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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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2
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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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3
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Gao F, Peng YG, Xiang X, Ni X, Zheng C, Yves S, Zhu XF, Alù A. Acoustic Higher-Order Topological Insulators Induced by Orbital-Interactions. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024:e2312421. [PMID: 38386009 DOI: 10.1002/adma.202312421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Revised: 01/31/2024] [Indexed: 02/23/2024]
Abstract
The discovery of higher-order topological insulator metamaterials, in analogy with their condensed-matter counterparts, has enabled various breakthroughs in photonics, mechanics, and acoustics. A common way of inducing higher-order topological wave phenomena is through pseudo-spins, which mimic the electron spins as a symmetry-breaking degree of freedom. Here, this work exploits degenerate orbitals in acoustic resonant cavities to demonstrate versatile, orbital-selective, higher-order topological corner states. Type-II corner states are theoretically investigated and experimentally demonstrated based on tailored orbital interactions, without the need for long-range hoppings that has so far served as a key ingredient for Type-II corner states in single-orbital systems. Due to the orthogonal nature of the degenerate p orbitals, this work also introduces a universal strategy to realize orbital-dependent edge modes, featuring high-Q edge states identified in bulk bands. These findings provide an understanding of the interplay between acoustic orbitals and topology, shedding light on orbital-related topological wave physics, as well as its applications for acoustic sensing and trapping.
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Affiliation(s)
- Feng Gao
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Yu-Gui Peng
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Xiao Xiang
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Xiang Ni
- School of Physics, Central South University, Changsha, 410083, China
| | - Chen Zheng
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, 430074, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
| | - Xue-Feng Zhu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, 430074, 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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4
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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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5
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Zhang JH, Mei F, Xiao L, Jia S. Dynamical Detection of Topological Spectral Density. PHYSICAL REVIEW LETTERS 2024; 132:036603. [PMID: 38307045 DOI: 10.1103/physrevlett.132.036603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Accepted: 12/18/2023] [Indexed: 02/04/2024]
Abstract
Local density of states (LDOS) is emerging as powerful means of exploring classical-wave topological phases. However, the current LDOS detection method remains rare and merely works for static situations. Here, we introduce a generic dynamical method to detect both the static and Floquet LDOS, based on an elegant connection between dynamics of chiral density and local spectral densities. Moreover, we find that the Floquet LDOS allows to measure out Floquet quasienergy spectra and identify topological π modes. As an example, we demonstrate that both the static and Floquet higher-order topological phase can be universally identified via LDOS detection, regardless of whether the topological corner modes are in energy gaps, bands, or continuous energy spectra without band gaps. Our study opens a new avenue utilizing dynamics to detect topological spectral densities and provides a universal approach of identifying static and Floquet topological phases.
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Affiliation(s)
- Jia-Hui Zhang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Feng Mei
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Liantuan Xiao
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Suotang Jia
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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6
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Ghosh AK, Nag T, Saha A. Generation of higher-order topological insulators using periodic driving. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:093001. [PMID: 37983922 DOI: 10.1088/1361-648x/ad0e2d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Accepted: 11/20/2023] [Indexed: 11/22/2023]
Abstract
Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.
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Affiliation(s)
- Arnob Kumar Ghosh
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
- Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
| | - Tanay Nag
- Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
- Department of Physics, BITS Pilani-Hyderabad Campus, Telangana 500078, India
| | - Arijit Saha
- Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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7
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Li X, Rui G, He J, Gu B. Degeneration of topological corner, hinge, and surface states in three-dimensional photonic crystals. OPTICS LETTERS 2023; 48:5332-5335. [PMID: 37831860 DOI: 10.1364/ol.500164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 09/15/2023] [Indexed: 10/15/2023]
Abstract
The third-order topological insulators based on three-dimensional (3D) photonic crystals (PCs) have hardly been achieved because the nontrivial bandgap in 3D PCs is difficult to form. In this Letter, we elaborately construct 3D Su-Schrieffer-Heeger lattice in which the periodic modulation of refractive index is uniform in three axis directions. The high-order topological PCs are characterized by the nontrivial bulk polarizations and the mirror eigenvalues. Such a structure can achieve topological 1-codimensional surface states, 2-codimensional hinge states, and 3-codimensional corner states. More importantly, it is found for the first time, to the best of our knowledge, that the topological states exhibit a degeneration behavior, i. e., the corner, and hinge state, or corner and surface states coexist at nearly the same frequency, but maintain their own mode properties. The multiple topological states in 3D PCs as well as the degeneration of topological states will open a new window for the study of topological photonics.
