1
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Xiang X, Peng YG, Gao F, Wu X, Wu P, Chen Z, Ni X, Zhu XF. Demonstration of Acoustic Higher-Order Topological Stiefel-Whitney Semimetal. PHYSICAL REVIEW LETTERS 2024; 132:197202. [PMID: 38804947 DOI: 10.1103/physrevlett.132.197202] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2023] [Accepted: 04/12/2024] [Indexed: 05/29/2024]
Abstract
The higher-order topological phases have attracted intense attention in the past years, which reveals various intriguing topological properties. Meanwhile, the enrichment of group symmetries with projective symmetry algebras redefines the fundamentals of topological matter and makes Stiefel-Whitney (SW) classes in classical wave systems possible. Here, we report the experimental realization of higher-order topological nodal loop semimetal in an acoustic system and obtain the inherent SW topological invariants. In stark contrast to higher-order topological semimetals relating to complex vector bundles, the hinge and surface states in the SW topological phase are protected by two distinctive SW topological charges relevant to real vector bundles. Our findings push forward the studies of SW class topology in classical wave systems, which also show possibilities in robust high-Q-resonance-based sensing and energy harvesting.
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Affiliation(s)
- Xiao Xiang
- 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
| | - Feng Gao
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xiaoxiao Wu
- Quantum Science and Technology Center and Advanced Materials Thrust, The Hong Kong University of Science and Technology (Guangzhou), Nansha, Guangzhou 511400, Guangdong, China
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - Peng Wu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Zhaoxian Chen
- College of Engineering and Applied Sciences, Collaborative Innovation Center of Advanced Microstructures, and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210023, China
| | - Xiang Ni
- School of Physics, Central South University, Changsha 410083, China
| | - Xue-Feng Zhu
- School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan 430074, China
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2
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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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3
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Gong J, Wang Y, Han Y, Cheng Z, Wang X, Yu ZM, Yao Y. Hidden Real Topology and Unusual Magnetoelectric Responses in Two-Dimensional Antiferromagnets. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024:e2402232. [PMID: 38684179 DOI: 10.1002/adma.202402232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2024] [Revised: 04/04/2024] [Indexed: 05/02/2024]
Abstract
Recently, the real topology has been attracting widespread interest in two dimensions (2D). Here, based on first-principles calculations and theoretical analysis, the monolayer Cr2Se2O (ML-CrSeO) is revealed as the first material example of a 2D antiferromagnetic (AFM) real Chern insulator (RCI) with topologically protected corner states. Unlike previous RCIs, it is found that the real topology of the ML-CrSeO is rooted in one certain mirror subsystem of the two spin channels, and cannot be directly obtained from all the valence bands in each spin channel as commonly believed. In particular, due to antiferromagnetism, the corner modes in ML-CrSeO exhibit strong corner-contrasted spin polarization, leading to spin-corner coupling (SCC). This SCC enables a direct connection between spin space and real space. Consequently, large and switchable net magnetization can be induced in the ML-CrSeO nanodisk by electrostatic means, such as potential step and in-plane electric field, and the corresponding magnetoelectric responses behave like a sign function, distinguished from that of the conventional multiferroic materials. This work considerably broadens the candidate range of RCI materials, and opens up a new direction for topo-spintronics and 2D AFM materials research.
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Affiliation(s)
- Jialin Gong
- School of Physical Science and Technology, Southwest University, Chongqing, 400715, China
| | - Yang Wang
- Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Yilin Han
- Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Zhenxiang Cheng
- Institute for Superconducting and Electronic Materials, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, 2500, Australia
| | - Xiaotian Wang
- School of Physical Science and Technology, Southwest University, Chongqing, 400715, China
- Institute for Superconducting and Electronic Materials, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, 2500, Australia
| | - Zhi-Ming Yu
- Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Yugui Yao
- Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing, 100081, China
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4
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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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5
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Hu S, Guo Z, Liu W, Chen S, Chen H. Hyperbolic metamaterial empowered controllable photonic Weyl nodal line semimetals. Nat Commun 2024; 15:2773. [PMID: 38555373 PMCID: PMC10981722 DOI: 10.1038/s41467-024-47125-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2023] [Accepted: 03/21/2024] [Indexed: 04/02/2024] Open
Abstract
Motivated by unique topological semimetals in condensed matter physics, we propose an effective Hamiltonian with four degrees of freedom to describe evolutions of photonic double Weyl nodal line semimetals in one-dimensional hyper-crystals, which supports the energy bands translating or rotating independently in the form of Weyl quasiparticles. Especially, owing to the unit cells without inversion symmetry, a pair of reflection-phase singularities carrying opposite topological charges emerge near each nodal line, and result in a unique bilateral drumhead surface state. After reducing radiation leakages and absorption losses, these two singularities gather together gradually, and form a quasi-bound state in the continuum (quasi-BIC) ring at the nodal line ultimately. Our work not only reports the first realization of controllable photonics Weyl nodal line semimetals, establishes a bridge between two independent topological concepts-BICs and Weyl semimetals, but also heralds new possibilities for unconventional device applications, such as dual-mode schemes for highly sensitive sensing and switching.
