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Jiang YC, Kariyado T, Hu X. Possible gapless helical edge states in hydrogenated graphene. Sci Rep 2024; 14:17829. [PMID: 39090149 PMCID: PMC11294590 DOI: 10.1038/s41598-024-68558-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 07/24/2024] [Indexed: 08/04/2024] Open
Abstract
Electronic band structures in hydrogenated graphene are theoretically investigated by means of first-principle calculations and an effective tight-binding model. It is shown that regularly designed hydrogenation to graphene gives rise to a large band gap about 1 eV. Remarkably, by changing the spatial pattern of the hydrogenation, topologically distinct states can be realized, where the topological nontriviality is detected by C 2 parity indices in bulk and confirmed by the existence of gapless edge/interface states as protected by the mirror and sublattice symmetries. The analysis of the wave functions reveals that the helical edge states in hydrogenated graphene with the appropriate design carry pseudospin currents that are reminiscent of the quantum spin Hall effect. Our work shows the potential of hydrogenated graphene in pseudospin-based device applications.
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Affiliation(s)
- Yong-Cheng Jiang
- Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, 305-0044, Japan
- Graduate School of Science and Technology, University of Tsukuba, Tsukuba, 305-8571, Japan
| | - Toshikaze Kariyado
- Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, 305-0044, Japan
| | - Xiao Hu
- Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba, 305-0044, Japan.
- Graduate School of Science and Technology, University of Tsukuba, Tsukuba, 305-8571, Japan.
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2
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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; 36: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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Zhan F, Qin Z, Xu DH, Zhou X, Ma DS, Wang R. Design of Antiferromagnetic Second-Order Band Topology with Rotation Topological Invariants in Two Dimensions. NANO LETTERS 2024; 24:7741-7747. [PMID: 38870320 DOI: 10.1021/acs.nanolett.4c01817] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2024]
Abstract
The existence of fractionally quantized topological corner charge serves as a key indicator for two-dimensional (2D) second-order topological insulators (SOTIs), yet it has not been experimentally observed in realistic materials. Here, based on effective model analysis and symmetry arguments, we propose a strategy for achieving SOTI phases with in-gap corner states in 2D systems with antiferromagnetic (AFM) order. We discover that the band topology originates from the interplay between intrinsic spin-orbital coupling and interlayer AFM exchange interactions. Using first-principles calculations, we show that the 2D AFM SOTI phase can be realized in (MnBi2Te4)(Bi2Te3)m films. Moreover, we demonstrate that the SOTI states are linked to rotation topological invariants under 3-fold rotation symmetry C3, resulting in fractionally quantized corner charge, i.e., n 3 | e | (mod e). Due to the great achievements in (MnBi2Te4)(Bi2Te3)m systems, our results providing reliable material candidates for experimentally accessible AFM SOTIs should draw intense attention.
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Affiliation(s)
- Fangyang Zhan
- Institute for Structure and Function & Department of Physics & Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 400044, People's Republic of China
| | - Zheng Qin
- Center of Quantum materials and devices, Chongqing University, Chongqing 400044, People's Republic of China
| | - Dong-Hui Xu
- Institute for Structure and Function & Department of Physics & Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 400044, People's Republic of China
- Center of Quantum materials and devices, Chongqing University, Chongqing 400044, People's Republic of China
| | - Xiaoyuan Zhou
- Center of Quantum materials and devices, Chongqing University, Chongqing 400044, People's Republic of China
| | - Da-Shuai Ma
- Institute for Structure and Function & Department of Physics & Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 400044, People's Republic of China
- Center of Quantum materials and devices, Chongqing University, Chongqing 400044, People's Republic of China
| | - Rui Wang
- Institute for Structure and Function & Department of Physics & Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 400044, People's Republic of China
- Center of Quantum materials and devices, Chongqing University, Chongqing 400044, People's Republic of China
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Li R, Zou X, Bai Y, Chen Z, Huang B, Dai Y, Niu C. Layer-coupled corner states in two-dimensional topological multiferroics. MATERIALS HORIZONS 2024; 11:2242-2247. [PMID: 38421336 DOI: 10.1039/d3mh01266b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/02/2024]
Abstract
The structural diversity and controllability in two-dimensional (2D) materials offers an intriguing platform for exploring a wide range of topological phenomena. The layer degree of freedom, as a novel technique for material manipulation, requires further investigation regarding its association with topological states. Here, using first-principles calculations and a tight-binding model, we propose a novel mechanism that couples the second-order topological corner states with the layer degree of freedom. By analyzing the edge states, topological indices, and spectra of nanoflakes, we identify ferromagnetic H'-Co2XF2 (X = C, N) as 2D second-order topological insulators with intrinsic ferroelectricity. Moreover, the topological corner states strongly couple with the layer degree of freedom, and, remarkably, ferroelectricity provides a nonvolatile handle to manipulate the layer-polarized corner states. These findings open an avenue for the manipulation of second-order topological states and establish a bridge between ferroelectricity and nontrivial topology.
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Affiliation(s)
- Runhan Li
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
| | - Xiaorong Zou
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
| | - Yingxi Bai
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
| | - Zhiqi Chen
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
| | - Baibiao Huang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
| | - Ying Dai
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
| | - Chengwang Niu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China.
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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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Fang T, Zhang T, Hu T, Wang Z. Atomic-Limit Mott Insulator in [4]Triangulene Frameworks. NANO LETTERS 2024; 24:3059-3066. [PMID: 38426713 DOI: 10.1021/acs.nanolett.3c04675] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/02/2024]
Abstract
Triangulene, one unique class of zigzag-edged triangular graphene molecules, has attracted tremendous research interest. In this work, as an ultimate phase of the Mott insulator, we present the realization of the atomic-limit Mott insulator in experimentally synthesized [4]triangulene frameworks ([4]-TGFs) from first-principles calculations. The frontier molecular orbitals of the nonmagnetic [4]triangulene consist of three coupled corner modes. After the isolated [4]triangulene is assembled into [4]-TGF, one special enantiomorphic flat band is created through the coupling of these corner modes, which is identified to be a second-order topological insulator with half-filled topological corner states at the Fermi level. Moreover, [4]-TGF prefers an antiferromagnetic ground state under Hubbard interactions, which further splits these metallic zero-energy states into an atomic-limit Mott insulator with spin-polarized corners. Since the fractional filling of topological corner states is a smoking-gun signature of higher-order topology, our results demonstrate a universal approach to explore the atomic-limit Mott insulators in higher-order topological materials.
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Affiliation(s)
- Tiancheng Fang
- Hefei National Research Center 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, People's Republic of China
| | - Tingfeng Zhang
- Hefei National Research Center 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, People's Republic of China
| | - Tianyi Hu
- Hefei National Research Center 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, People's Republic of China
| | - Zhengfei Wang
- Hefei National Research Center 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, People's Republic of China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230088, People's Republic of China
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7
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Jiang YC, Kariyado T, Hu X. Topological electronic states in holey graphyne. NANOTECHNOLOGY 2024; 35:195201. [PMID: 38295413 DOI: 10.1088/1361-6528/ad2483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 01/31/2024] [Indexed: 02/02/2024]
Abstract
We unveil that the holey graphyne (HGY), a two-dimensional carbon allotrope where benzene rings are connected by two -C≡C- bonds fabricated recently in a bottom-up way, exhibits topological electronic states. Using first-principles calculations and Wannier tight-binding modeling, we discover a higher-order topological invariant associated withC2symmetry of the material, and show that the resultant corner modes appear in nanoflakes matching to the structure of precursor reported previously, which are ready for direct experimental observations. In addition, we find that a band inversion between emergentg-like andh-like orbitals gives rise to a nontrivial topology characterized byZ2invariant protected by an energy gap as large as 0.52 eV, manifesting helical edge states mimicking those in the prominent quantum spin Hall effect, which can be accessed experimentally after hydrogenation in HGY. We hope these findings trigger interests towards exploring the topological electronic states in HGY and related future electronics applications.
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Affiliation(s)
- Yong-Cheng Jiang
- Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan
- Graduate School of Science and Technology, University of Tsukuba, Tsukuba 305-8571, Japan
| | - Toshikaze Kariyado
- Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan
| | - Xiao Hu
- Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan
- Graduate School of Science and Technology, University of Tsukuba, Tsukuba 305-8571, Japan
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8
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Chen M, Kong X, Xie X, Liu X, Li J, Peeters FM, Li L. Tunable valley polarization effect and second-order topological state in monolayer FeClSH. Phys Chem Chem Phys 2024; 26:3285-3295. [PMID: 38197170 DOI: 10.1039/d3cp05127g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
In two-dimensional (2D) materials, breaking the inversion symmetry plays an important role in valleytronics. Ferrovalley (FV) materials can achieve spontaneous valley polarization (VP) without additional modulation due to the magnetic exchange interaction and strong spin-orbit coupling. Using first-principles calculations, we predict a new 2D material, Janus FeClSH, which exhibits a large spontaneous VP. This monolayer is a perfect FV material, where the valence band maximum and conduction band minimum are located at the K/K' point. A large VP of 102.95 meV is spontaneously generated for the case of out-of-plane magnetization. Additionally, we propose that the irradiating circularly polarized light can be used to realize VP for the case of in-plane magnetization. Remarkably, a triangular nanoflake of FeClSH with armchair edges can show nontrivial corner states, exhibiting a second-order topological insulator (SOTI) state. The VP effect and SOTI state are tunable with the Hubbard U parameter, making the FeClSH monolayer promising for the study of the coupling between VP and SOTI.
