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18
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Classification of time-reversal-invariant crystals with gauge structures. Nat Commun 2023; 14:743. [PMID: 36765052 PMCID: PMC9918504 DOI: 10.1038/s41467-023-36447-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 01/26/2023] [Indexed: 02/12/2023] Open
Abstract
A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain largely unexplored. Despite recent advances in artificial crystals, whose intrinsic gauge structures necessarily require a projective description, a unified theory is yet to be established. Here, we establish such a unified theory by exhaustively classifying and representing all 458 projective symmetry algebras of time-reversal-invariant crystals from 17 wallpaper groups in two dimensions-189 of which are algebraically non-equivalent. We discover three physical signatures resulting from projective symmetry algebras, including the shift of high-symmetry momenta, an enforced nontrivial Zak phase, and a spinless eight-fold nodal point. Our work offers a theoretical foundation for the field of artificial crystals and opens the door to a wealth of topological states and phenomena beyond the existing paradigms.
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19
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Meng Y, Lin S, Shi BJ, Wei B, Yang L, Yan B, Zhu Z, Xi X, Wang Y, Ge Y, Yuan SQ, Chen J, Liu GG, Sun HX, Chen H, Yang Y, Gao Z. Spinful Topological Phases in Acoustic Crystals with Projective PT Symmetry. PHYSICAL REVIEW LETTERS 2023; 130:026101. [PMID: 36706409 DOI: 10.1103/physrevlett.130.026101] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 12/09/2022] [Indexed: 06/18/2023]
Abstract
For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological phases. However, only recently has it been realized theoretically that in the presence of gauge symmetry, the algebraic structure of symmetries can be projectively represented, which possibly enables the switch between spinless and spinful topological phases. Here, we report the experimental demonstration of this idea by realizing spinful topological phases in "spinless" acoustic crystals with projective space-time inversion symmetry. In particular, we realize a one-dimensional topologically gapped phase characterized by a 2Z winding number, which features double-degenerate bands in the entire Brillouin zone and two pairs of degenerate topological boundary modes. Our Letter thus overcomes a fundamental constraint on topological phases by spin classes.
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Affiliation(s)
- Yan Meng
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Shuxin Lin
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bin-Jie Shi
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Bin Wei
- SKLSM, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
- Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Linyun Yang
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bei Yan
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhenxiao Zhu
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiang Xi
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yin Wang
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yong Ge
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Shou-Qi Yuan
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Jingming Chen
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Gui-Geng Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Hong-Xiang Sun
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
- State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China; International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining 314400, China; Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua 321099, China; Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Zhen Gao
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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20
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Weiner M, Ni X, Alù A, Khanikaev AB. Synthetic Pseudo-Spin-Hall effect in acoustic metamaterials. Nat Commun 2022; 13:6332. [PMID: 36284095 PMCID: PMC9596417 DOI: 10.1038/s41467-022-34072-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 10/13/2022] [Indexed: 11/10/2022] Open
Abstract
While vector fields naturally offer additional degrees of freedom for emulating spin, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. First, we show that evanescent sound waves in perforated films possess transverse angular momentum locked to their propagation direction which enables their directional excitation. Second, we demonstrate that lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum, enabling control of the propagation of modes both in the bulk and along the edges. Our results open a new degree of control of radiation and propagation of acoustic waves thus offering new design approaches for acoustic devices. Controlling emission and propagation of acoustic waves offers new design opportunities for acoustic devices. Here the authors demonstrate such controls thanks to the emergence of a synthetic pseudo-spin in two-dimensional acoustic metamaterial.
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Affiliation(s)
- Matthew Weiner
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, New York, NY, USA.,Physics Program, Graduate Center of the City University of New York, New York, NY, USA.,Department of Physics, City College of New York, New York, NY, USA.,Nokia Bell Labs, New Providence, NJ, USA
| | - Xiang Ni
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, New York, NY, USA.,Physics Program, Graduate Center of the City University of New York, New York, NY, USA.,Advanced Science Research Center, City University of New York, New York, NY, USA
| | - Andrea Alù
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, New York, NY, USA.,Physics Program, Graduate Center of the City University of New York, New York, NY, USA.,Advanced Science Research Center, City University of New York, New York, NY, USA
| | - Alexander B Khanikaev
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, New York, NY, USA. .,Physics Program, Graduate Center of the City University of New York, New York, NY, USA. .,Department of Physics, City College of New York, New York, NY, USA.