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Affiliation(s)
- Shengyu Hu
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, 200092, Shanghai, China
| | - Zhiwei Guo
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, 200092, Shanghai, China.
| | - Wenwei Liu
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, 300071, Tianjin, China
- Renewable Energy Conversion and Storage Center, Nankai University, 300071, Tianjin, China
- Smart Sensing Interdisciplinary Science Center, Nankai University, 300071, Tianjin, China
| | - Shuqi Chen
- The Key Laboratory of Weak Light Nonlinear Photonics, Ministry of Education, School of Physics and TEDA Institute of Applied Physics, Nankai University, 300071, Tianjin, China
- Renewable Energy Conversion and Storage Center, Nankai University, 300071, Tianjin, China
- Smart Sensing Interdisciplinary Science Center, Nankai University, 300071, Tianjin, China
- The Collaborative Innovation Center of Extreme Optics, Shanxi University, 030006, Taiyuan, Shanxi, China
| | - Hong Chen
- MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, 200092, Shanghai, China
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6
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Ma Q, Pu Z, Ye L, Lu J, Huang X, Ke M, He H, Deng W, Liu Z. Observation of Higher-Order Nodal-Line Semimetal in Phononic Crystals. PHYSICAL REVIEW LETTERS 2024; 132:066601. [PMID: 38394560 DOI: 10.1103/physrevlett.132.066601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 01/05/2024] [Indexed: 02/25/2024]
Abstract
Higher-order topological insulators and semimetals, which generalize the conventional bulk-boundary correspondence, have attracted extensive research interest. Among them, higher-order Weyl semimetals feature twofold linear crossing points in three-dimensional momentum space, 2D Fermi-arc surface states, and 1D hinge states. Higher-order nodal-point semimetals possessing Weyl points or Dirac points have been implemented. However, higher-order nodal-line or nodal-surface semimetals remain to be further explored in experiments in spite of many previous theoretical efforts. In this work, we realize a second-order nodal-line semimetal in 3D phononic crystals. The bulk nodal lines, 2D drumhead surface states guaranteed by Zak phases, and 1D flat hinge states attributed to k_{z}-dependent quadrupole moments are observed in simulations and experiments. Our findings of nondispersive surface and hinge states may promote applications in acoustic sensing and energy harvesting.
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Affiliation(s)
- Qiyun Ma
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Zhenhang Pu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Liping Ye
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jiuyang Lu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xueqin Huang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, 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
| | - 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
| | - Weiyin Deng
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, 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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7
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Pan Y, Cui C, Chen Q, Chen F, Zhang L, Ren Y, Han N, Li W, Li X, Yu ZM, Chen H, Yang Y. Real higher-order Weyl photonic crystal. Nat Commun 2023; 14:6636. [PMID: 37857622 PMCID: PMC10587095 DOI: 10.1038/s41467-023-42457-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 10/11/2023] [Indexed: 10/21/2023] Open
Abstract
Higher-order Weyl semimetals are a family of recently predicted topological phases simultaneously showcasing unconventional properties derived from Weyl points, such as chiral anomaly, and multidimensional topological phenomena originating from higher-order topology. The higher-order Weyl semimetal phases, with their higher-order topology arising from quantized dipole or quadrupole bulk polarizations, have been demonstrated in phononics and circuits. Here, we experimentally discover a class of higher-order Weyl semimetal phase in a three-dimensional photonic crystal (PhC), exhibiting the concurrence of the surface and hinge Fermi arcs from the nonzero Chern number and the nontrivial generalized real Chern number, respectively, coined a real higher-order Weyl PhC. Notably, the projected two-dimensional subsystem with kz = 0 is a real Chern insulator, belonging to the Stiefel-Whitney class with real Bloch wavefunctions, which is distinguished fundamentally from the Chern class with complex Bloch wavefunctions. Our work offers an ideal photonic platform for exploring potential applications and material properties associated with the higher-order Weyl points and the Stiefel-Whitney class of topological phases.