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Affiliation(s)
- Mengteng Chen
- School of Science, Hebei University of Technology, Tianjin 300401, China.
| | - Xiangru Kong
- College of Sciences, Northeastern University, Shenyang 110819, China.
| | - Xiao Xie
- School of Science, Hebei University of Technology, Tianjin 300401, China.
| | - Xiaobiao Liu
- School of Science, Henan Agricultural University, Zhengzhou 450002, China
| | - Jia Li
- School of Science, Hebei University of Technology, Tianjin 300401, China.
| | - François M Peeters
- Centre for Quantum Metamaterials, HSE University, Moscow 101000, Russia
- Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, 60455-760 Fortaleza, Ceará, Brazil
| | - Linyang Li
- School of Science, Hebei University of Technology, Tianjin 300401, China.
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9
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Lahiri S, Basu S. Second order topology in a band engineered Chern insulator. Sci Rep 2024; 14:1880. [PMID: 38253745 PMCID: PMC10810362 DOI: 10.1038/s41598-024-52321-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 01/17/2024] [Indexed: 01/24/2024] Open
Abstract
Haldane model is a celebrated tight binding toy model of a Chern insulator in a 2D honeycomb lattice that exhibits quantized Hall conductance in the absence of an external magnetic field. In our work, we deform the bands of the Haldane model smoothly by varying one of its three nearest neighbour hopping amplitudes ([Formula: see text]), while keeping the other two (t) fixed. This breaks the [Formula: see text] symmetry of the Hamiltonian, while the [Formula: see text] symmetry is preserved. The symmetry breaking causes the Dirac cones to shift from the K and the K[Formula: see text] points in the Brillouin zone (BZ) to an intermediate M point. This is evident from the Berry curvature plots which show a similar shift in the corresponding values as a function of the deformation parameter, namely [Formula: see text]. We observe two different topological phases of which, one is a topological insulator (TI) and the other is a second order topological insulator (SOTI). The Chern number (C) remains perfectly quantized at a value of [Formula: see text] for the TI phase and it goes to zero in the SOTI phase. Furthermore, the evolution of the Wannier charge center (WCC) as the band is smoothly deformed shows a jump in the TI phase indicating the presence of conducting edge modes. We also study the SOTI phase and diagonalize the real space Hamiltonian on a rhombic supercell which shows the presence of in-gap zero energy corner modes. The polarization of the system, namely [Formula: see text] and [Formula: see text], are evaluated, along the x and the y directions, respectively. We see that both [Formula: see text] and [Formula: see text] are quantized in the SOTI phase owing to the presence of the inversion symmetry of the system. Finally we establish the SOTI phase as an example of a topological phase with zero Berry curvature and provide an analogy with the two dimensional Su-Schrieffer-Heeger model.
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Affiliation(s)
- Srijata Lahiri
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India.
| | - Saurabh Basu
- Department of Physics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India
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Wang A, Li Y, Yang G, Yan D, Huang Y, Guo Z, Gao J, Huang J, Zeng Q, Qian D, Wang H, Guo X, Meng F, Zhang Q, Gu L, Zhou X, Liu G, Qu F, Qian T, Shi Y, Wang Z, Lu L, Shen J. A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta 2Pd 3Te 5. Nat Commun 2023; 14:7647. [PMID: 37996440 PMCID: PMC10667360 DOI: 10.1038/s41467-023-43361-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 11/02/2023] [Indexed: 11/25/2023] Open
Abstract
The interplay between topology and interaction always plays an important role in condensed matter physics and induces many exotic quantum phases, while rare transition metal layered material (TMLM) has been proved to possess both. Here we report a TMLM Ta2Pd3Te5 has the two-dimensional second-order topology (also a quadrupole topological insulator) with correlated edge states - Luttinger liquid. It is ascribed to the unconventional nature of the mismatch between charge- and atomic- centers induced by a remarkable double-band inversion. This one-dimensional protected edge state preserves the Luttinger liquid behavior with robustness and universality in scale from micro- to macro- size, leading to a significant anisotropic electrical transport through two-dimensional sides of bulk materials. Moreover, the bulk gap can be modulated by the thickness, resulting in an extensive-range phase diagram for Luttinger liquid. These provide an attractive model to study the interaction and quantum phases in correlated topological systems.
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Affiliation(s)
- Anqi Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
| | - Yupeng Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Guang Yang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Dayu Yan
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Yuan Huang
- Advanced Research Institute of Multidisciplinary Science, Beijing Institute of Technology, 100081, Beijing, China
| | - Zhaopeng Guo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Jiacheng Gao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
| | - Jierui Huang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
| | - Qiaochu Zeng
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Degui Qian
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Hao Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Xingchen Guo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
| | - Fanqi Meng
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Qinghua Zhang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Yangtze River Delta Physics Research Center Co. Ltd, 213300, Liyang, China
| | - Lin Gu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
- Songshan Lake Materials Laboratory, 523808, Dongguan, China
| | - Xingjiang Zhou
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
- Songshan Lake Materials Laboratory, 523808, Dongguan, China
| | - Guangtong Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Songshan Lake Materials Laboratory, 523808, Dongguan, China
| | - Fanming Qu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
- Songshan Lake Materials Laboratory, 523808, Dongguan, China
| | - Tian Qian
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- Songshan Lake Materials Laboratory, 523808, Dongguan, China
| | - Youguo Shi
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China.
- Songshan Lake Materials Laboratory, 523808, Dongguan, China.
| | - Zhijun Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China.
| | - Li Lu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China.
- Songshan Lake Materials Laboratory, 523808, Dongguan, China.
| | - Jie Shen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
- Songshan Lake Materials Laboratory, 523808, Dongguan, China.
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11
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Zhang X, Wang X, He T, Wang L, Yu WW, Liu Y, Liu G, Cheng Z. Magnetic topological materials in two-dimensional: theory, material realization and application prospects. Sci Bull (Beijing) 2023; 68:2639-2657. [PMID: 37734982 DOI: 10.1016/j.scib.2023.09.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Revised: 07/12/2023] [Accepted: 08/23/2023] [Indexed: 09/23/2023]
Abstract
Two-dimensional (2D) magnetism and nontrivial band topology are both areas of research that are currently receiving significant attention in the study of 2D materials. Recently, a novel class of materials has emerged, known as 2D magnetic topological materials, which elegantly combine 2D magnetism and nontrivial topology. This field has garnered increasing interest, especially due to the emergence of several novel magnetic topological states that have been generalized into the 2D scale. These states include antiferromagnetic topological insulators/semimetals, second-order topological insulators, and topological half-metals. Despite the rapid advancements in this emerging research field in recent years, there have been few comprehensive summaries of the state-of-the-art progress. Therefore, this review aims to provide a thorough analysis of current progress on 2D magnetic topological materials. We cover various 2D magnetic topological insulators, a range of 2D magnetic topological semimetals, and the novel 2D topological half-metals, systematically analyzing the basic topological theory, the course of development, the material realization, and potential applications. Finally, we discuss the challenges and prospects for 2D magnetic topological materials, highlighting the potential for future breakthroughs in this exciting field.
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Affiliation(s)
- Xiaoming Zhang
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, and School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Xiaotian Wang
- School of Physical Science and Technology, Southwest University, Chongqing 400715, China
| | - Tingli He
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, and School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Lirong Wang
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, and School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China
| | - Wei-Wang Yu
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, and 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, and 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, and School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China.
| | - Zhenxiang Cheng
- Institute for Superconducting and Electronic Materials (ISEM), University of Wollongong, Wollongong 2500, Australia.
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12
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Xie B, Huang R, Jia S, Lin Z, Hu J, Jiang Y, Ma S, Zhan P, Lu M, Wang Z, Chen Y, Zhang S. Bulk-local-density-of-state correspondence in topological insulators. Nat Commun 2023; 14:7347. [PMID: 37963897 PMCID: PMC10646048 DOI: 10.1038/s41467-023-42449-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Accepted: 10/11/2023] [Indexed: 11/16/2023] Open
Abstract
In the quest to connect bulk topological quantum numbers to measurable parameters in real materials, current established approaches often necessitate specific conditions, limiting their applicability. Here we propose and demonstrate an approach to link the non-trivial hierarchical bulk topology to the multidimensional partition of local density of states (LDOS), denoted as the bulk-LDOS correspondence. In finite-size topologically nontrivial photonic crystals, we observe the LDOS partitioned into three distinct regions: a two-dimensional interior bulk area, a one-dimensional edge region, and zero-dimensional corner sites. Contrarily, topologically trivial cases exhibit uniform LDOS distribution across the entire two-dimensional bulk area. Our findings provide a general framework for distinguishing topological insulators and uncovering novel aspects of topological directional band-gap materials, even in the absence of in-gap states.
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Affiliation(s)
- Biye Xie
- New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
- School of Science and Engineering, The Chinese University of Hong Kong, 518172, Shenzhen, China
| | - Renwen Huang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
- School of Physics, Nanjing University, 210093, Nanjing, China
| | - Shiyin Jia
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
- School of Physics, Nanjing University, 210093, Nanjing, China
| | - Zemeng Lin
- New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Junzheng Hu
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
- School of Physics, Nanjing University, 210093, Nanjing, China
| | - Yao Jiang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
- School of Physics, Nanjing University, 210093, Nanjing, China
| | - Shaojie Ma
- New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Peng Zhan
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China.