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21
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Yang L, Wang Y, Meng Y, Zhu Z, Xi X, Yan B, Lin S, Chen J, Shi BJ, Ge Y, Yuan SQ, Chen H, Sun HX, Liu GG, Yang Y, Gao Z. Observation of Dirac Hierarchy in Three-Dimensional Acoustic Topological Insulators. PHYSICAL REVIEW LETTERS 2022; 129:125502. [PMID: 36179186 DOI: 10.1103/physrevlett.129.125502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 08/24/2022] [Indexed: 06/16/2023]
Abstract
Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional topological corner states in a third-order 3D TI. Our Letter not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.
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Affiliation(s)
- Linyun Yang
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yin Wang
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yan Meng
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhenxiao Zhu
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiang Xi
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bei Yan
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Shuxin Lin
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jingming Chen
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bin-Jie Shi
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yong Ge
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Shou-Qi Yuan
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
- ZJU-Hangzhou Global Science and Technology Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices and Smart Systems of Zhejiang, ZJU-UIUC Institute, Zhejiang University, Hangzhou 310027, China
| | - Hong-Xiang Sun
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
- State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Gui-Geng Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
- ZJU-Hangzhou Global Science and Technology Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices and Smart Systems of Zhejiang, ZJU-UIUC Institute, Zhejiang University, Hangzhou 310027, China
| | - Zhen Gao
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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22
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Meng F, Lin Z, Li W, Yan P, Zheng Y, Li X, Jiang J, Jia B, Huang X. Observation of Emergent Dirac Physics at the Surfaces of Acoustic Higher-Order Topological Insulators. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:2201568. [PMID: 36035068 PMCID: PMC9404400 DOI: 10.1002/advs.202201568] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Revised: 04/29/2022] [Indexed: 05/19/2023]
Abstract
Using 3D sonic crystals as acoustic higher-order topological insulators (HOTIs), 2D surface states described by spin-1 Dirac equations at the interfaces between the two sonic crystals with distinct topology but the same crystalline symmetry are discovered. It is found that the Dirac mass can be tuned by the geometry of the two sonic crystals. The sign reversal of the Dirac mass reveals a surface topological transition where the surface states exhibit zero refractive index behavior. When the surface states are gapped, 1D hinge states emerge due to the topology of the gapped surface states. The zero refractive index behavior and the emergent topological hinge states are confirmed experimentally. This study reveals a multidimensional Wannier orbital control that leads to extraordinary properties of surface states and unveils an interesting topological mechanism for the control of surface waves.
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Affiliation(s)
- Fei Meng
- Hubei Key Laboratory of Roadway Bridge and Structure EngineeringWuhan University of TechnologyWuhanHubei430070P. R. China
- Centre of Translational AtomaterialsFaculty of ScienceEngineering and TechnologySwinburne University of TechnologyHawthornVIC3122Australia
| | - Zhi‐Kang Lin
- School of Physical Science and Technologyand Collaborative Innovation Center of Suzhou Nano Science and TechnologySoochow UniversitySuzhou215006P. R. China
| | - Weibai Li
- Centre of Translational AtomaterialsFaculty of ScienceEngineering and TechnologySwinburne University of TechnologyHawthornVIC3122Australia
| | - Peiguang Yan
- Key Laboratory of Optoelectronic Devices and SystemsCollege of Physics and Optoelectronic EngineeringShenzhen UniversityShenzhen518060P. R. China
| | - Yun Zheng
- State Key Laboratory of Geomechanics and Geotechnical EngineeringInstitute of Rock and Soil MechanicsChinese Academy of SciencesWuhan430071P. R. China
| | - Xinping Li
- Hubei Key Laboratory of Roadway Bridge and Structure EngineeringWuhan University of TechnologyWuhanHubei430070P. R. China
| | - Jian‐Hua Jiang
- School of Physical Science and Technologyand Collaborative Innovation Center of Suzhou Nano Science and TechnologySoochow UniversitySuzhou215006P. R. China
| | - Baohua Jia
- Centre of Translational AtomaterialsFaculty of ScienceEngineering and TechnologySwinburne University of TechnologyHawthornVIC3122Australia
| | - Xiaodong Huang
- Centre of Translational AtomaterialsFaculty of ScienceEngineering and TechnologySwinburne University of TechnologyHawthornVIC3122Australia
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Du J, Li T, Fan X, Zhang Q, Qiu C. Acoustic Realization of Surface-Obstructed Topological Insulators. PHYSICAL REVIEW LETTERS 2022; 128:224301. [PMID: 35714247 DOI: 10.1103/physrevlett.128.224301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without bulk closure and exhibits as an obstruction of higher-dimensional boundary states. Here, we report the first experimental realization of three-dimensional surface-obstructed topological insulators with using acoustic crystals. Our acoustic measurements demonstrate unambiguously the emergence of one-dimensional topological hinge states in the middle of the bulk and surface band gaps, as a direct manifestation of the higher-order band topology. Together with comparative measurements for the trivial and phase-transition-point insulators, our experimental data conclusively evidence the unique bulk-boundary physics for the surface-obstructed band topology. That is, the topological phase transition is determined by the closure of the surface gap, rather than by closing the bulk gap. Our study might spur on new activities to deepen the understanding of such elusive topological phases.
