1
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Liu Z, Cao PC, Xu L, Xu G, Li Y, Huang J. Higher-Order Topological In-Bulk Corner State in Pure Diffusion Systems. PHYSICAL REVIEW LETTERS 2024; 132:176302. [PMID: 38728705 DOI: 10.1103/physrevlett.132.176302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Accepted: 03/26/2024] [Indexed: 05/12/2024]
Abstract
Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form similarity between Schrödinger equation and diffusion equation, research on higher-order topological insulators has been extended from condensed matter physics to thermal diffusion. Unfortunately, all the corner states of thermal higher-order topological insulator reside within the band gap. Another kind of corner state, which is embedded in the bulk states, has not been realized in pure diffusion systems so far. Here, we construct higher-dimensional Su-Schrieffer-Heeger models based on sphere-rod structure to elucidate these corner states, which we term "in-bulk corner states." Because of the anti-Hermitian properties of diffusive Hamiltonian, we investigate the thermal behavior of these corner states through theoretical calculation, simulation, and experiment. Furthermore, we study the different thermal behaviors of in-bulk corner state and in-gap corner state. Our results would open a different gate for diffusive topological states and provide a distinct application for efficient heat dissipation.
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Affiliation(s)
- Zhoufei Liu
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
| | - Pei-Chao Cao
- State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, The Electromagnetics Academy of Zhejiang University, Zhejiang University, Haining 314400, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Liujun Xu
- Graduate School of China Academy of Engineering Physics, Beijing 100193, China
| | - Guoqiang Xu
- Department of Electrical and Computer Engineering, National University of Singapore, Kent Ridge 117583, Republic of Singapore
| | - Ying Li
- State Key Laboratory of Extreme Photonics and Instrumentation, ZJU-Hangzhou Global Scientific and Technological Innovation Center, Zhejiang University, Hangzhou 310027, China
- International Joint Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang, The Electromagnetics Academy of Zhejiang University, Zhejiang University, Haining 314400, China
- Shaoxing Institute of Zhejiang University, Zhejiang University, Shaoxing 312000, China
| | - Jiping Huang
- Department of Physics, State Key Laboratory of Surface Physics, and Key Laboratory of Micro and Nano Photonic Structures (MOE), Fudan University, Shanghai 200438, China
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2
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Yang YB, Wang JH, Li K, Xu Y. Higher-order topological phases in crystalline and non-crystalline systems: a review. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:283002. [PMID: 38574683 DOI: 10.1088/1361-648x/ad3abd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 04/04/2024] [Indexed: 04/06/2024]
Abstract
In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.
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Affiliation(s)
- Yan-Bin Yang
- Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong Special Administrative Region of China, People's Republic of China
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jiong-Hao Wang
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Kai Li
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - Yong Xu
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
- Hefei National Laboratory, Hefei 230088, People's Republic of China
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3
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Wu HC, Xu HS, Xie LC, Jin L. Edge State, Band Topology, and Time Boundary Effect in the Fine-Grained Categorization of Chern Insulators. PHYSICAL REVIEW LETTERS 2024; 132:083801. [PMID: 38457698 DOI: 10.1103/physrevlett.132.083801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 01/10/2024] [Indexed: 03/10/2024]
Abstract
We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern numbers are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wave function overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wave function overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern numbers. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings.