- School of Physics, Nanjing University, 210093, Nanjing, China.
| | - Minghui Lu
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China.
- Department of Materials Science and Engineering, Nanjing University, 210093, Nanjing, China.
| | - Zhenlin Wang
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
- School of Physics, Nanjing University, 210093, Nanjing, China
| | - Yanfeng Chen
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, 210093, Nanjing, China
- Department of Materials Science and Engineering, Nanjing University, 210093, Nanjing, China
| | - Shuang Zhang
- New Cornerstone Science Laboratory, Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China.
- Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong, China.
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13
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Hu T, Zhong W, Zhang T, Wang W, Wang ZF. Identifying topological corner states in two-dimensional metal-organic frameworks. Nat Commun 2023; 14:7092. [PMID: 37925474 PMCID: PMC10625601 DOI: 10.1038/s41467-023-42884-1] [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: 06/22/2023] [Accepted: 10/24/2023] [Indexed: 11/06/2023] Open
Abstract
Due to the diversity of molecular building blocks, the two-dimensional (2D) metal-organic frameworks (MOFs) are ideal platforms to realize exotic lattice models in condensed matter theory. In this work, we demonstrate the universal existence of topological corner states in 2D MOFs with a star lattice configuration, and confirm the intriguing higher-order nontrivial topology in the energy window between two Kagome-bands, or between Dirac-band and four-band. Furthermore, combining first-principles calculations and scanning tunneling microscopy measurements, the unique topological corner state is directly identified in monolayer Ni3(HITP)2 (HITP = 2,3,6,7,10,11-hexaiminotriphenylene) grown on the Au(111) substrate. Our results not only illustrate the first organic topological state in the experiments, but also offer an exciting opportunity to study higher-order topology in 2D MOFs with the large insulating band gap.
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Affiliation(s)
- Tianyi Hu
- Hefei National Research Center 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
| | - Weiliang Zhong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
| | - Tingfeng Zhang
- Hefei National Research Center 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
| | - Weihua Wang
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
| | - Z F Wang
- Hefei National Research Center 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.
- Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui, 230088, China.
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14
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Zhang T, Hu T, Zhang Y, Wang Z. Pseudospin Polarized Dual-Higher-Order Topology in Hydrogen-Substituted Graphdiyne. NANO LETTERS 2023; 23:8319-8325. [PMID: 37643363 DOI: 10.1021/acs.nanolett.3c02684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
Although the topological band theory is applicable to both Fermionic and bosonic systems, the same electronic and phononic topological phases are seldom reported in one natural material. In this work, we show the presence of a dual-higher-order topology in hydrogen-substituted graphdiyne (H-GDY) by first-principles calculations. The intriguing enantiomorphic flat-bands are realized in both electronic and phononic bands of H-GDY, which is confirmed to be an organic 2D second-order topological insulator (SOTI). Most importantly, we found that the topological corner states are pseudospin polarized in H-GDY, exhibiting a clockwise or counterclockwise texture perpendicular to the radial direction. Our results not only identify the existence of the dual-higher-order topology in covalent organic frameworks but also uncover a unique pseudospin polarization-coordinate locking relation, further extending the well-known spin-momentum locking relation in conventional topological insulators.
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Affiliation(s)
- Tingfeng Zhang
- 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
| | - Yongqi Zhang
- 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
- Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui 230088, China
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15
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Li R, Zhang L, Chen T, Wang D. On-Surface Two-Dimensional Polymerization: Advances, Challenges, and Prospects. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:12521-12532. [PMID: 37651313 DOI: 10.1021/acs.langmuir.3c00880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Two-dimensional polymers (2DPs) are molecularly thin networks consisting of monomers covalently linked in at least two directions in the molecular plane. Because of the unique structural features and emergent physicochemical properties, 2DPs promise application potentials in catalysis, chemical sensing, and organic electronic devices. On-surface synthesis is of great interest to fabricate 2DPs with atomic precision, and the properties of the 2DPs can be characterized in situ through scanning probe techniques. In this Perspective, we first introduce the recent developments of on-surface 2D polymerization, including the design principle, the synthetic reactions, and the factors affecting the synthesis of 2DPs on surface. Then, we summarize some major challenges in this field, including the fabrication of high-quality 2DPs and the study of the intrinsic electronic properties of 2DPs, and we discuss some of the available solutions to address these issues.
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Affiliation(s)
- Ruoning Li
- CAS Key Laboratory of Molecular Nanostructure and Nanotechnology, CAS Research/Education Center for Excellence in Molecular Sciences, Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Longzhu Zhang
- CAS Key Laboratory of Molecular Nanostructure and Nanotechnology, CAS Research/Education Center for Excellence in Molecular Sciences, Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Ting Chen
- CAS Key Laboratory of Molecular Nanostructure and Nanotechnology, CAS Research/Education Center for Excellence in Molecular Sciences, Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
| | - Dong Wang
- CAS Key Laboratory of Molecular Nanostructure and Nanotechnology, CAS Research/Education Center for Excellence in Molecular Sciences, Beijing National Laboratory for Molecular Sciences (BNLMS), Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, P. R. China
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16
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Liu G, Jiang H, Guo Z, Zhang X, Jin L, Liu C, Liu Y. Magnetic Second-Order Topological Insulators in 2H-Transition Metal Dichalcogenides. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2023; 10:e2301952. [PMID: 37518836 PMCID: PMC10520633 DOI: 10.1002/advs.202301952] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Revised: 06/24/2023] [Indexed: 08/01/2023]
Abstract
The transition metal dichalcogenides, 2H-VX2 (X = S, Se, Te), are identified as two-dimensional second-order topological insulator (SOTI) with a ferromagnetic ground state by first-principles calculations. The 2H-VX2 (X = S, Se, Te) materials have a nontrivial band gap in two spin channels is found and exhibit topologically protected corner states with spin-polarization. These corner states only accommodate the quantized fractional charge (e/3). And the charge is bound at the corners of the nanodisk geometry 2H-VX2 (X = S, Se, Te) in real space. The corner states are robust against symmetry-breaking perturbations, which makes them more easily detectable in experiments. Further, it is demonstrated that the SOTI properties of 2H-VX2 (X = S, Se, Te) materials can be maintained in the presence of spin-orbit coupling and are stable against magnetization. Overall, the results reveal 2H-VX2 (X = S, Se, Te) as an ideal platform for the exploration of magnetic SOTI and suggest its great potential in experimental detection.
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Affiliation(s)
- Guodong Liu
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
| | - Haoqian Jiang
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
| | - Zhenzhou Guo
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
| | - Xiaoming Zhang
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
| | - Lei Jin
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
| | - Cong Liu
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
| | - Ying Liu
- State Key Laboratory of Reliability and Intelligence of Electrical EquipmentHebei University of TechnologyTianjin300130China
- School of Materials Science and EngineeringHebei University of TechnologyTianjin300130China
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17
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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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18
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Zhu WQ, Shan WY. Theoretical studies of magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators. Sci Rep 2023; 13:12599. [PMID: 37537224 PMCID: PMC10400575 DOI: 10.1038/s41598-023-39644-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 07/28/2023] [Indexed: 08/05/2023] Open
Abstract
Optical approaches are useful for studying the electronic and spin structure of materials. Here, based on the tight-binding model and linear response theory, we investigate the magneto-optical Kerr and Faraday effects in two-dimensional second-order topological insulators (SOTI) with external magnetization. We find that orbital-dependent Zeeman term induces band crossings for SOTI phase, which are absent for trivial phase. In the weak-magnetization regime, these crossings give rise to giant jumps (peaks) of Kerr and Faraday angles (ellipticity) for SOTI phase. In the strong-magnetization regime, we find that two nearly flat bands are formed at the high-symmetry point of Brillouin zone of SOTI phase. These flat bands give rise to two successive giant jumps (peaks) of Kerr and Faraday angles (ellipticity). These phenomena provide new possibilities to characterize and detect the two-dimensional SOTI phase.
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Affiliation(s)
- Wan-Qing Zhu
- Department of Physics, School of Physics and Materials Science, Guangzhou University, Guangzhou, 510006, China
| | - Wen-Yu Shan
- Department of Physics, School of Physics and Materials Science, Guangzhou University, Guangzhou, 510006, China.
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19
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Bai Y, Mao N, Li R, Dai Y, Huang B, Niu C. Engineering Second-Order Corner States in 2D Multiferroics. SMALL (WEINHEIM AN DER BERGSTRASSE, GERMANY) 2023; 19:e2206574. [PMID: 36642812 DOI: 10.1002/smll.202206574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Revised: 12/18/2022] [Indexed: 06/17/2023]
Abstract
The understanding and manipulate of the second-order corner states are central to both fundamental physics and future topotronics applications. Despite the fact that numerous second-order topological insulators (SOTIs) are achieved, the efficient engineering in a given material remains elusive. Here, the emergence of 2D multiferroics SOTIs in SbAs and BP5 monolayers is theoretically demonstrated, and an efficient and straightforward way for engineering the nontrivial corner states by ferroelasticity and ferroelectricity is remarkably proposed. With ferroelectric polarization of SbAs and BP5 monolayers, the nontrivial corner states emerge in the mirror symmetric corners and are perpendicular to orientations of the in-plane spontaneous polarization. And remarkably the spatial distribution of the corner states can be effectively tuned by a ferroelastic switching. At the intermediate states of both ferroelectric and ferroelastic switchings, the corner states disappear. These finding not only combines exotic SOTIs with multiferroics but also pave the way for experimental discovery of 2D tunable SOTIs.