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Affiliation(s)
- Juan Du
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Tianzi Li
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xiying Fan
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Qicheng Zhang
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
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Brillouin Klein bottle from artificial gauge fields. Nat Commun 2022; 13:2215. [PMID: 35468905 PMCID: PMC9038716 DOI: 10.1038/s41467-022-29953-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 04/10/2022] [Indexed: 11/23/2022] Open
Abstract
A Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under \documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb{Z}}}_{2}$$\end{document}Z2 gauge fields, i.e., hopping amplitudes with phases ±1, the fundamental domain of momentum space can assume the topology of a Klein bottle. This drastic change of the Brillouin zone theory is due to the projective symmetry algebra enforced by the gauge field. Remarkably, the non-orientability of the Brillouin Klein bottle corresponds to the topological classification by a \documentclass[12pt]{minimal}
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\begin{document}$${{\mathbb{Z}}}_{2}$$\end{document}Z2 invariant, in contrast to the Chern number valued in \documentclass[12pt]{minimal}
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\begin{document}$${\mathbb{Z}}$$\end{document}Z for the usual Brillouin torus. The result is a novel Klein bottle insulator featuring topological modes at two edges related by a nonlocal twist, radically distinct from all previous topological insulators. Our prediction can be readily achieved in various artificial crystals, and the discovery opens a new direction to explore topological physics by gauge-field-modified fundamental structures of physics. Topological states are exploited based on crystalline symmetry, but under artificial gauge fields, symmetries may satisfy projective algebras, which remains less studied. Here, the authors reveal that projective symmetry algebra leads to momentum-space nonsymmorphic symmetry, resulting in new topological states over a momentum-space Klein bottle.
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25
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Yamada SS, Li T, Lin M, Peterson CW, Hughes TL, Bahl G. Bound states at partial dislocation defects in multipole higher-order topological insulators. Nat Commun 2022; 13:2035. [PMID: 35440648 PMCID: PMC9018851 DOI: 10.1038/s41467-022-29785-5] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 03/28/2022] [Indexed: 11/08/2022] Open
Abstract
The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of boundary states in the insulating gap is not always necessary since they can be hidden in the bulk energy bands, obscured by boundary artifacts of non-topological origin, or, in the case of higher-order topology, they can be gapped altogether. Recently, exotic defects of translation symmetry called partial dislocations have been proposed to trap gapless topological modes in some materials. Here we present experimental observations of partial-dislocation-induced topological modes in 2D and 3D insulators. We particularly focus on multipole higher-order topological insulators built from circuit-based resonator arrays, since crucially they are not sensitive to full dislocation defects, and they have a sublattice structure allowing for stacking faults and partial dislocations.
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Affiliation(s)
- Sasha S Yamada
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Tianhe Li
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Mao Lin
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Christopher W Peterson
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Taylor L Hughes
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - Gaurav Bahl
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
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26
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Benalcazar WA, Cerjan A. Chiral-Symmetric Higher-Order Topological Phases of Matter. PHYSICAL REVIEW LETTERS 2022; 128:127601. [PMID: 35394298 DOI: 10.1103/physrevlett.128.127601] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 02/17/2022] [Indexed: 06/14/2023]
Abstract
We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by "multipole chiral numbers," bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order topological phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.