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Affiliation(s)
- H C Wu
- School of Physics, Nankai University, Tianjin 300071, China
- School of Physics, Zhengzhou University, Zhengzhou 450001, China
| | - H S Xu
- School of Physics, Nankai University, Tianjin 300071, China
| | - L C Xie
- School of Physics, Nankai University, Tianjin 300071, China
| | - L Jin
- School of Physics, Nankai University, Tianjin 300071, China
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4
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Ma Q, Pu Z, Ye L, Lu J, Huang X, Ke M, He H, Deng W, Liu Z. Observation of Higher-Order Nodal-Line Semimetal in Phononic Crystals. PHYSICAL REVIEW LETTERS 2024; 132:066601. [PMID: 38394560 DOI: 10.1103/physrevlett.132.066601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 01/05/2024] [Indexed: 02/25/2024]
Abstract
Higher-order topological insulators and semimetals, which generalize the conventional bulk-boundary correspondence, have attracted extensive research interest. Among them, higher-order Weyl semimetals feature twofold linear crossing points in three-dimensional momentum space, 2D Fermi-arc surface states, and 1D hinge states. Higher-order nodal-point semimetals possessing Weyl points or Dirac points have been implemented. However, higher-order nodal-line or nodal-surface semimetals remain to be further explored in experiments in spite of many previous theoretical efforts. In this work, we realize a second-order nodal-line semimetal in 3D phononic crystals. The bulk nodal lines, 2D drumhead surface states guaranteed by Zak phases, and 1D flat hinge states attributed to k_{z}-dependent quadrupole moments are observed in simulations and experiments. Our findings of nondispersive surface and hinge states may promote applications in acoustic sensing and energy harvesting.
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Affiliation(s)
- Qiyun Ma
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Zhenhang Pu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Liping Ye
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Jiuyang Lu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Xueqin Huang
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Manzhu Ke
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Hailong He
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Weiyin Deng
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
| | - Zhengyou Liu
- Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China
- Institute for Advanced Studies, Wuhan University, Wuhan 430072, China
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5
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Qian C, Jiang Y, Jin J, Christensen T, Soljačić M, Kildishev AV, Zhen B. Topological electromagnetic waves in dispersive and lossy plasma crystals. Sci Rep 2023; 13:20445. [PMID: 37993725 PMCID: PMC10665461 DOI: 10.1038/s41598-023-47848-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 11/19/2023] [Indexed: 11/24/2023] Open
Abstract
Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on dielectric materials with weak dispersions, this study focuses on topological phases in dispersive materials and presents a numerical study of Chern insulators in gaseous-phase plasma cylinder cells. We develop a numerical framework to address the complex material dispersion arising from the plasma medium and external magnetic fields and identify Chern insulator phases that are experimentally achievable. Using this numerical tool, we also explain the flat bands commonly observed in periodic plasmonic structures, via local resonances, and how edge states change as the edge termination is periodically modified. This work opens up opportunities for exploring band topology in new materials with non-trivial dispersions and has potential radio frequency (RF) applications, ranging from plasma-based lighting to plasma propulsion engines.
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Affiliation(s)
- Chen Qian
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, 19104, USA
| | - Yue Jiang
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, 19104, USA
| | - Jicheng Jin
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, 19104, USA
| | - Thomas Christensen
- Massachusetts Institute of Technology, Department of Physics, Cambridge, 02139, USA
| | - Marin Soljačić
- Massachusetts Institute of Technology, Department of Physics, Cambridge, 02139, USA
| | - Alexander V Kildishev
- Elmore Family School of Electrical and Computer Engineering, Purdue University West Lafayette, Birck Nanotechnology Center and Purdue Quantum Science and Engineering Institute (PQSEI), West Lafayette, 47907, USA
| | - Bo Zhen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, 19104, USA.
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6
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Lan Z, Chen Y, Zhu J, Su Z. Quadrupole topological phases and filling anomaly in all-dielectric Lieb lattice photonic crystals. OPTICS LETTERS 2023; 48:5747-5750. [PMID: 37910749 DOI: 10.1364/ol.505145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 10/06/2023] [Indexed: 11/03/2023]
Abstract
While higher-order photonic topological corner states typically are created in systems with nontrivial bulk dipole polarization, they could also be created in systems with vanishing dipole polarization but with nontrivial quadrupole topology, which though is less explored. In this work, we show that simple all-dielectric photonic crystals in the Lieb lattice can host a topologically nontrivial quadrupole bandgap. Through a combination of symmetry analysis of the eigenmodes and explicit calculations of the Wannier bands and their polarization using the Wilson loop method, we demonstrate that the Lieb photonic crystals can have a bandgap with vanishing dipole polarization but with nontrivial quadrupole topology. The nontrivial bulk quadrupole moment could result in edge-localized polarization and topological corner states in systems with open edges. Interestingly, the indices of the corner states show an unusual "3+1" pattern compared to previously known "2+2" pattern, and this new pattern leads to unusual filling anomaly when the corner states are filled. Our work could not only deepen our understanding about quadrupole topology in simple all-dielectric photonic crystals but could also offer new opportunities for practical applications in integrated photonic devices.