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Affiliation(s)
- Yingxi Bai
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China
| | - Ning Mao
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China
| | - Runhan Li
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China
| | - Ying Dai
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China
| | - Baibiao Huang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China
| | - Chengwang Niu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan, 250100, China
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20
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Li H, Lim JH, Lv Y, Li N, Kang B, Lee JY. Graphynes and Graphdiynes for Energy Storage and Catalytic Utilization: Theoretical Insights into Recent Advances. Chem Rev 2023; 123:4795-4854. [PMID: 36921251 DOI: 10.1021/acs.chemrev.2c00729] [Citation(s) in RCA: 15] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2023]
Abstract
Carbon allotropes have contributed to all aspects of people's lives throughout human history. As emerging carbon-based low-dimensional materials, graphyne family members (GYF), represented by graphdiyne, have a wide range potential applications due to their superior physical and chemical properties. In particular, graphdiyne (GDY), as the leader of the graphyne family, has been practically applied to various research fields since it was first successfully synthesized. GYF have a large surface area, both sp and sp2 hybridization, and a certain band gap, which was considered to originate from the overlap of carbon 2pz orbitals and the inhomogeneous π-bonds of carbon atoms in different hybridization forms. These properties mean GYF-based materials still have many potential applications to be developed, especially in energy storage and catalytic utilization. Since most of the GYF have yet to be synthesized and applications of successfully synthesized GYF have not been developed for a long time, theoretical results in various application fields should be shared to experimentalists to attract more intentions. In this Review, we summarized and discussed the synthesis, structural properties, and applications of GYF-based materials from the theoretical insights, hoping to provide different viewpoints and comments.
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Affiliation(s)
- Hao Li
- Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea
| | - Jong Hyeon Lim
- Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea
| | - Yipin Lv
- School of Chemistry and Chemical Engineering, University of Jinan, Jinan, Shandong 250022, P. R. China
| | - Nannan Li
- Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea
| | - Baotao Kang
- School of Chemistry and Chemical Engineering, University of Jinan, Jinan, Shandong 250022, P. R. China
| | - Jin Yong Lee
- Department of Chemistry, Sungkyunkwan University, Suwon 440-746, Korea
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21
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Lasisi KH, Abass OK, Zhang K, Ajibade TF, Ajibade FO, Ojediran JO, Okonofua ES, Adewumi JR, Ibikunle PD. Recent advances on graphyne and its family members as membrane materials for water purification and desalination. Front Chem 2023; 11:1125625. [PMID: 36742031 PMCID: PMC9895114 DOI: 10.3389/fchem.2023.1125625] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 01/04/2023] [Indexed: 01/21/2023] Open
Abstract
Graphyne and its family members (GFMs) are allotropes of carbon (a class of 2D materials) having unique properties in form of structures, pores and atom hybridizations. Owing to their unique properties, GFMs have been widely utilized in various practical and theoretical applications. In the past decade, GFMs have received considerable attention in the area of water purification and desalination, especially in theoretical and computational aspects. More recently, GFMs have shown greater prospects in achieving optimal separation performance than the experimentally derived commercial polyamide membranes. In this review, recent theoretical and computational advances made in the GFMs research as it relates to water purification and desalination are summarized. Brief details on the properties of GFMs and the commonly used computational methods were described. More specifically, we systematically reviewed the various computational approaches employed with emphasis on the predicted permeability and selectivity of the GFM membranes. Finally, the current challenges limiting their large-scale practical applications coupled with the possible research directions for overcoming the challenges are proposed.
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Affiliation(s)
- Kayode Hassan Lasisi
- Key Laboratory of Urban Pollutant Conversion, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, China
| | - Olusegun K. Abass
- Department of Civil Engineering, and ReNEWACT Laboratory, Landmark University, Omu-Aran, Kwara State, Nigeria,*Correspondence: Olusegun K. Abass, ,
| | - Kaisong Zhang
- Key Laboratory of Marine Environment and Ecology, Ministry of Education, Ocean University of China, Qingdao, China
| | - Temitope Fausat Ajibade
- Department of Civil and Environmental Engineering, Federal University of Technology, Akure, Nigeria
| | | | - John O. Ojediran
- Department of Agricultural and Biosystems Engineering, Landmark University, Omu-Aran, Kwara State, Nigeria
| | | | - James Rotimi Adewumi
- Department of Civil and Environmental Engineering, Federal University of Technology, Akure, Nigeria
| | - Peter D. Ibikunle
- Department of Civil Engineering, and ReNEWACT Laboratory, Landmark University, Omu-Aran, Kwara State, Nigeria
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22
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Li R, Mao N, Wu X, Huang B, Dai Y, Niu C. Robust Second-Order Topological Insulators with Giant Valley Polarization in Two-Dimensional Honeycomb Ferromagnets. NANO LETTERS 2023; 23:91-97. [PMID: 36326600 DOI: 10.1021/acs.nanolett.2c03680] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Magnetic topological states have attracted great attention that provide exciting platforms for exploring prominent physical phenomena and applications of topological spintronics. Here, using a tight-binding model and first-principles calculations, we put forward that, in contrast to previously reported magnetic second-order topological insulators (SOTIs), robust SOTIs can emerge in two-dimensional ferromagnets regardless of magnetization directions. Remarkably, we identify intrinsic ferromagnetic 2H-RuCl2 and Janus VSSe monolayers as experimentally feasible candidates of predicted robust SOTIs with the emergence of nontrivial corner states along different magnetization directions. Moreover, under out-of-plane magnetization, we unexpectedly point out that the valley polarization of SOTIs can be huge and much larger than that of the known ferrovalley materials, opening up a technological avenue to bridge the valleytronics and higher-order topology with high possibility of innovative applications in topological spintronics and valleytronics.
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Affiliation(s)
- Runhan Li
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan250100, China
| | - Ning Mao
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan250100, China
| | - Xinming Wu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan250100, China
| | - Baibiao Huang
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan250100, China
| | - Ying Dai
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan250100, China
| | - Chengwang Niu
- School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan250100, China
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Ni X, Huang H, Brédas JL. Organic Higher-Order Topological Insulators: Heterotriangulene-Based Covalent Organic Frameworks. J Am Chem Soc 2022; 144:22778-22786. [PMID: 36469524 DOI: 10.1021/jacs.2c11229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
The ability to design and control the chemical characteristics of covalent organic frameworks (COFs) offers a new avenue for the development of functional materials, especially with respect to topological properties. Based on density functional theory calculations, by varying the core units through the choice of bridging groups [O, C═O, CH2, or C(CH3)2] and the linker units [acetylene, diacetylene, or benzene], we have designed heterotriangulene-based COFs that are predicted to be two-dimensional higher-order topological insulators (TIs). The higher-order TI characteristics of these COFs are identified via their topological invariants and the presence of in-gap topological corner modes and gapped edge states. The frontier molecular orbital energies of the building moieties play an important role in determining the size of the higher-order TI gap, which we find to be highly dependent on linker units. We also examined the deposition of the COFs on a boron nitride substrate to assess the feasibility of experimental observation of a higher-order TI phase in the organic layer. This work thus provides new insights into heterotriangulene-based COFs and guidance for the exploration of purely organic topological materials.
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Affiliation(s)
- Xiaojuan Ni
- Department of Chemistry and Biochemistry, The University of Arizona, Tucson, Arizona85721-0088, United States
| | - Huaqing Huang
- School of Physics, Peking University, Beijing100871, China.,Collaborative Innovation Center of Quantum Matter, Beijing100871, China
| | - Jean-Luc Brédas
- Department of Chemistry and Biochemistry, The University of Arizona, Tucson, Arizona85721-0088, United States
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24
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Chen D, Jiang Z, Tang Y, Zhou J, Gu Y, He JJ, Yuan J. Electrical and magnetic properties of antiferromagnetic semiconductor MnSi 2N 4 monolayer. Front Chem 2022; 10:1103704. [PMID: 36569959 PMCID: PMC9781922 DOI: 10.3389/fchem.2022.1103704] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2022] [Accepted: 11/28/2022] [Indexed: 12/12/2022] Open
Abstract
Two-dimensional antiferromagnetic semiconductors have triggered significant attention due to their unique physical properties and broad application. Based on first-principles calculations, a novel two-dimensional (2D) antiferromagnetic material MnSi2N4 monolayer is predicted. The calculation results show that the two-dimensional MnSi2N4 prefers an antiferromagnetic state with a small band gap of 0.26 eV. MnSi2N4 has strong antiferromagnetic coupling which can be effectively tuned under strain. Interestingly, the MnSi2N4 monolayer exhibits a half-metallic ferromagnetic properties under an external magnetic field, in which the spin-up electronic state displays a metallic property, while the spin-down electronic state exhibits a semiconducting characteristic. Therefore, 100% spin polarization can be achieved. Two-dimensional MnSi2N4 monolayer has potential application in the field of high-density information storage and spintronic devices.