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Affiliation(s)
- Wladimir A Benalcazar
- Department of Physics, Princeton University, Princeton, New Jersey 08542, USA
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Alexander Cerjan
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
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27
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Li T, Du J, Zhang Q, Li Y, Fan X, Zhang F, Qiu C. Acoustic Möbius Insulators from Projective Symmetry. PHYSICAL REVIEW LETTERS 2022; 128:116803. [PMID: 35362999 DOI: 10.1103/physrevlett.128.116803] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 01/25/2022] [Indexed: 06/14/2023]
Abstract
In the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here, we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Möbius-twisted topological phases. Experimentally, we realize two Möbius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Möbius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4π periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.
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Affiliation(s)
- Tianzi Li
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Juan Du
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Qicheng Zhang
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Yitong Li
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xiying Fan
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
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28
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Xue H, Wang Z, Huang YX, Cheng Z, Yu L, Foo YX, Zhao YX, Yang SA, Zhang B. Projectively Enriched Symmetry and Topology in Acoustic Crystals. PHYSICAL REVIEW LETTERS 2022; 128:116802. [PMID: 35363008 DOI: 10.1103/physrevlett.128.116802] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2021] [Accepted: 01/27/2022] [Indexed: 06/14/2023]
Abstract
Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a Z_{2} gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator, and graphenelike semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology and opens the door to a vast unexplored land of topological states by projective symmetries.
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Affiliation(s)
- Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Zihao Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yue-Xin Huang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Zheyu Cheng
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Letian Yu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Y X Foo
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
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29
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Abstract
Topological mechanics is rapidly emerging as an attractive field of research where mechanical waveguides can be designed and controlled via topological methods. With the development of topological phases of matter, recent advances have shown that topological states have been realized in the elastic media exploiting analogue quantum Hall effect, analogue quantum spin Hall effect, analogue quantum valley Hall effect, higher-order topological physics, topological pump, topological lattice defects and so on. This review aims to introduce the experimental and theoretical achievements with defect-immune protected elastic waves in mechanical systems based on the abovementioned methods, respectively. From these discussions, we predict the possible perspective of topological mechanics.
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30
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Wang W, Chen ZG, Ma G. Synthetic Three-Dimensional Z×Z_{2} Topological Insulator in an Elastic Metacrystal. PHYSICAL REVIEW LETTERS 2021; 127:214302. [PMID: 34860114 DOI: 10.1103/physrevlett.127.214302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2021] [Revised: 07/21/2021] [Accepted: 10/12/2021] [Indexed: 06/13/2023]
Abstract
We report a three-dimensional (3D) topological insulator (TI) formed by stacking identical layers of Chern insulators in a hybrid real-synthetic space. By introducing staggered interlayer hopping that respects mirror symmetry, the bulk bands possess an additional Z_{2} topological invariant along the stacking dimension, which, together with the nontrivial Chern numbers, endows the system with a Z×Z_{2} topology. A 4-tuple topological index characterizes the system's bulk bands. Consequently, two distinct types of topological surface modes (TSMs) are found localized on different surfaces. Type-I TSMs are gapless and are protected by Chern numbers, whereas type-II gapped TSMs are protected by Z_{2} bulk polarization in the stacking direction. Remarkably, each type-II TSM band is also topologically nontrivial, giving rise to second-order topological hinge modes (THMs). Both types of TSMs and the THMs are experimentally observed in an elastic metacrystal.
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Affiliation(s)
- Wei Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Ze-Guo Chen
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | - Guancong Ma
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
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31
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Xue H, Jia D, Ge Y, Guan YJ, Wang Q, Yuan SQ, Sun HX, Chong YD, Zhang B. Observation of Dislocation-Induced Topological Modes in a Three-Dimensional Acoustic Topological Insulator. PHYSICAL REVIEW LETTERS 2021; 127:214301. [PMID: 34860093 DOI: 10.1103/physrevlett.127.214301] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2021] [Accepted: 10/20/2021] [Indexed: 06/13/2023]
Abstract
The interplay between real-space topological lattice defects and the reciprocal-space topology of energy bands can give rise to novel phenomena, such as one-dimensional topological modes bound to screw dislocations in three-dimensional topological insulators. We obtain direct experimental observations of dislocation-induced helical modes in an acoustic analog of a weak three-dimensional topological insulator. The spatial distribution of the helical modes is found through spin-resolved field mapping, and verified numerically by tight-binding and finite-element calculations. These one-dimensional helical channels can serve as robust waveguides in three-dimensional media. Our experiment paves the way to studying novel physical modes and functionalities enabled by topological lattice defects in three-dimensional classical topological materials.