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8
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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: 4] [Impact Index Per Article: 4.0] [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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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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10
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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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11
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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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12
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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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13
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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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14
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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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15
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Mu H, Liu B, Hu T, Wang Z. Kekulé Lattice in Graphdiyne: Coexistence of Phononic and Electronic Second-Order Topological Insulator. NANO LETTERS 2022; 22:1122-1128. [PMID: 35044189 DOI: 10.1021/acs.nanolett.1c04239] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Topological physics has been extensively studied in different kinds of bosonic and Fermionic systems, but the coexistence of topological phonons and electrons in one single material has seldom been reported. Recently, graphdiyne has been proposed as a two-dimensional (2D) electronic second-order topological insulator (SOTI). In this work, we found that graphdiyne is equivalent to Kekulé lattice, also realizing a 2D phononic SOTI in both out-of-plane and in-plane modes. Depending on edge terminations, the characterized topological corner states can be either inside or outside the bulk gap and are tunable by the local corner potential. Most remarkably, a unique selectivity of space and symmetry is revealed in the electron-phonon coupling between the localized phononic and electronic topological corner states. Our results not only demonstrate the phononic higher-order band topology in a real carbon material but also provide an opportunity to investigate the interplay between phononic and electronic higher-order topological states.
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Affiliation(s)
- Haimen Mu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Bing Liu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Tianyi Hu
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhengfei Wang
- Hefei National Laboratory for Physical Sciences at the Microscale, CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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16
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Topological dislocation modes in three-dimensional acoustic topological insulators. Nat Commun 2022; 13:508. [PMID: 35082291 PMCID: PMC8791950 DOI: 10.1038/s41467-022-28182-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 01/13/2022] [Indexed: 11/08/2022] Open
Abstract
Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences have been presented for this intriguing topological observable in solid-state systems, owing to the huge challenges in creating controllable dislocations and conclusively identifying topological signals. Here, using a three-dimensional acoustic weak topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented control over wave propagations.
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17
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Abstract
Recently, Prof. Jianhua Jiang from Soochow University of China accepted an interview from Light: Science & Applications. Prof. Jiang works on topological photonics, topological phononics, and nonequilibrium physics. On this issue, he discusses the challenges and opportunities in topological photonics, topological phononics, and other topological synthetic systems. He also shares his experiences in cutting-edge research, the education of graduate students, and other challenges faced by junior researchers. Finally, he gives remarks and suggestions for Light: Science & Applications. Light People is a featured column of high-end interviews with outstanding scientists. It is our great honor to invite Prof. Jianhua Jiang, an outstanding young scientist, to showcase his research life and the story behind his success.
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Affiliation(s)
- Ying Zhang
- Light Publishing Group, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 3888 Dong Nan Hu Road, 130033, Changchun, China.
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18
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Geng ZG, Peng YG, Lv H, Xiong Z, Chen Z, Zhu XF. Square-root-like higher-order topological states in three-dimensional sonic crystals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:104001. [PMID: 34874306 DOI: 10.1088/1361-648x/ac3f65] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2021] [Accepted: 12/02/2021] [Indexed: 06/13/2023]
Abstract
The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at theK-Hdirection induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in thezdirection. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.