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Affiliation(s)
- Dongke Chen
- School of Physics and Materials Science Nanchang University, Nanchang, China,School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang, China
| | - Zhengyu Jiang
- School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang, China
| | - Ying Tang
- School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang, China
| | - Junlei Zhou
- School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang, China
| | - Yuzhou Gu
- School of Physics and Electronic Engineering, Jiangsu University, Zhenjiang, China
| | - Jing-Jing He
- College of Information Science and Technology, Nanjing Forestry University, Nanjing, China
| | - Jiaren Yuan
- School of Physics and Materials Science Nanchang University, Nanchang, China,*Correspondence: Jiaren Yuan,
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25
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Hu T, Zhang T, Mu H, Wang Z. Intrinsic Second-Order Topological Insulator in Two-Dimensional Covalent Organic Frameworks. J Phys Chem Lett 2022; 13:10905-10911. [PMID: 36394555 DOI: 10.1021/acs.jpclett.2c02683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
As an intriguing topological phase, higher-order topological insulators have attracted tremendous attention, but the candidate materials are limited in artificial and inorganic systems. In this work, we propose a universal approach to search for two-dimensional (2D) second-order topological insulators (SOTIs) in covalent organic frameworks (COFs) with C3 symmetric cores. The underlying mechanism is illustrated through tight-binding calculations in a star lattice, showing the 2D SOTI in an overlooked energy window between two Kagome-bands with four types of nontrivial band structures. The emergence of the unique topological edge and corner states can be understood from the Su-Schrieffer-Heeger model. Furthermore, using the frontier orbital of the monomer building block as an indicator, the 2D SOTI is directly confirmed in three realistic COFs by first-principles calculations. Our results not only extend the concept of organic topological insulators from first-order to second-order but also demonstrate the universal existence of intrinsic higher-order topology in 2D COFs.
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Affiliation(s)
- Tianyi Hu
- Hefei National Research Center 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, Anhui230026, China
| | - Tingfeng Zhang
- Hefei National Research Center 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, Anhui230026, China
| | - Haimen Mu
- Hefei National Research Center 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, Anhui230026, China
| | - Zhengfei Wang
- Hefei National Research Center 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, Anhui230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei, Anhui230088, China
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26
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Shang C, Liu S, Shao R, Han P, Zang X, Zhang X, Salama KN, Gao W, Lee CH, Thomale R, Manchon A, Zhang S, Cui TJ, Schwingenschlögl U. Experimental Identification of the Second-Order Non-Hermitian Skin Effect with Physics-Graph-Informed Machine Learning. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:e2202922. [PMID: 36372546 PMCID: PMC9799024 DOI: 10.1002/advs.202202922] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Revised: 07/13/2022] [Indexed: 06/16/2023]
Abstract
Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems. The topological invariant of the bulk in d dimensions corresponds to the number of (d - 1)-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that nth order topological phases feature (d - n)-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. An unsupervised approach-physics-graph-informed machine learning (PGIML)-to enhance the data mining ability of machine learning with limited domain knowledge is introduced. Through PGIML, the second-order NHSE in a 2D non-Hermitian topoelectrical circuit is experimentally demonstrated. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.
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Affiliation(s)
- Ce Shang
- King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), Thuwal, 23955-6900, Saudi Arabia
| | - Shuo Liu
- State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China
| | - Ruiwen Shao
- State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China
| | - Peng Han
- King Abdullah University of Science and Technology (KAUST), Computer, Electrical, and Mathematical Sciences and Engineering Division (CEMSE), Thuwal, 23955-6900, Saudi Arabia
| | - Xiaoning Zang
- King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), Thuwal, 23955-6900, Saudi Arabia
| | - Xiangliang Zhang
- King Abdullah University of Science and Technology (KAUST), Computer, Electrical, and Mathematical Sciences and Engineering Division (CEMSE), Thuwal, 23955-6900, Saudi Arabia
- Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Khaled Nabil Salama
- King Abdullah University of Science and Technology (KAUST), Computer, Electrical, and Mathematical Sciences and Engineering Division (CEMSE), Thuwal, 23955-6900, Saudi Arabia
| | - Wenlong Gao
- Paderborn University, Department of Physics, Warburger Str. 100, 33098, Paderborn, Germany
| | - Ching Hua Lee
- Department of Physics, National University of Singapore, Singapore, 117551, Republic of Singapore
| | - Ronny Thomale
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074, Würzburg, Germany
| | | | - Shuang Zhang
- Department of Physics, The University of Hong Kong, Hong Kong, China
| | - Tie Jun Cui
- State Key Laboratory of Millimeter Waves, Southeast University, Nanjing, 210096, China
| | - Udo Schwingenschlögl
- King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering Division (PSE), Thuwal, 23955-6900, Saudi Arabia
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Abstract
Two-dimensional (2D) polymers have garnered widespread interest because of their intriguing physicochemical properties. Envisaged applications in fields including nanodevices, solid-state chemistry, physical organic chemistry, and condensed matter physics, however, demand high-quality and large-scale production. In this perspective, we first introduce exotic band structures of organic frameworks holding honeycomb, kagome, and Lieb lattices. We further discuss how mesoscale ordered 2D polymers can be synthesized by means of choosing suitable monomers and optimizing growth conditions. We describe successful polymerization strategies to introducing a non-benzenoid subunit into a π-conjugated carbon lattice via delicately designed monomer precursors. Also, to obviate transfer and restore the intrinsic properties of π-conjugated polymers, new paradigms of aryl-aryl coupling on inert surfaces are discussed. Recent achievements in the photopolymerization demonstrate the need for monomer design. We conclude the potential applications of these organic networks and project the future possibilities in providing new insights into on-surface polymerization.
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Affiliation(s)
- Tianchao Niu
- Beihang Hangzhou Innovation Institute Yuhang, Xixi Octagon City, Yuhang District, Hangzhou 310023, China
| | - Chenqiang Hua
- Beihang Hangzhou Innovation Institute Yuhang, Xixi Octagon City, Yuhang District, Hangzhou 310023, China
| | - Miao Zhou
- Beihang Hangzhou Innovation Institute Yuhang, Xixi Octagon City, Yuhang District, Hangzhou 310023, China
- School of Physics, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100191, China
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28
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Mao N, Li R, Dai Y, Huang B, Yan B, Niu C. Orbital Shift-Induced Boundary Obstructed Topological Materials with a Large Energy Gap. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:e2202564. [PMID: 35905489 PMCID: PMC9507389 DOI: 10.1002/advs.202202564] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 06/08/2022] [Indexed: 06/15/2023]
Abstract
Boundary obstructed topological phases caused by Wannier orbital shift between ordinary atomic sites are proposed, which, however, cannot be indicated by symmetry eigenvalues at high symmetry momenta (symmetry indicators) in bulk. On the open boundary, Wannier charge centers can shift to different atoms from those in bulk, leading to in-gap surface states, higher-order hinge states or corner states. To demonstrate such orbital shift-induced boundary obstructed topological insulators, eight material candidates are predicted, all of which are overlooked in the present topological databases. Metallic surface states, hinge states, or corner states cover the large bulk energy gap (e.g., more than 1 eV in TlGaTe2 ) at related boundary, which are ready for experimental detection. Additionally, these materials are also fragile topological insulators with hourglass-like surface states.
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Affiliation(s)
- Ning Mao
- School of PhysicsState Key Laboratory of Crystal MaterialsShandong UniversityJinan250100China
| | - Runhan Li
- School of PhysicsState Key Laboratory of Crystal MaterialsShandong UniversityJinan250100China
| | - Ying Dai
- School of PhysicsState Key Laboratory of Crystal MaterialsShandong UniversityJinan250100China
| | - Baibiao Huang
- School of PhysicsState Key Laboratory of Crystal MaterialsShandong UniversityJinan250100China
| | - Binghai Yan
- Department of Condensed Matter PhysicsWeizmann Institute of ScienceRehovotIsrael
| | - Chengwang Niu
- School of PhysicsState Key Laboratory of Crystal MaterialsShandong UniversityJinan250100China
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29
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Wang C, Liu F, Huang H. Effective Model for Fractional Topological Corner Modes in Quasicrystals. PHYSICAL REVIEW LETTERS 2022; 129:056403. [PMID: 35960584 DOI: 10.1103/physrevlett.129.056403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 07/06/2022] [Indexed: 06/15/2023]
Abstract
High-order topological insulators (HOTIs), as generalized from topological crystalline insulators, are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special k points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and momentum is no longer a good quantum number. Here, we develop a low-energy effective model underlying HOTI states in 2D quasicrystals for all possible rotational symmetries. By implementing a novel Fourier transform developed recently for quasicrystals and approximating the long-wavelength behavior by their large-scale average, we construct an effective k·p Hamiltonian to capture the band inversion at the center of a pseudo-Brillouin zone. We show that an in-plane Zeeman field can induce mass kinks at the intersection of adjacent edges of a 2D quasicrystal topological insulators and generate corner modes (CMs) with fractional charge, protected by rotational symmetries. Our model predictions are confirmed by numerical tight-binding calculations. Furthermore, when the quasicrystal is proximitized by an s-wave superconductor, Majorana CMs can also be created by tuning the field strength and chemical potential. Our work affords a generic approach to studying the low-energy physics of quasicrystals, in association with topological excitations and fractional statistics.