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7
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Li X, Rui G, He J, Gu B. Degeneration of topological corner, hinge, and surface states in three-dimensional photonic crystals. OPTICS LETTERS 2023; 48:5332-5335. [PMID: 37831860 DOI: 10.1364/ol.500164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 09/15/2023] [Indexed: 10/15/2023]
Abstract
The third-order topological insulators based on three-dimensional (3D) photonic crystals (PCs) have hardly been achieved because the nontrivial bandgap in 3D PCs is difficult to form. In this Letter, we elaborately construct 3D Su-Schrieffer-Heeger lattice in which the periodic modulation of refractive index is uniform in three axis directions. The high-order topological PCs are characterized by the nontrivial bulk polarizations and the mirror eigenvalues. Such a structure can achieve topological 1-codimensional surface states, 2-codimensional hinge states, and 3-codimensional corner states. More importantly, it is found for the first time, to the best of our knowledge, that the topological states exhibit a degeneration behavior, i. e., the corner, and hinge state, or corner and surface states coexist at nearly the same frequency, but maintain their own mode properties. The multiple topological states in 3D PCs as well as the degeneration of topological states will open a new window for the study of topological photonics.
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8
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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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9
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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10
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Hu W, Liu C, Dai X, Wen S, Xiang Y. Second harmonic generation by matching the phase distributions of topological corner and edge states. OPTICS LETTERS 2023; 48:2341-2344. [PMID: 37126269 DOI: 10.1364/ol.489194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Second harmonic generation (SHG) in topological photonic crystals is chiefly concerned with frequency conversion between the same topological states. However, little attention has been paid to the effect of coupling between different topological states on the SHG. In this study, we propose a method for achieving optimal SHG in a topological cavity by matching the phase distributions of the electric fields of the topological corner state (TCS) and topological edge state (TES). Our results show that the intrinsic efficiency can be improved when the phase distributions of the fundamental wave within the TCS and the second harmonic wave within the TES have the same symmetry. Otherwise, conversion efficiency will be greatly inhibited. With this method, we achieved an optimal intrinsic efficiency of 0.165%. Such a platform may enable the development of integrated nanoscale light sources and on-chip frequency converters.
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Wang Q, Qian J, Jiang L. Non-Hermitian kagome photonic crystal with a totally topological spatial mode selection. OPTICS EXPRESS 2023; 31:5363-5377. [PMID: 36823818 DOI: 10.1364/oe.482836] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
Recently, the study of non-Hermitian topological edge and corner states in sonic crystals (SCs) and photonic crystals (PCs) has drawn much attention. In this paper, we propose a Wannier-type higher-order topological insulator (HOTI) model based on the kagome PC containing dimer units and study its non-Hermitian topological corner states. When balanced gain and loss are introduced into the dimer units with a proper parity-time symmetric setting, the system will show asymmetric Wannier bands and can support two Hermitian corner states and two pairs of complex-conjugate or pseudo complex-conjugate non-Hermitian corner states. These topological corner states are solely confined at three corners of the triangular supercell constructed by the trivial and non-trivial kagome PCs, corresponding to a topological spatial mode selection effect. As compared to the non-Hermitian quadrupole-type HOTIs, the non-Hermitian Wannier-type HOTIs can realize totally topological spatial mode selection by using much lower coefficients of gain and loss. Our results pave the way for the development of novel non-Hermitian photonic topological devices based on Wannier-type HOTIs.