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Affiliation(s)
- Zhi-Guo Geng
- College of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, People's Republic of China
| | - Yu-Gui Peng
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China
| | - Huanzhao Lv
- School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072, People's Republic of China
| | - Zhan Xiong
- College of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, People's Republic of China
| | - Zhaojiang Chen
- College of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang 321004, People's Republic of China
| | - Xue-Feng Zhu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People's Republic of China
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19
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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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20
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Zheng LY, Christensen J. Dirac Hierarchy in Acoustic Topological Insulators. PHYSICAL REVIEW LETTERS 2021; 127:156401. [PMID: 34678007 DOI: 10.1103/physrevlett.127.156401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Accepted: 09/09/2021] [Indexed: 06/13/2023]
Abstract
Dirac cones are essential features of the electronic band structure of materials like graphene and topological insulators (TIs). Lately, this avenue has found a growing interest in classical wave physics by using engineered artificial lattices. Here, we demonstrate an acoustic 3D honeycomb lattice that features a Dirac hierarchy comprising an eightfold bulk Dirac cone, a 2D fourfold surface state Dirac cone, and a 1D twofold hinge state Dirac cone. The lifting of the Dirac degeneracy in each hierarchy authorizes the 3D lattice to appear as a first-order TI with 2D topological surface states, a second-order TI exhibiting 1D hinge states, and a third-order TI of 0D midgap corner states. Analytically we discuss the topological origin of the surface, hinge, and corner states, which are all characterized by out-of-plane and in-plane winding numbers. Our study offers new routes to control sound and vibration for acoustic steering and guiding, on-chip ultrasonic energy concentration, and filtering to name a few.
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Affiliation(s)
- Li-Yang Zheng
- Department of Physics, Universidad Carlos III de Madrid, ES-28916 Leganès, Madrid, Spain
| | - Johan Christensen
- Department of Physics, Universidad Carlos III de Madrid, ES-28916 Leganès, Madrid, Spain
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21
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Huang H, Chen J, Huo S. Recent advances in topological elastic metamaterials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:503002. [PMID: 34534976 DOI: 10.1088/1361-648x/ac27d8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2021] [Accepted: 09/17/2021] [Indexed: 06/13/2023]
Abstract
Topological elastic metamaterials have emerged as a new frontier in the quest of topological phases in condensed matter physics. Their exotic topological properties open a wealth of promising engineering-oriented applications that are difficult to realize with traditional elastic metamaterials, such as robust and defect insensitive waveguiding, signal sensing, and splitting. In this review, we retrospectively examine the underlying physical concept of topologically ordered states of elastic waves, starting from the one-dimensional example based on the Su-Schrieffer-Heeger model. We then move on to two-dimensional topological metamaterials, discussing elastic analogues of quantum Hall, pseudospin-Hall, valley-Hall phases. Finally, we survey the latest developments in the field including three-dimensional elastic topological phases and higher-order topological insulators. Altogether, this paper provides a comprehensive overview of the flourishing research frontier on topological elastic metamaterials, and highlights prominent future directions in this field.
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Affiliation(s)
- Hongbo Huang
- State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Jiujiu Chen
- State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, People's Republic of China
| | - Shaoyong Huo
- College of Mechanical Engineering, University of South China, Hengyang 421001, People's Republic of China
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22
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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: 4] [Impact Index Per Article: 1.3] [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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23
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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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24
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Zhang X, Tian Y, Jiang JH, Lu MH, Chen YF. Observation of higher-order non-Hermitian skin effect. Nat Commun 2021; 12:5377. [PMID: 34508089 PMCID: PMC8433224 DOI: 10.1038/s41467-021-25716-y] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2021] [Accepted: 08/23/2021] [Indexed: 11/09/2022] Open
Abstract
Beyond the scope of Hermitian physics, non-Hermiticity fundamentally changes the topological band theory, leading to interesting phenomena, e.g., non-Hermitian skin effect, as confirmed in one-dimensional systems. However, in higher dimensions, these effects remain elusive. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional acoustic higher-order topological insulators. We find that non-Hermiticity drives wave localizations toward opposite edges upon different spin polarizations. More interestingly, for finite systems with both edges and corners, the higher-order non-Hermitian skin effect leads to wave localizations toward two opposite corners for all the bulk, edge and corner states in a spin-dependent manner. We further show that such a skin effect enables rich wave manipulation by configuring the non-Hermiticity. Our study reveals the intriguing interplay between higher-order topology and non-Hermiticity, which is further enriched by the pseudospin degree of freedom, unveiling a horizon in the study of non-Hermitian physics.