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Affiliation(s)
- Citian Wang
- School of Physics, Peking University, Beijing 100871, China
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA
| | - Huaqing Huang
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Center for High Energy Physics, Peking University, Beijing 100871, China
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30
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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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31
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Su B, Huang Y, Hou YH, Li J, Yang R, Ma Y, Yang Y, Zhang G, Zhou X, Luo J, Chen Z. Persistence of Monoclinic Crystal Structure in 3D Second-Order Topological Insulator Candidate 1T'-MoTe 2 Thin Flake Without Structural Phase Transition. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2022; 9:e2101532. [PMID: 34923770 PMCID: PMC8844473 DOI: 10.1002/advs.202101532] [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: 05/31/2021] [Revised: 10/29/2021] [Indexed: 05/29/2023]
Abstract
A van der Waals material, MoTe2 with a monoclinic 1T' crystal structure is a candidate for 3D second-order topological insulators (SOTIs) hosting gapless hinge states and insulating surface states. However, due to the temperature-induced structural phase transition, the monoclinic 1T' structure of MoTe2 is transformed into the orthorhombic Td structure as the temperature is lowered, which hinders the experimental verification and electronic applications of the predicted SOTI state at low temperatures. Here, systematic Raman spectroscopy studies of the exfoliated MoTe2 thin flakes with variable thicknesses at different temperatures, are presented. As a spectroscopic signature of the orthorhombic Td structure of MoTe2 , the out-of-plane vibration mode D at ≈ 125 cm-1 is always visible below a certain temperature in the multilayer flakes thicker than ≈ 27.7 nm, but vanishes in the temperature range from 80 to 320 K when the flake thickness becomes lower than ≈ 19.5 nm. The absence of the out-of-plane vibration mode D in the Raman spectra here demonstrates not only the disappearance of the monoclinic-to-orthorhombic phase transition but also the persistence of the monoclinic 1T' structure in the MoTe2 thin flakes thinner than ≈ 19.5 nm at low temperatures down to 80 K, which may be caused by the high enough density of the holes introduced during the gold-enhanced exfoliation process and exposure to air. The MoTe2 thin flakes with the low-temperature monoclinic 1T' structure provide a material platform for realizing SOTI states in van der Waals materials at low temperatures, which paves the way for developing a new generation of electronic devices based on SOTIs.
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Affiliation(s)
- Bo Su
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Physical SciencesUniversity of Chinese Academy of SciencesBeijing100190China
| | - Yuan Huang
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
| | - Yan Hui Hou
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Materials Science and EngineeringTianjin University of TechnologyTianjin300384China
| | - Jiawei Li
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Physical SciencesUniversity of Chinese Academy of SciencesBeijing100190China
| | - Rong Yang
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
| | - Yongchang Ma
- School of Materials Science and EngineeringTianjin University of TechnologyTianjin300384China
| | - Yang Yang
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
| | - Guangyu Zhang
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Physical SciencesUniversity of Chinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
- Collaborative Innovation Center of Quantum MatterBeijingChina
| | - Xingjiang Zhou
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Physical SciencesUniversity of Chinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
- Collaborative Innovation Center of Quantum MatterBeijingChina
| | - Jianlin Luo
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Physical SciencesUniversity of Chinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
- Collaborative Innovation Center of Quantum MatterBeijingChina
| | - Zhi‐Guo Chen
- Beijing National Laboratory for Condensed Matter PhysicsInstitute of PhysicsChinese Academy of SciencesBeijing100190China
- School of Physical SciencesUniversity of Chinese Academy of SciencesBeijing100190China
- Songshan Lake Materials LaboratoryDongguan523808China
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32
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Chen C, Zeng XT, Chen Z, Zhao YX, Sheng XL, Yang SA. Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne. PHYSICAL REVIEW LETTERS 2022; 128:026405. [PMID: 35089745 DOI: 10.1103/physrevlett.128.026405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Revised: 11/11/2021] [Accepted: 12/21/2021] [Indexed: 06/14/2023]
Abstract
Real topological phases featuring real Chern numbers and second-order boundary modes have been a focus of current research, but finding their material realization remains a challenge. Here, based on first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized three-dimensional (3D) graphdiyne as the first realistic example of the recently proposed second-order real nodal-line semimetal. We show that the material hosts a pair of real nodal rings, each protected by two topological charges: a real Chern number and a 1D winding number. The two charges generate distinct topological boundary modes at distinct boundaries. The real Chern number leads to a pair of hinge Fermi arcs, whereas the winding number protects a double drumhead surface bands. We develop a low-energy model for 3D graphdiyne which captures the essential topological physics. Experimental aspects and possible topological transition to a 3D real Chern insulator phase are discussed.
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Affiliation(s)
- Cong Chen
- School of Physics, Beihang University, Beijing 100191, China
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Xu-Tao Zeng
- School of Physics, Beihang University, Beijing 100191, China
| | - Ziyu Chen
- School of Physics, Beihang University, Beijing 100191, China
| | - Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Xian-Lei Sheng
- School of Physics, Beihang University, Beijing 100191, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
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33
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Xie Z, Zhang B, Ge Y, Zhu Y, Nie G, Song Y, Lim CK, Zhang H, Prasad PN. Chemistry, Functionalization, and Applications of Recent Monoelemental Two-Dimensional Materials and Their Heterostructures. Chem Rev 2021; 122:1127-1207. [PMID: 34780169 DOI: 10.1021/acs.chemrev.1c00165] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
The past decades have witnessed a rapid expansion in investigations of two-dimensional (2D) monoelemental materials (Xenes), which are promising materials in various fields, including applications in optoelectronic devices, biomedicine, catalysis, and energy storage. Apart from graphene and phosphorene, recently emerging 2D Xenes, specifically graphdiyne, borophene, arsenene, antimonene, bismuthene, and tellurene, have attracted considerable interest due to their unique optical, electrical, and catalytic properties, endowing them a broader range of intriguing applications. In this review, the structures and properties of these emerging Xenes are summarized based on theoretical and experimental results. The synthetic approaches for their fabrication, mainly bottom-up and top-down, are presented. Surface modification strategies are also shown. The wide applications of these emerging Xenes in nonlinear optical devices, optoelectronics, catalysis, biomedicine, and energy application are further discussed. Finally, this review concludes with an assessment of the current status, a description of existing scientific and application challenges, and a discussion of possible directions to advance this fertile field.
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Affiliation(s)
- Zhongjian Xie
- Institute of Pediatrics, Shenzhen Children's Hospital, Shenzhen 518038, Guangdong, P.R. China.,Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Institute of Microscale Optoelectronics, and Otolaryngology Department of the First Affiliated Hospital, Shenzhen Second People's Hospital, Health Science Center, Shenzhen University, Shenzhen 518060, P.R. China
| | - Bin Zhang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Institute of Microscale Optoelectronics, and Otolaryngology Department of the First Affiliated Hospital, Shenzhen Second People's Hospital, Health Science Center, Shenzhen University, Shenzhen 518060, P.R. China
| | - Yanqi Ge
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Institute of Microscale Optoelectronics, and Otolaryngology Department of the First Affiliated Hospital, Shenzhen Second People's Hospital, Health Science Center, Shenzhen University, Shenzhen 518060, P.R. China
| | - Yao Zhu
- Shenzhen Medical Ultrasound Engineering Center, Department of Ultrasonography, Shenzhen People's Hospital, Second Clinical Medical College of Jinan University, First Clinical Medical College of Southern University of Science and Technology, Shenzhen 518020, China
| | - Guohui Nie
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Institute of Microscale Optoelectronics, and Otolaryngology Department of the First Affiliated Hospital, Shenzhen Second People's Hospital, Health Science Center, Shenzhen University, Shenzhen 518060, P.R. China
| | - YuFeng Song
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Institute of Microscale Optoelectronics, and Otolaryngology Department of the First Affiliated Hospital, Shenzhen Second People's Hospital, Health Science Center, Shenzhen University, Shenzhen 518060, P.R. China
| | - Chang-Keun Lim
- Department of Chemical and Materials Engineering, School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan City 010000, Kazakhstan
| | - Han Zhang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Institute of Microscale Optoelectronics, and Otolaryngology Department of the First Affiliated Hospital, Shenzhen Second People's Hospital, Health Science Center, Shenzhen University, Shenzhen 518060, P.R. China
| | - Paras N Prasad
- Institute for Lasers, Photonics, and Biophotonics and Department of Chemistry, University at Buffalo, State University of New York, Buffalo 14260-3000, United States
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34
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Guo J, Sun J, Zhu X, Li CA, Guo H, Feng S. Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:035603. [PMID: 34663768 DOI: 10.1088/1361-648x/ac30b4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Accepted: 10/18/2021] [Indexed: 06/13/2023]
Abstract
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
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Affiliation(s)
- Jiaojiao Guo
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Junsong Sun
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Xingchuan Zhu
- Center for Basic Teaching and Experiment, Nanjing University of Science and Technology, Jiangyin 214443, People's Republic of China
| | - Chang-An Li
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, D-97074 Würzburg, Germany
| | - Huaiming Guo
- Department of Physics, Beihang University, Beijing, 100191, People's Republic of China
| | - Shiping Feng
- Department of Physics, Beijing Normal University, Beijing, 100875, People's Republic of China
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35
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Higher-order topological insulator in cubic semiconductor quantum wells. Sci Rep 2021; 11:21060. [PMID: 34702881 PMCID: PMC8548307 DOI: 10.1038/s41598-021-00577-z] [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: 05/22/2021] [Accepted: 10/07/2021] [Indexed: 11/30/2022] Open
Abstract
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion. We show that the appearance of corner states does not depend solely on the crystallographic orientation of the meeting edges, but also on the growth orientation of the quantum well. Our theoretical results significantly extend the application potential of topological quantum wells based on IV, II–VI and III–V semiconductors with diamond or zinc-blende structures.