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Affiliation(s)
- Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Ding Jia
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yong Ge
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yi-Jun Guan
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Qiang Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Shou-Qi Yuan
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Hong-Xiang Sun
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Y D Chong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
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32
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Zhao PL, Qiang XB, Lu HZ, Xie XC. Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator. PHYSICAL REVIEW LETTERS 2021; 127:176601. [PMID: 34739297 DOI: 10.1103/physrevlett.127.176601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 09/16/2021] [Indexed: 06/13/2023]
Abstract
Topological insulators (TIs) are an exciting discovery because of their robustness against disorder and interactions. Recently, second-order TIs have been attracting increasing attention, because they host topologically protected 1D hinge states in 3D or 0D corner states in 2D. A significantly critical issue is whether the second-order TIs also survive interactions, but it is still unexplored. We study the effects of weak Coulomb interactions on a 3D second-order TI, with the help of renormalization-group calculations. We find that the 3D second-order TIs are always unstable, suffering from two types of topological phase transitions. One is from second-order TI to TI, the other is to normal insulator. The first type is accompanied by emergent time-reversal and inversion symmetries and has a dynamical critical exponent κ=1. The second type does not have the emergent symmetries but has nonuniversal dynamical critical exponents κ<1. Our results may inspire more inspections on the stability of higher-order topological states of matter and related novel quantum criticalities.
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Affiliation(s)
- Peng-Lu Zhao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Xiao-Bin Qiang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - Hai-Zhou Lu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
- Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China
| | - X C Xie
- International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
- CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences, West Building 3, No. 10, Xibeiwang East Road, Haidian District, Beijing 100193, China
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33
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Qiu H, Xiao M, Zhang F, Qiu C. Higher-Order Dirac Sonic Crystals. PHYSICAL REVIEW LETTERS 2021; 127:146601. [PMID: 34652168 DOI: 10.1103/physrevlett.127.146601] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 09/10/2021] [Indexed: 06/13/2023]
Abstract
Discovering new topological phases of matter is a major theme in fundamental physics and materials science. Dirac semimetal provides an exceptional platform for exploring topological phase transitions under symmetry breaking. Recent theoretical studies have revealed that a three-dimensional Dirac semimetal can harbor fascinating hinge states, a higher-order topological manifestation not known before. However, its realization in experiment is yet to be achieved. In this Letter, we propose a minimum model to construct a spinless higher-order Dirac semimetal protected by C_{6v} symmetry. By breaking different symmetries, this parent phase transitions into a variety of novel topological phases including higher-order topological insulator, higher-order Weyl semimetal, and higher-order nodal-ring semimetal. Furthermore, for the first time, we experimentally realize this unprecedented higher-order topological phase in a sonic crystal and present an unambiguous observation of the desired hinge states via momentum-space spectroscopy and real-space visualization. Our findings may offer new opportunities to manipulate classical waves such as sound and light.
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Affiliation(s)
- Huahui Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Meng Xiao
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Fan Zhang
- Department of Physics, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Chunyin Qiu
- Key Laboratory of Artificial Micro- and Nano-Structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
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34
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Xu C, Chen ZG, Zhang G, Ma G, Wu Y. Multi-dimensional wave steering with higher-order topological phononic crystal. Sci Bull (Beijing) 2021; 66:1740-1745. [PMID: 36654381 DOI: 10.1016/j.scib.2021.05.013] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Revised: 04/18/2021] [Accepted: 05/13/2021] [Indexed: 01/20/2023]
Abstract
The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the lattice. The multitude of topological states brings diverse possibilities of wave manipulations. Through judicious engineering of the boundary modes, we experimentally demonstrate two functionalities at different dimensions: 2D negative refraction of sound wave enabled by a first-order topological surface state with negative dispersion, and a 3D acoustic interferometer leveraging on second-order topological hinge states. Our work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.