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Affiliation(s)
- Yuang Pan
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Chaoxi Cui
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China
- Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing, 100081, China
| | - Qiaolu Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Fujia Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Li 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 Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Yudong Ren
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Ning Han
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Wenhao 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 Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Xinrui 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 Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China
| | - Zhi-Ming Yu
- Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology, Beijing, 100081, China.
- Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing, 100081, China.
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China.
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China.
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China.
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China.
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou, 310027, China.
- International Joint Innovation Center, The Electromagnetics Academy at Zhejiang University, Zhejiang University, Haining, 314400, China.
- Key Lab. of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, Jinhua Institute of Zhejiang University, Zhejiang University, Jinhua, 321099, China.
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing, 312000, China.
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8
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Zhang X, He T, Liu Y, Dai X, Liu G, Chen C, Wu W, Zhu J, Yang SA. Magnetic Real Chern Insulator in 2D Metal-Organic Frameworks. NANO LETTERS 2023; 23:7358-7363. [PMID: 37535707 DOI: 10.1021/acs.nanolett.3c01723] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/05/2023]
Abstract
Real Chern insulators have attracted great interest, but so far, their material realization is limited to nonmagnetic crystals and systems without spin-orbit coupling. Here, we reveal the magnetic real Chern insulator (MRCI) state in a recently synthesized metal-organic framework material Co3(HITP)2. Its ground state with in-plane ferromagnetic ordering hosts a nontrivial real Chern number, enabled by the C2zT symmetry and robustness against spin-orbit coupling. Distinct from previous nonmagnetic examples, the topological corner zero modes of MRCIs are spin-polarized. Furthermore, under small tensile strains, the material undergoes a topological phase transition from the MRCI to a magnetic double-Weyl semimetal phase, via a pseudospin-1 critical state. Similar physics can also be found in closely related materials Mn3(HITP)2 and Fe3(HITP)2, which also exist. Possible experimental detections and implications of an emerging magnetic flat band in the system are discussed.
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Affiliation(s)
- Xiaoming Zhang
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Tingli He
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Ying Liu
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Xuefang Dai
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Guodong Liu
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Cong Chen
- Department of Physics, The University of Hong Kong, Hong Kong, China
- HKU-UCAS Joint Institute of Theoretical and Computational Physics at Hong Kong, Hong Kong, China
| | - Weikang Wu
- Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials (Ministry of Education), Shandong University, Jinan 250061, China
| | - Jiaojiao Zhu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
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9
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Xiao Z, Kawabata K, Luo X, Ohtsuki T, Shindou R. Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes. PHYSICAL REVIEW LETTERS 2023; 131:056301. [PMID: 37595207 DOI: 10.1103/physrevlett.131.056301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Revised: 02/23/2023] [Accepted: 06/23/2023] [Indexed: 08/20/2023]
Abstract
We study quantum phase transitions of three-dimensional disordered systems in the chiral classes (AIII and BDI) with and without weak topological indices. We show that the systems with a nontrivial weak topological index universally exhibit an emergent thermodynamic phase where wave functions are delocalized along one spatial direction but exponentially localized in the other two spatial directions, which we call the quasilocalized phase. Our extensive numerical study clarifies that the critical exponent of the Anderson transition between the metallic and quasilocalized phases, as well as that between the quasilocalized and localized phases, are different from that with no weak topological index, signaling the new universality classes induced by topology. The quasilocalized phase and concomitant topological Anderson transition manifest themselves in the anisotropic transport phenomena of disordered weak topological insulators and nodal-line semimetals, which exhibit the metallic behavior in one direction but the insulating behavior in the other directions.