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36
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Higher-order topological Mott insulator on the pyrochlore lattice. Sci Rep 2021; 11:20270. [PMID: 34642375 PMCID: PMC8511174 DOI: 10.1038/s41598-021-99213-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2021] [Accepted: 09/14/2021] [Indexed: 11/09/2022] Open
Abstract
We provide the first unbiased evidence for a higher-order topological Mott insulator in three dimensions by numerically exact quantum Monte Carlo simulations. This insulating phase is adiabatically connected to a third-order topological insulator in the noninteracting limit, which features gapless modes around the corners of the pyrochlore lattice and is characterized by a [Formula: see text] spin-Berry phase. The difference between the correlated and non-correlated topological phases is that in the former phase the gapless corner modes emerge only in spin excitations being Mott-like. We also show that the topological phase transition from the third-order topological Mott insulator to the usual Mott insulator occurs when the bulk spin gap solely closes.
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37
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Huang H, Liu F. Structural buckling induced higher-order topology. Natl Sci Rev 2021; 9:nwab170. [PMID: 36091716 PMCID: PMC9450183 DOI: 10.1093/nsr/nwab170] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Revised: 08/03/2021] [Accepted: 08/24/2021] [Indexed: 11/27/2022] Open
Abstract
Higher-order topological insulator (HOTI) states, such as two-dimension (2D) HOTI featured with topologically protected corner modes at the intersection of two gapped crystalline boundaries, have attracted much recent interest. However, the physical mechanism underlying the formation of HOTI states is not fully understood, which has hindered our fundamental understanding and discovery of HOTI materials. Here we propose a mechanistic approach to induce higher-order topological phases via structural buckling of 2D topological crystalline insulators (TCIs). While in-plane mirror symmetry is broken by structural buckling, which destroys the TCI state, the combination of mirror and rotation symmetry is preserved in the buckled system, which gives rise to the HOTI state. We demonstrate that this approach is generally applicable to various 2D lattices with different symmetries and buckling patterns, opening a horizon of possible materials to realize 2D HOTIs. The HOTIs so generated are also shown to be robust against buckling height fluctuation and in-plane displacement. A concrete example is given for the buckled \documentclass[12pt]{minimal}
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}{}$\beta $\end{document}-Sb monolayer from first-principles calculations. Our finding not only enriches our fundamental understanding of higher-order topology, but also opens a new route to discovering HOTI materials.
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Affiliation(s)
- Huaqing Huang
- School of Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Center for High Energy Physics, Peking University, Beijing 100871, China
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, UT 84112, USA
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38
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Huang H, Fan J, Li D, Liu F. Generic Orbital Design of Higher-Order Topological Quasicrystalline Insulators with Odd Five-Fold Rotation Symmetry. NANO LETTERS 2021; 21:7056-7062. [PMID: 34350755 DOI: 10.1021/acs.nanolett.1c02661] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In addition to crystals, topological phases in quasicrystals and disorder systems have drawn increasing attention lately. Here, we propose a generic double band-inversion mechanism underlying the higher-order topological phase in quasicrystals, that is.,"higher-order topological quasicrystalline insulator" (HOTQI), which exploits local atomic orbital and lattice symmetries. It is generally applicable to both quasicrystals and crystals with either odd-rotational (OR) or even-rotational symmetry (ERS), different from previous HOTI mechanisms whose applicability is limited by symmetry types. The HOTQI is characterized by topological corner states at the nonordinary corners of pentagonal (octagonal) samples of five-fold (eight-fold) quasicrystals, which violate the translational invariance and ordinary crystalline symmetries. The role of quasicrystalline symmetry, the robustness against symmetry breaking, and possible experimental realizations are discussed. Our findings not only provide a concrete example of HOTQIs that is incompatible with classical crystallographic symmetry but also offer useful guidance to the search of higher-order topological materials and metamaterials.
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Affiliation(s)
- Huaqing Huang
- School of Physics, Peking University, Beijing 100871, China
- Center for High Energy Physics, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Jiahao Fan
- School of Physics, Peking University, Beijing 100871, China
| | - Dexin Li
- School of Physics, Peking University, Beijing 100871, China
| | - Feng Liu
- Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, United States
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Li CA, Zhang SB, Li J, Trauzettel B. Higher-Order Fabry-Pérot Interferometer from Topological Hinge States. PHYSICAL REVIEW LETTERS 2021; 127:026803. [PMID: 34296912 DOI: 10.1103/physrevlett.127.026803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 04/23/2021] [Accepted: 06/09/2021] [Indexed: 06/13/2023]
Abstract
We propose an intrinsic three-dimensional Fabry-Pérot type interferometer, coined "higher-order interferometer," that is based on the chiral hinge states of second-order topological insulators and cannot be mapped to an equivalent two-dimensional setting because of higher-order topological obstructions. Quantum interference patterns in the two-terminal conductance of this interferometer are controllable not only by tuning the strength but also, particularly, by rotating the direction of the magnetic field applied perpendicularly to the transport direction. Remarkably, the conductance exhibits a characteristic beating pattern with multiple frequencies depending on the field strength and direction in a unique fashion. Our novel interferometer thus provides feasible and robust magnetotransport signatures for hinge states of higher-order topological insulators.
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Affiliation(s)
- Chang-An Li
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - Song-Bo Zhang
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
| | - Jian Li
- School of Science, Westlake University, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China
| | - Björn Trauzettel
- Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany
- Würzburg-Dresden Cluster of Excellence ct.qmat, Germany
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40
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Wang JH, Yang YB, Dai N, Xu Y. Structural-Disorder-Induced Second-Order Topological Insulators in Three Dimensions. PHYSICAL REVIEW LETTERS 2021; 126:206404. [PMID: 34110216 DOI: 10.1103/physrevlett.126.206404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 04/22/2021] [Indexed: 06/12/2023]
Abstract
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge modes protected by crystalline symmetries. Since amorphous solids are ubiquitous, it is important to ask whether such a second-order topological insulator can exist in an amorphous system without any spatial order. Here, we predict the existence of a second-order topological insulating phase in an amorphous system without any crystalline symmetry. Such a topological phase manifests in the winding number of the quadrupole moment, the quantized longitudinal conductance, and the hinge states. Furthermore, in stark contrast to the viewpoint that structural disorder should be detrimental to the higher-order topological phase, we remarkably find that structural disorder can induce a second-order topological insulator from a topologically trivial phase in a regular geometry. We finally demonstrate the existence of a second-order topological phase in amorphous systems with time-reversal symmetry.
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Affiliation(s)
- Jiong-Hao Wang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yan-Bin Yang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Ning Dai
- 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
- Shanghai Qi Zhi Institute, Shanghai 200030, People's Republic of China
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41
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Zhao YX, Chen C, Sheng XL, Yang SA. Switching Spinless and Spinful Topological Phases with Projective PT Symmetry. PHYSICAL REVIEW LETTERS 2021; 126:196402. [PMID: 34047612 DOI: 10.1103/physrevlett.126.196402] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2020] [Revised: 01/21/2021] [Accepted: 04/07/2021] [Indexed: 06/12/2023]
Abstract
A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry PT satisfies (PT)^{2}=±1 for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamental classes via Z_{2} projective representations. For PT symmetry, this occurs when P inverses the gauge transformation needed to recover the original Z_{2} gauge connections under P. As a result, we can achieve topological phases originally unique for spinful systems in a spinless system, and vice versa. We explicitly demonstrate the claimed mechanism with several concrete models, such as Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems, and real topological phases in spinful systems. Possible experimental realization of these models is discussed. Our work breaks a fundamental limitation on topological phases and opens an unprecedented possibility to realize intriguing topological phases in previously impossible systems.
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Affiliation(s)
- Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Cong Chen
- School of Physics, and Key Laboratory of Micro-nano Measurement-Manipulation and Physics, Beihang University, Beijing 100191, China
| | - Xian-Lei Sheng
- School of Physics, and Key Laboratory of Micro-nano Measurement-Manipulation and Physics, Beihang University, Beijing 100191, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
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42
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Zhou L. Floquet Second-Order Topological Phases in Momentum Space. NANOMATERIALS (BASEL, SWITZERLAND) 2021; 11:1170. [PMID: 33947026 PMCID: PMC8146154 DOI: 10.3390/nano11051170] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Revised: 04/04/2021] [Accepted: 04/26/2021] [Indexed: 11/30/2022]
Abstract
Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are demonstrated in a two-dimensional extension of the quantum double-kicked rotor. The found Floquet HOTPs are protected by chiral symmetry and characterized by a pair of topological invariants, which could take arbitrarily large integer values with the increase of kicking strengths. These topological numbers are shown to be measurable from the chiral dynamics of wave packets. Under open boundary conditions, multiple quartets Floquet corner modes with zero and π quasienergies emerge in the system and coexist with delocalized bulk states at the same quasienergies, forming second-order Floquet topological bound states in the continuum. The number of these corner modes is further counted by the bulk topological invariants according to the relation of bulk-corner correspondence. Our findings thus extend the study of HOTPs to momentum-space lattices and further uncover the richness of HOTPs and corner-localized bound states in continuum in Floquet systems.