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12
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He L, Wu J, Jin J, Mele EJ, Zhen B. Polaritonic Chern Insulators in Monolayer Semiconductors. PHYSICAL REVIEW LETTERS 2023; 130:043801. [PMID: 36763440 DOI: 10.1103/physrevlett.130.043801] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
Systems with strong light-matter interaction open up new avenues for studying topological phases of matter. Examples include exciton polaritons, mixed light-matter quasiparticles, where the topology of the polaritonic band structure arises from the collective coupling between matter wave and optical fields strongly confined in periodic dielectric structures. Distinct from light-matter interaction in a uniform environment, the spatially varying nature of the optical fields leads to a fundamental modification of the well-known optical selection rules, which were derived under the plane wave approximation. Here we identify polaritonic Chern insulators by coupling valley excitons in transition metal dichalcogenides to photonic Bloch modes in a dielectric photonic crystal slab. We show that polaritonic Dirac points, which are markers for topological phase transition points, can be constructed from the collective coupling between valley excitons and photonic Dirac cones in the presence of both time-reversal and inversion symmetries. Lifting exciton valley degeneracy by breaking time-reversal symmetry leads to gapped polaritonic bands with nonzero Chern numbers. Through numerical simulations, we predict polaritonic chiral edge states residing inside the topological gaps. Our Letter paves the way for the further study of strong exciton-photon interaction in nanophotonic structures and for exploring polaritonic topological phases and their practical applications in polaritonic devices.
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Affiliation(s)
- Li He
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jingda Wu
- Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
| | - Jicheng Jin
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Eugene J Mele
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Bo Zhen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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13
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Jin J, He L, Lu J, Mele EJ, Zhen B. Floquet Quadrupole Photonic Crystals Protected by Space-Time Symmetry. PHYSICAL REVIEW LETTERS 2022; 129:063902. [PMID: 36018645 DOI: 10.1103/physrevlett.129.063902] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Revised: 08/25/2021] [Accepted: 07/19/2022] [Indexed: 06/15/2023]
Abstract
High-order topological phases, such as those with nontrivial quadrupole moments [1,2], protect edge states that are themselves topological insulators in lower dimensions. So far, most quadrupole phases of light are explored in linear optical systems, which are protected by spatial symmetries [3] or synthetic symmetries [1,2,4-7]. Here we present Floquet quadrupole phases in driven nonlinear photonic crystals that are protected by space-time screw symmetries [8]. We start by illustrating space-time symmetries by tracking the trajectory of instantaneous optical axes of the driven media. Our Floquet quadrupole phase is then confirmed in two independent ways: symmetry indices at high-symmetry momentum points and calculations of the nested Wannier bands. Our Letter presents a general framework to analyze symmetries in driven optical materials and paves the way to further exploring symmetry-protected topological phases in Floquet systems and their optoelectronic applications.
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Affiliation(s)
- Jicheng Jin
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Li He
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jian Lu
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Eugene J Mele
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Bo Zhen
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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14
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Li Y, Fan C, Hu X, Ao Y, Lu C, Chan CT, Kennes DM, Gong Q. Effective Hamiltonian for Photonic Topological Insulator with Non-Hermitian Domain Walls. PHYSICAL REVIEW LETTERS 2022; 129:053903. [PMID: 35960552 DOI: 10.1103/physrevlett.129.053903] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Accepted: 07/12/2022] [Indexed: 06/15/2023]
Abstract
The gain and loss in photonic lattices provide possibilities for many functional phenomena. In this Letter, we consider photonic topological insulators with different types of gain-loss domain walls, which will break the translational symmetry of the lattices. A method is proposed to construct effective Hamiltonians, which accurately describe states and the corresponding energies at the domain walls for different types of photonic topological insulators and domain walls with arbitrary shapes. We also consider domain-induced higher-order topological states in two-dimensional non-Hermitian Aubry-André-Harper lattices and use our method to explain such phenomena successfully. Our results reveal the physics in photonic topological insulators with gain-loss domain walls, which provides advanced pathways for manipulation of non-Hermitian topological states in photonic systems.