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Affiliation(s)
- Zhenyu Xiao
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Kohei Kawabata
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan
| | - Xunlong Luo
- Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China
| | - Tomi Ohtsuki
- Physics Division, Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan
| | - Ryuichi Shindou
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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10
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Xue H, Chen ZY, Cheng Z, Dai JX, Long Y, Zhao YX, Zhang B. Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal. Nat Commun 2023; 14:4563. [PMID: 37507388 PMCID: PMC10382567 DOI: 10.1038/s41467-023-40252-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 07/19/2023] [Indexed: 07/30/2023] Open
Abstract
Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence-while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system.
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Affiliation(s)
- Haoran Xue
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Z Y Chen
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, China
| | - Zheyu Cheng
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - J X Dai
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, China
| | - Yang Long
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore
| | - Y X Zhao
- Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China.
- HK Institute of Quantum Science & Technology, The University of Hong Kong, Hong Kong, China.
| | - Baile Zhang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore.
- Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore, Singapore.
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Pu Z, He H, Luo L, Ma Q, Ye L, Ke M, Liu Z. Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum. PHYSICAL REVIEW LETTERS 2023; 130:116103. [PMID: 37001063 DOI: 10.1103/physrevlett.130.116103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2022] [Accepted: 02/27/2023] [Indexed: 06/19/2023]
Abstract
Higher-order topological phases have raised widespread interest in recent years with the occurrence of the topological boundary states of dimension two or more less than that of the system bulk. The higher-order topological states have been verified in gapped phases, in a wide variety of systems, such as photonic and acoustic systems, and recently also observed in gapless semimetal phase, such as Weyl and Dirac phases, in systems alike. The higher-order topology is signaled by the hinge states emerging in the common band gaps of the bulk states and the surface states. In this Letter, we report our first prediction and observation of a new type of hinge states, the bound hinge states in the continuum (BHICs) bulk band, in a higher-order Weyl semimetal implemented in phononic crystal. In contrast to the hinge state in gap, which is characterized by the bulk polarization, the BHIC is identified by the nontrivial surface polarization. The finding of the topological BHICs broadens our insight to the topological states, and may stimulate similar researches in other systems such as electronic, photonic, and cold atoms systems. Our Letter may pave the way toward high-Q acoustic devices in application.
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Affiliation(s)
- Zhenhang Pu
- 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
| | - Licheng Luo
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Qiyun Ma
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Liping Ye
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, 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
| | - 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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Yang T, Ding S, Liu Y, Wu Z, Zhang G. An ideal Weyl nodal ring with a large drumhead surface state in the orthorhombic compound TiS 2. Phys Chem Chem Phys 2022; 24:8208-8216. [PMID: 35319049 DOI: 10.1039/d2cp00424k] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Topological metals or semimetals have attracted great research attention and interest in condensed matter physics and chemistry due to their exotic properties. Different from the conventional topological insulators, topological metals or semimetals are characterized by distinct topological surface states, such as a Fermi arc or a drumhead surface state, which are often used in experiments to verify the corresponding topological properties. However, the current study in this field is strongly limited in the experimental characterization because of the extreme lack of perfect material candidates with a clean band structure and clear surface states. In this work, based on theoretical calculations, we propose a new topological semimetal TiS2, which has an orthorhombic structure and exhibits excellent stability. Calculated electronic band structures reveal that there is a single Weyl nodal ring in the ky = 0 plane. A detailed symmetry analysis is provided and the corresponding surface state is calculated, which exhibits both a large energy variation of 1.5 eV and wide space distribution without and with the spin orbit coupling effect. Besides, the surface states are well separated from the bulk state. These ideal features together make TiS2 a promising nodal line semimetal for experimental investigation. In combination with the other two isostructural compounds TiSe2 and TiTe2 with similar properties, their further experimental synthesis and characterization can be highly expected and the corresponding study for the topological nodal line state can thus be greatly facilitated.
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Affiliation(s)
- Tie Yang
- School of Physical Science and Technology, Southwest University, Chongqing 400715, China.,School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
| | - Shoubing Ding
- School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
| | - Ying Liu
- School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Zhimin Wu
- School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
| | - Gang Zhang
- Institute of High Performance Computing, Agency for Science, Technology and Research, Connexis, 138632, Singapore.
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