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Affiliation(s)
- Longwen Zhou
- Department of Physics, College of Information Science and Engineering, Ocean University of China, Qingdao 266100, China
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43
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Jin L, Wang L, Zhang X, Liu Y, Dai X, Gao H, Liu G. Fully spin-polarized Weyl fermions and in/out-of-plane quantum anomalous Hall effects in a two-dimensional d 0 ferromagnet. NANOSCALE 2021; 13:5901-5909. [PMID: 33725053 DOI: 10.1039/d0nr07556f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The quantum anomalous Hall effect (QAHE) in intrinsic ferromagnets has attracted considerable attention recently. Previously, studies of the QAHE have mostly focused on the default assumption of out-of-plane magnetization. In fact, the QAHE can also be achieved via in-plane magnetization, but such candidate materials are very scarce. Here, we find that two-dimensional (2D) YN2 not only possesses the previously reported out-of-plane QAHE, but it also possesses a tunable in-plane QAHE. More importantly, unlike the previously reported in-plane QAHE in d/f-type ferromagnets, here we report the effect in a 2D d0 ferromagnet, namely YN2, for the first time. In the ground state, a YN2 monolayer has a half-metal band structure, and manifests six pairs of fully spin-polarized Weyl points at the Fermi level. When spin-orbit coupling is included, the YN2 monolayer can realize multiple topological phases, determined based on the magnetization direction. Under in-plane magnetization, the YN2 monolayer shows either the Weyl state or in-plane QAHE state. Remarkably, the Chern number (±1) and the propagating direction of QAHE edge channels can be continuously switched via shifting the direction of the in-plane magnetic field. When magnetization is applied out-of-plane, the YN2 monolayer realizes an out-of-plane QAHE phase with a high Chern number of 3. The nontrivial edge states for all the topological phases in the YN2 monolayer have been clearly identified. This work suggests that 2D YN2 is an excellent candidate for investigating in-plane QAHE phases in d0 ferromagnets.
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Affiliation(s)
- Lei Jin
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China.
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44
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Liu B, Xian L, Mu H, Zhao G, Liu Z, Rubio A, Wang ZF. Higher-Order Band Topology in Twisted Moiré Superlattice. PHYSICAL REVIEW LETTERS 2021; 126:066401. [PMID: 33635687 DOI: 10.1103/physrevlett.126.066401] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 01/21/2021] [Indexed: 06/12/2023]
Abstract
The two-dimensional (2D) twisted bilayer materials with van der Waals coupling have ignited great research interests, paving a new way to explore the emergent quantum phenomena by twist degree of freedom. Generally, with the decreasing of twist angle, the enhanced interlayer coupling will gradually flatten the low-energy bands and isolate them by two high-energy gaps at zero and full filling, respectively. Although the correlation and topological physics in the low-energy flat bands have been intensively studied, little information is available for these two emerging gaps. In this Letter, we predict a 2D second-order topological insulator (SOTI) for twisted bilayer graphene and twisted bilayer boron nitride in both zero and full filling gaps. Employing a tight-binding Hamiltonian based on first-principles calculations, three unique fingerprints of 2D SOTI are identified, that is, nonzero bulk topological index, gapped topological edge state, and in-gap topological corner state. Most remarkably, the 2D SOTI exists in a wide range of commensurate twist angles, which is robust to microscopic structure disorder and twist center, greatly facilitating the possible experimental measurement. Our results not only extend the higher-order band topology to massless and massive twisted moiré superlattice, but also demonstrate the importance of high-energy bands for fully understanding the nontrivial electronics.
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Affiliation(s)
- 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
| | - Lede Xian
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - 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
| | - Gan Zhao
- 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
| | - Zhao 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
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center for Computational Quantum Physics, Simons Foundation Flatiron Institute, New York, New York 10010, USA
- Nano-Bio Spectroscopy Group, Departamento de Fisica de Materiales, Universidad del País Vasco, UPV/EHU-20018 San Sebastián, Spain
| | - Z F 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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45
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Meng W, Liu W, Zhang X, Liu Y, Dai X, Liu G. Novel topological states of nodal points and nodal rings in 2D planar octagon TiB 4. NANOSCALE 2021; 13:3194-3200. [PMID: 33527968 DOI: 10.1039/d0nr08015b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Topological states of matter in two-dimensional (2D) materials have received increasing attention due to their potential applications in nanoscale spintronics. Here, we report the presence of unique topological electronic properties in a 2D planar octagon TiB4 compound. Particularly, without considering the spin-orbit coupling (SOC), we found that the material showed a coexistence of novel quadratic node (QN), and two different types of nodal rings (NRs), namely type-I and type-II. The protection mechanism of fermions has been fully clarified in this study. Furthermore, these fermions showed clear edge states. It is worth noting that QN had a topological charge of 2 since it is different from linear nodes and exhibit clear Fermi arc edge states. Under lattice strain, we found that the system could further exhibit rich topological phase transition. When SOC was included, we determined that these crossing points open very tiny energy gaps, which were smaller than previously reported 3D and 2D examples. These results show that monolayer TiB4 is an excellent nodal point and nodal ring semimetal, which also provides a feasible member for studying potential entanglements among multiple fermions.
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Affiliation(s)
- Weizhen Meng
- State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China.
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46
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47
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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: 35] [Impact Index Per Article: 8.8] [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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48
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Wang K, Dai JX, Shao LB, Yang SA, Zhao YX. Boundary Criticality of PT-Invariant Topology and Second-Order Nodal-Line Semimetals. PHYSICAL REVIEW LETTERS 2020; 125:126403. [PMID: 33016751 DOI: 10.1103/physrevlett.125.126403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Accepted: 08/06/2020] [Indexed: 06/11/2023]
Abstract
For conventional topological phases, the boundary gapless modes are determined by bulk topological invariants. Based on developing an analytic method to solve higher-order boundary modes, we present PT-invariant 2D topological insulators and 3D topological semimetals that go beyond this bulk-boundary correspondence framework. With unchanged bulk topological invariants, their first-order boundaries undergo transitions separating different phases with second-order boundary zero modes. For the 2D topological insulator, the helical edge modes appear at the transition point for two second-order topological insulator phases with diagonal and off-diagonal corner zero modes, respectively. Accordingly, for the 3D topological semimetal, the criticality corresponds to surface helical Fermi arcs of a Dirac semimetal phase. Interestingly, we find that the 3D system generically belongs to a novel second-order nodal-line semimetal phase, possessing gapped surfaces but a pair of diagonal or off-diagonal hinge Fermi arcs.
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Affiliation(s)
- Kai Wang
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Jia-Xiao Dai
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - L B Shao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Shengyuan A Yang
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Y X Zhao
- National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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49
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Chen C, Song Z, Zhao JZ, Chen Z, Yu ZM, Sheng XL, Yang SA. Universal Approach to Magnetic Second-Order Topological Insulator. PHYSICAL REVIEW LETTERS 2020; 125:056402. [PMID: 32794859 DOI: 10.1103/physrevlett.125.056402] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 07/06/2020] [Indexed: 06/11/2023]
Abstract
We propose a universal practical approach to realize magnetic second-order topological insulator (SOTI) materials, based on properly breaking the time reversal symmetry in conventional (first-order) topological insulators. The approach works for both three dimensions (3D) and two dimensions (2D), and is particularly suitable for 2D, where it can be achieved by coupling a quantum spin Hall insulator with a magnetic substrate. Using first-principles calculations, we predict bismuthene on EuO(111) surface as the first realistic system for a two-dimensional magnetic SOTI. We explicitly demonstrate the existence of the protected corner states. Benefitting from the large spin-orbit coupling and sizable magnetic proximity effect, these corner states are located in a boundary gap ∼83 meV, and hence can be readily probed in experiment. By controlling the magnetic phase transition, a topological phase transition between a first-order TI and a SOTI can be simultaneously achieved in the system. The effect of symmetry breaking, the connection with filling anomaly, and the experimental detection are discussed.
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Affiliation(s)
- Cong Chen
- Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing 100191, China
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
| | - Zhida Song
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jian-Zhou Zhao
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- Sichuan Co-Innovation Center for New Energetic Materials, Southwest University of Science and Technology, Mianyang 621010, China
| | - Ziyu Chen
- Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing 100191, China
| | - Zhi-Ming Yu
- Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
- Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing 100081, China
| | - Xian-Lei Sheng
- Key Laboratory of Micro-nano Measurement-Manipulation and Physics (Ministry of Education), School of Physics, Beihang University, Beijing 100191, China
- 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
- Center for Quantum Transport and Thermal Energy Science, School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China
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Ren Y, Qiao Z, Niu Q. Engineering Corner States from Two-Dimensional Topological Insulators. PHYSICAL REVIEW LETTERS 2020; 124:166804. [PMID: 32383951 DOI: 10.1103/physrevlett.124.166804] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2020] [Accepted: 04/08/2020] [Indexed: 06/11/2023]
Abstract
We theoretically demonstrate that the second-order topological insulator with robust corner states can be realized in two-dimensional Z_{2} topological insulators by applying an in-plane Zeeman field. The Zeeman field breaks the time-reversal symmetry and thus destroys the Z_{2} topological phase. Nevertheless, it respects some crystalline symmetries and thus can protect the higher-order topological phase. By taking the Kane-Mele model as a concrete example, we find that spin-helical edge states along zigzag boundaries are gapped out by the Zeeman field whereas the in-gap corner state at the intersection between two zigzag edges arises, which is independent of the field orientation. We further show that the corner states are robust against the out-of-plane Zeeman field, staggered sublattice potentials, Rashba spin-orbit coupling, and the buckling of honeycomb lattices, making them experimentally feasible. Similar behaviors can also be found in the well-known Bernevig-Hughes-Zhang model.
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Affiliation(s)
- Yafei Ren
- ICQD, Hefei National Laboratory for Physical Sciences at Microscale, CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Zhenhua Qiao
- ICQD, Hefei National Laboratory for Physical Sciences at Microscale, CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qian Niu
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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