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Affiliation(s)
- Changqing Xu
- Division of Computer, Electrical and Mathematical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
| | - Ze-Guo Chen
- Department of Physics, Hong Kong Baptist University, Hong Kong, China
| | - Guanqing Zhang
- Department of Physics, Hong Kong Baptist University, Hong Kong, China
| | - Guancong Ma
- Department of Physics, Hong Kong Baptist University, Hong Kong, China.
| | - Ying Wu
- Division of Computer, Electrical and Mathematical Science and Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.
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35
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Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries. Proc Natl Acad Sci U S A 2021; 118:2100691118. [PMID: 34413190 PMCID: PMC8403875 DOI: 10.1073/pnas.2100691118] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA-the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.
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Shao LB, Liu Q, Xiao R, Yang SA, Zhao YX. Gauge-Field Extended k·p Method and Novel Topological Phases. PHYSICAL REVIEW LETTERS 2021; 127:076401. [PMID: 34459642 DOI: 10.1103/physrevlett.127.076401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 07/01/2021] [Indexed: 06/13/2023]
Abstract
Although topological artificial systems, like acoustic and photonic crystals and cold atoms in optical lattices were initially motivated by simulating topological phases of electronic systems, they have their own unique features such as the spinless time-reversal symmetry and tunable Z_{2} gauge fields. Hence, it is fundamentally important to explore new topological phases based on these features. Here, we point out that the Z_{2} gauge field leads to two fundamental modifications of the conventional k·p method: (i) The little co-group must include the translations with nontrivial algebraic relations. (ii) The algebraic relations of the little co-group are projectively represented. These give rise to higher-dimensional irreducible representations and therefore highly degenerate Fermi points. Breaking the primitive translations can transform the Fermi points to interesting topological phases. We demonstrate our theory by two models: a rectangular π-flux model exhibiting graphenelike semimetal phases, and a graphite model with interlayer π flux that realizes the real second-order nodal-line semimetal phase with hinge helical modes. Their physical realizations with a general bright-dark mechanism are discussed. Our finding opens a new direction to explore novel topological phases unique to crystalline systems with gauge fields and establishes the approach to analyze these phases.
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Affiliation(s)
- L B Shao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Q Liu
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - R Xiao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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Al Ba’ba’a H, Zhu X, Wang Q. Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2020.0820] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Mechanical topological insulators have enabled a myriad of unprecedented characteristics that are otherwise not conceivable in traditional periodic structures. While rich in dynamics, new developments in the domain of mechanical topological systems are hindered by their inherent inability to exhibit negative elastic or inertial couplings owing to the inevitable loss of dynamical stability. The aim of this paper is, therefore, to remedy this challenge by introducing a class of architected inertial metamaterials (AIMs) as a platform for designing mechanical lattices with novel topological and dispersion traits. We show that carefully coupling elastically supported masses via moment-free rigid linkages invokes a dynamically stable negative inertial coupling, which is essential for topological classes in need of such negative interconnection. The potential of the proposed AIMs is demonstrated via three examples: (i) a mechanical analogue of Majorana edge states, (ii) a square diatomic AIM that can sustain the quantum valley Hall effect (classically arising in hexagonal lattices), and (iii) a square tetratomic AIM with topological corner modes. We envision that the presented framework will pave the way for a plethora of robust topological mechanical systems.
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Affiliation(s)
- H. Al Ba’ba’a
- Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089, USA
| | - X. Zhu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, People’s Republic of China
| | - Q. Wang
- Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA 90089, USA
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Ciaburro G, Iannace G. Modeling acoustic metamaterials based on reused buttons using data fitting with neural network. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2021; 150:51. [PMID: 34340477 DOI: 10.1121/10.0005479] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Accepted: 06/07/2021] [Indexed: 06/13/2023]
Abstract
Metamaterials are designed by arranging artificial structural elements according to periodic geometries to obtain advantageous and unusual properties when they are hit by waves. Initially designed to interact with electromagnetic waves, their use naturally extended to sound waves, proving to be particularly useful for the construction of containment and soundproofing systems in buildings. In this work, a new metamaterial has been developed with the use of a polyvinyl chloride membrane on which buttons have been glued. Two types of buttons were used, with different weights, placing them on the membrane according to a radial geometry. Each sample of metamaterial was subjected to sound absorption coefficient measurements using the impedance tube. Measurements were made using the samples by setting three configurations, creating a cavity with different thicknesses. The results of the measurements were subsequently used as input for training a simulation model based on artificial neural networks. The model showed an excellent generalization capacity, returning estimates of the acoustic absorption coefficient of the metamaterial very similar to the measured value. Subsequently, the model was used to perform a sensitivity analysis to evaluate the contribution of the various input variables on the returned output.