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Affiliation(s)
- Xiujuan Zhang
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, China
| | - Yuan Tian
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, China
| | - Jian-Hua Jiang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China.
| | - Ming-Hui Lu
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
| | - Yan-Feng Chen
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, China.
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
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25
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Kruk SS, Gao W, Choi DY, Zentgraf T, Zhang S, Kivshar Y. Nonlinear Imaging of Nanoscale Topological Corner States. NANO LETTERS 2021; 21:4592-4597. [PMID: 34008406 DOI: 10.1021/acs.nanolett.1c00449] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are insensitive to certain types of perturbations, thus naturally enhancing robustness of photonic circuitries. Conventionally, the N-dimensional bulk modes correspond to (N - 1)-dimensional boundary states. The higher-order bulk-boundary correspondence relates N-dimensional bulk to boundary states with dimensionality reduced by more than 1. A special interest lies in miniaturization of such higher-order topological states to the nanoscale. Here, we realize nanoscale topological corner states in metasurfaces with C6-symmetric honeycomb lattices. We directly observe nanoscale topology-empowered edge and corner localizations of light and enhancement of light-matter interactions via a nonlinear imaging technique. Control of light at the nanoscale empowered by topology may facilitate miniaturization and on-chip integration of classical and quantum photonic devices.
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Affiliation(s)
- Sergey S Kruk
- Nonlinear Physics Center, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
- Department of Physics, Paderborn University, 33098 Paderborn, Germany
| | - Wenlong Gao
- Nonlinear Physics Center, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
- Department of Physics, Paderborn University, 33098 Paderborn, Germany
| | - Duk-Yong Choi
- Laser Physics Center, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Thomas Zentgraf
- Department of Physics, Paderborn University, 33098 Paderborn, Germany
| | - Shuang Zhang
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT United Kingdom
- Department of Physics and Department of Electrical & Electronic Engineering, University of Hong Kong, Hong Kong, China
| | - Yuri Kivshar
- Nonlinear Physics Center, Research School of Physics, Australian National University, Canberra, Australian Capital Territory 2601, Australia
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26
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Fleury R. The sound of Weyl hinges. NATURE MATERIALS 2021; 20:716-718. [PMID: 34045698 DOI: 10.1038/s41563-021-01018-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Affiliation(s)
- R Fleury
- Laboratory of Wave Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
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27
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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: 8] [Impact Index Per Article: 2.7] [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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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: 9] [Impact Index Per Article: 3.0] [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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Zhang X, Liu L, Lu MH, Chen YF. Valley-Selective Topological Corner States in Sonic Crystals. PHYSICAL REVIEW LETTERS 2021; 126:156401. [PMID: 33929224 DOI: 10.1103/physrevlett.126.156401] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2020] [Accepted: 02/25/2021] [Indexed: 06/12/2023]
Abstract
Higher-order topological insulators (HOTIs), a new horizon of topological phases of matter, host lower-dimensional corner or hinge states, providing important stepping stones to the realization of robust topological waveguides in higher dimensions. The nontrivial band topology that gives rise to the corner or hinge states is usually enabled by certain crystalline symmetries. As a result, higher-order topological boundary states are tied to specific corners or hinges, lacking the flexibility of switching and selecting. Here, we report the experimental realization of topologically switchable and valley-selective corner states in a two-dimensional sonic crystal. Such intriguing properties are enabled by exploiting the higher-order topology assisted with the valley degree of freedom. For this purpose, we realize a valley HOTI of second-order topology characterized by the nontrivial bulk polarization. Interestingly, the hosted corner states are found to be valley dependent and therefore enable flexible control and manipulation on the wave localization. Topological switch on or off and valley selection of the corner states are directly observed through spatial scanning of the sound field. We further design an arbitrary structure of complex patterns containing corners with various intersection angles, among which selected corners can be illuminated or darkened upon valley selection. The reported valley HOTI and the valley-selective corner states provide fundamental understanding on the interplay between higher-order topology and valley degree of freedom and pave the way for lower-dimensional valleytronics, which may find potential applications in integrated acoustics and photonics.