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Affiliation(s)
- Giuseppe Ciaburro
- Università della Campania "Luigi Vanvitelli," Via San Lorenzo, 81031 Aversa (Ce), Italy
| | - Gino Iannace
- Università della Campania "Luigi Vanvitelli," Via San Lorenzo, 81031 Aversa (Ce), Italy
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Niu J, Yan T, Zhou Y, Tao Z, Li X, Liu W, Zhang L, Jia H, Liu S, Yan Z, Chen Y, Yu D. Simulation of higher-order topological phases and related topological phase transitions in a superconducting qubit. Sci Bull (Beijing) 2021; 66:1168-1175. [PMID: 36654354 DOI: 10.1016/j.scib.2021.02.035] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Revised: 01/08/2021] [Accepted: 02/23/2021] [Indexed: 01/20/2023]
Abstract
Higher-order topological phases give rise to new bulk and boundary physics, as well as new classes of topological phase transitions. While the realization of higher-order topological phases has been confirmed in many platforms by detecting the existence of gapless boundary modes, a direct determination of the higher-order topology and related topological phase transitions through the bulk in experiments has still been lacking. To bridge the gap, in this work we carry out the simulation of a two-dimensional second-order topological phase in a superconducting qubit. Owing to the great flexibility and controllability of the quantum simulator, we observe the realization of higher-order topology directly through the measurement of the pseudo-spin texture in momentum space of the bulk for the first time, in sharp contrast to previous experiments based on the detection of gapless boundary modes in real space. Also through the measurement of the evolution of pseudo-spin texture with parameters, we further observe novel topological phase transitions from the second-order topological phase to the trivial phase, as well as to the first-order topological phase with nonzero Chern number. Our work sheds new light on the study of higher-order topological phases and topological phase transitions.
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Affiliation(s)
- Jingjing Niu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Tongxing Yan
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yuxuan Zhou
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Ziyu Tao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiaole Li
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Weiyang Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Libo Zhang
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Hao Jia
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Song Liu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| | - Zhongbo Yan
- School of Physics, Sun Yat-sen University, Guangzhou 510275, China.
| | - Yuanzhen Chen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China.
| | - Dapeng Yu
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China; Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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Wei Q, Zhang X, Deng W, Lu J, Huang X, Yan M, Chen G, Liu Z, Jia S. Higher-order topological semimetal in acoustic crystals. NATURE MATERIALS 2021; 20:812-817. [PMID: 33589800 DOI: 10.1038/s41563-021-00933-4] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 01/17/2021] [Indexed: 06/12/2023]
Abstract
The notion of higher-order topological insulators has endowed materials with topological states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological insulator can host topologically protected 1D hinge states, referred to as the second-order topological insulator, or 0D corner states, referred to as the third-order topological insulator. Similarly, a 3D higher-order topological semimetal can be envisaged if it hosts states on the 1D hinges. Here we report the realization of a second-order topological Weyl semimetal in a 3D-printed acoustic crystal, which possesses Weyl points in 3D momentum space, 2D Fermi arc states on surfaces and 1D gapless states on hinges. Like the arc surface states, the hinge states also connect the projections of the Weyl points. Our experimental results evidence the existence of the higher-order topological semimetal, which may pave the way towards innovative acoustic devices.
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Affiliation(s)
- Qiang Wei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China
| | - Xuewei Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China
| | - Weiyin Deng
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
| | - Jiuyang Lu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
| | - Xueqin Huang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
| | - Mou Yan
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
| | - Gang Chen
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, China.
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China.
- Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan, China.
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nanostructures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan, China.
- Institute for Advanced Studies, Wuhan University, Wuhan, China.