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Affiliation(s)
- Xiujuan Zhang
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
| | - Le Liu
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
- School of Physics, Nanjing University, Nanjing 210093, China
| | - Ming-Hui Lu
- National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China
- Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210093, China
- Collaborative Innovation Center of Advanced Microstructures, 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
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Computation and data driven discovery of topological phononic materials. Nat Commun 2021; 12:1204. [PMID: 33619273 PMCID: PMC7900202 DOI: 10.1038/s41467-021-21293-2] [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: 06/10/2020] [Accepted: 01/21/2021] [Indexed: 11/20/2022] Open
Abstract
The discovery of topological quantum states marks a new chapter in both condensed matter physics and materials sciences. By analogy to spin electronic system, topological concepts have been extended into phonons, boosting the birth of topological phononics (TPs). Here, we present a high-throughput screening and data-driven approach to compute and evaluate TPs among over 10,000 real materials. We have discovered 5014 TP materials and grouped them into two main classes of Weyl and nodal-line (ring) TPs. We have clarified the physical mechanism for the occurrence of single Weyl, high degenerate Weyl, individual nodal-line (ring), nodal-link, nodal-chain, and nodal-net TPs in various materials and their mutual correlations. Among the phononic systems, we have predicted the hourglass nodal net TPs in TeO3, as well as the clean and single type-I Weyl TPs between the acoustic and optical branches in half-Heusler LiCaAs. In addition, we found that different types of TPs can coexist in many materials (such as ScZn). Their potential applications and experimental detections have been discussed. This work substantially increases the amount of TP materials, which enables an in-depth investigation of their structure-property relations and opens new avenues for future device design related to TPs. Topological phononic (TP) materials are attracting wide attentions and it is more difficult to seek TP materials compared to electronic materials. Here, the authors present a high-throughput screening and data-driven approach to discover 5014 TP materials and further clarify the mechanism for the occurrence of various TPs.
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Mizoguchi T, Kuno Y, Hatsugai Y. Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics. PHYSICAL REVIEW LETTERS 2021; 126:016802. [PMID: 33480756 DOI: 10.1103/physrevlett.126.016802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.
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Affiliation(s)
- Tomonari Mizoguchi
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
| | - Yoshihito Kuno
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
| | - Yasuhiro Hatsugai
- Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
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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: 9] [Impact Index Per Article: 2.3] [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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Qi Y, Qiu C, Xiao M, He H, Ke M, Liu Z. Acoustic Realization of Quadrupole Topological Insulators. PHYSICAL REVIEW LETTERS 2020; 124:206601. [PMID: 32501055 DOI: 10.1103/physrevlett.124.206601] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2019] [Accepted: 04/29/2020] [Indexed: 06/11/2023]
Abstract
A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here, we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge, and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping.
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Affiliation(s)
- Yajuan Qi
- 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
| | - 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
| | - Hailong He
- 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
| | - Manzhu Ke
- 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
| | - 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
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Observation of an acoustic octupole topological insulator. Nat Commun 2020; 11:2442. [PMID: 32415220 PMCID: PMC7229046 DOI: 10.1038/s41467-020-16350-1] [Citation(s) in RCA: 67] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2019] [Accepted: 04/21/2020] [Indexed: 12/30/2022] Open
Abstract
Berry phase associated with energy bands in crystals can lead to quantised observables like quantised dipole polarizations in one-dimensional topological insulators. Recent theories have generalised the concept of quantised dipoles to multipoles, resulting in the discovery of multipole topological insulators which exhibit a hierarchy of multipole topology: a quantised octupole moment in a three-dimensional bulk induces quantised quadrupole moments on its two-dimensional surfaces, which in turn induce quantised dipole moments on one-dimensional hinges. Here, we report on the realisation of an octupole topological insulator in a three-dimensional acoustic metamaterial. We observe zero-dimensional topological corner states, one-dimensional gapped hinge states, two-dimensional gapped surface states, and three-dimensional gapped bulk states, representing the hierarchy of octupole, quadrupole and dipole moments. Conditions for forming a nontrivial octupole moment are demonstrated by comparisons with two different lattice configurations having trivial octupole moments. Our work establishes the multipole topology and its full hierarchy in three-dimensional geometries.
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Long Y, Ren J, Chen H. Unsupervised Manifold Clustering of Topological Phononics. PHYSICAL REVIEW LETTERS 2020; 124:185501. [PMID: 32441973 DOI: 10.1103/physrevlett.124.185501] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 04/13/2020] [Indexed: 06/11/2023]
Abstract
Classification of topological phononics is challenging due to the lack of universal topological invariants and the randomness of structure patterns. Here, we show the unsupervised manifold learning for clustering topological phononics without any a priori knowledge, neither topological invariants nor supervised trainings, even when systems are imperfect or disordered. This is achieved by exploiting the real-space projection operator about finite phononic lattices to describe the correlation between oscillators. We exemplify the efficient unsupervised manifold clustering in typical phononic systems, including a one-dimensional Su-Schrieffer-Heeger-type phononic chain with random couplings, amorphous phononic topological insulators, higher-order phononic topological states, and a non-Hermitian phononic chain with random dissipations. The results would inspire more efforts on applications of unsupervised machine learning for topological phononic devices and beyond.
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Affiliation(s)
- Yang Long
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Jie Ren
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
| | - Hong Chen
- Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, China
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Ni X, Li M, Weiner M, Alù A, Khanikaev AB. Demonstration of a quantized acoustic octupole topological insulator. Nat Commun 2020; 11:2108. [PMID: 32355274 PMCID: PMC7193630 DOI: 10.1038/s41467-020-15705-y] [Citation(s) in RCA: 64] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 12/10/2019] [Indexed: 12/03/2022] Open
Abstract
Recently introduced quantized multipole topological insulators (QMTIs) reveal new types of gapped boundary states, which themselves represent lower-dimensional topological phases and host symmetry protected zero-dimensional corner states. Inspired by these predictions, tremendous efforts have been devoted to the experimental observation of quantized quadrupole topological phase. However, due to stringent requirements of anti-commuting reflection symmetries, it is challenging to achieve higher-order quantized multipole moments, such as octupole moments, in a three-dimensional structure. Here, we overcome this challenge, and experimentally realize the acoustic analogue of a quantized octupole topological insulator using negatively coupled resonators. We confirm by first-principle studies that our design possesses a quantized octupole topological phase, and experimentally demonstrate spectroscopic evidence of a hierarchy of boundary modes, observing 3rd order topological corner states. Furthermore, we reveal topological phase transitions from higher- to lower-order multipole moments. Our work offers a pathway to explore higher-order topological states in 3D classical platforms.
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Affiliation(s)
- Xiang Ni
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, 140th Street and Convent Avenue, New York, NY, 10031, USA
- Physics Program, Graduate Center of the City University of New York, New York, NY, 10016, USA
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA
| | - Mengyao Li
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, 140th Street and Convent Avenue, New York, NY, 10031, USA
- Physics Program, Graduate Center of the City University of New York, New York, NY, 10016, USA
| | - Matthew Weiner
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, 140th Street and Convent Avenue, New York, NY, 10031, USA
- Physics Program, Graduate Center of the City University of New York, New York, NY, 10016, USA
| | - Andrea Alù
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, 140th Street and Convent Avenue, New York, NY, 10031, USA.
- Physics Program, Graduate Center of the City University of New York, New York, NY, 10016, USA.
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, 10031, USA.
| | - Alexander B Khanikaev
- Department of Electrical Engineering, Grove School of Engineering, City College of the City University of New York, 140th Street and Convent Avenue, New York, NY, 10031, USA.
- Physics Program, Graduate Center of the City University of New York, New York, NY, 10016, USA.
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