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China
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41
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Luo L, Wang HX, Lin ZK, Jiang B, Wu Y, Li F, Jiang JH. Observation of a phononic higher-order Weyl semimetal. NATURE MATERIALS 2021; 20:794-799. [PMID: 33859382 DOI: 10.1038/s41563-021-00985-6] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 03/15/2021] [Indexed: 06/12/2023]
Abstract
Weyl semimetals (WSMs)1 exhibit phenomena such as Fermi arc surface states, pseudo-gauge fields and quantum anomalies that arise from topological band degeneracy in crystalline solids for electrons1 and metamaterials for photons2 and phonons3. Here we report a higher-order Weyl semimetal (HOWSM) in a phononic system that exhibits topologically protected boundary states in multiple dimensions. We created the physical realization of the HOWSM in a chiral phononic crystal with uniaxial screw symmetry. Using acoustic pump-probe spectroscopies, we observed coexisting chiral Fermi arc states on two-dimensional surfaces and dispersive hinge arc states on one-dimensional hinge boundaries. These topological boundary states link the projections of the Weyl points (WPs) in different dimensions and directions, and hence demonstrate the higher-order topological physics4-8 in WSMs. Our study further establishes the fundamental connection between higher-order topology and Weyl physics in crystalline materials and should stimulate further work on other potential materials, such as higher-order topological nodal-line semimetals.
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Affiliation(s)
- Li Luo
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
| | - Hai-Xiao Wang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China
- School of Physical Science and Technology, Guangxi Normal University, Guilin, China
| | - Zhi-Kang Lin
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China
| | - Bin Jiang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China
| | - Ying Wu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China
| | - Feng Li
- School of Physics, Beijing Institute of Technology, Beijing, China.
| | - Jian-Hua Jiang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China.
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42
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Zhao YX, Chen C, Sheng XL, Yang SA. Switching Spinless and Spinful Topological Phases with Projective PT Symmetry. PHYSICAL REVIEW LETTERS 2021; 126:196402. [PMID: 34047612 DOI: 10.1103/physrevlett.126.196402] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Revised: 01/21/2021] [Accepted: 04/07/2021] [Indexed: 06/12/2023]
Abstract
A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry PT satisfies (PT)^{2}=±1 for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamental classes via Z_{2} projective representations. For PT symmetry, this occurs when P inverses the gauge transformation needed to recover the original Z_{2} gauge connections under P. As a result, we can achieve topological phases originally unique for spinful systems in a spinless system, and vice versa. We explicitly demonstrate the claimed mechanism with several concrete models, such as Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems, and real topological phases in spinful systems. Possible experimental realization of these models is discussed. Our work breaks a fundamental limitation on topological phases and opens an unprecedented possibility to realize intriguing topological phases in previously impossible systems.
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Affiliation(s)
- Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Cong Chen
- School of Physics, and Key Laboratory of Micro-nano Measurement-Manipulation and Physics, Beihang University, Beijing 100191, China
| | - Xian-Lei Sheng
- School of Physics, and Key Laboratory of Micro-nano Measurement-Manipulation and Physics, Beihang University, Beijing 100191, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
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Gao H, Xue H, Gu Z, Liu T, Zhu J, Zhang B. Non-Hermitian route to higher-order topology in an acoustic crystal. Nat Commun 2021; 12:1888. [PMID: 33767167 PMCID: PMC7994416 DOI: 10.1038/s41467-021-22223-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 02/22/2021] [Indexed: 11/12/2022] Open
Abstract
Topological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.
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Affiliation(s)
- He Gao
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China
| | - Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
| | - Zhongming Gu
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China
| | - Tuo Liu
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China
| | - Jie Zhu
- Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China.
- The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, China.
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, Singapore.
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Cerjan A, Jürgensen M, Benalcazar WA, Mukherjee S, Rechtsman MC. Observation of a Higher-Order Topological Bound State in the Continuum. PHYSICAL REVIEW LETTERS 2020; 125:213901. [PMID: 33274969 DOI: 10.1103/physrevlett.125.213901] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2020] [Accepted: 10/13/2020] [Indexed: 06/12/2023]
Abstract
Higher-order topological insulators are a recently discovered class of materials that can possess zero-dimensional localized states regardless of the dimension of the system. Here, we experimentally demonstrate that the topological corner-localized modes of higher-order topological systems can be symmetry-protected bound states in the continuum; these states do not hybridize with the surrounding bulk states of the lattice even in the absence of a bulk band gap. This observation expands the scope of bulk-boundary correspondence by showing that protected boundary-localized states can be found within topological bands, in addition to being found in between them.
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Affiliation(s)
- Alexander Cerjan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Marius Jürgensen
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Wladimir A Benalcazar
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Sebabrata Mukherjee
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Mikael C Rechtsman
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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