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Affiliation(s)
- Yandong Li
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, People's Republic of China
| | - Chongxiao Fan
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, People's Republic of China
- Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Hamburg, Germany
| | - Xiaoyong Hu
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, People's Republic of China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China
| | - Yutian Ao
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, People's Republic of China
| | - Cuicui Lu
- Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrane Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, People's Republic of China
| | - C T Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - Dante M Kennes
- Institute for Theory of Statistical Physics, RWTH Aachen University, and JARA Fundamentals of Future Information Technology, 52062 Aachen, Germany
- Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Hamburg, Germany
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics & Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, People's Republic of China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China
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15
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Benalcazar WA, Cerjan A. Chiral-Symmetric Higher-Order Topological Phases of Matter. PHYSICAL REVIEW LETTERS 2022; 128:127601. [PMID: 35394298 DOI: 10.1103/physrevlett.128.127601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 02/17/2022] [Indexed: 06/14/2023]
Abstract
We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by "multipole chiral numbers," bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order topological phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.
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Affiliation(s)
- Wladimir A Benalcazar
- Department of Physics, Princeton University, Princeton, New Jersey 08542, USA
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Alexander Cerjan
- Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
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16
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Liang L, Zhou X, Hu JH, Wang HX, Jiang JH, Hou B. Rainbow trapping based on higher-order topological corner modes. OPTICS LETTERS 2022; 47:1454-1457. [PMID: 35290337 DOI: 10.1364/ol.451770] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2021] [Accepted: 02/02/2022] [Indexed: 06/14/2023]
Abstract
The recent advancements in higher-order topology have provided unprecedented opportunities in optical device designs and applications. Here, we propose a new, to the best of our knowledge, method to realize rainbow trapping based on higher-order topological corner modes (HOTCMs), which are constructed by two configurations of breathing kagome photonic crystals with distinct topological phases. Interestingly, the HOTCMs localized at corners with different geometric configurations are found to be frequency dispersive and thus initiate the possible application in realizing rainbow trapping. By designing a polygon structure containing several configurations of corners, we demonstrate that the HOTCMs can be excited with the frequency sequence locked to the corner order (clockwise/anticlockwise direction) in the polygon. The reported HOTCMs provide a new mechanism to realize multiple-frequency trapping, which may find potential applications in future integrated photonics.
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17
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Yan Q, Cao E, Sun Q, Ao Y, Hu X, Shi X, Gong Q, Misawa H. Near-Field Imaging and Time-Domain Dynamics of Photonic Topological Edge States in Plasmonic Nanochains. NANO LETTERS 2021; 21:9270-9278. [PMID: 34670093 DOI: 10.1021/acs.nanolett.1c03324] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Time-domain dynamic evolution properties of topological states play an important role in both fundamental physics study and practical applications of topological photonics. However, owing to the absence of available ultrafast time-domain dynamic characterization methods, studies have mostly focused on the frequency-domain-based properties, and there are few reports demonstrating the time-domain-based properties. Here, we measured the dynamic near-field responses of plasmonic topological structures of gold nanochains with the configuration of the Su-Schrieffer-Heeger model by using ultrahigh spatial-temporal resolution photoemission electron microscopy. The dephasing time of plasmonic topological edge states increases with increasing the bulk lattice number that has a threshold requirement and finally reaches saturation. We directly revealed through simulation that there is a transient bulk state in the evolution of topological edge states, that is, the energy undergoes relaxation from oscillation between the bulk lattice and the edge. This work shows a new perspective of time-domain dynamic topological photonics.
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Affiliation(s)
- Qiuchen Yan
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan
| | - En Cao
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan
| | - Quan Sun
- Yangtze Delta Institute of Optoelectronics, Peking University, Nantong, Jiangsu 226010, P.R. China
| | - Yutian Ao
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
| | - Xiaoyong Hu
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
- Yangtze Delta Institute of Optoelectronics, Peking University, Nantong, Jiangsu 226010, P.R. China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, P.R. China
| | - Xu Shi
- Creative Research Institution, Hokkaido University, Sapporo 001-0021, Japan
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter and Frontiers Science Center for Nano-optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, P.R. China
- Yangtze Delta Institute of Optoelectronics, Peking University, Nantong, Jiangsu 226010, P.R. China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, P.R. China
| | - Hiroaki Misawa
- Research Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan
- Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan
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18
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Wu Y, Yan M, Lin ZK, Wang HX, Li F, Jiang JH. On-chip higher-order topological micromechanical metamaterials. Sci Bull (Beijing) 2021; 66:1959-1966. [PMID: 36654165 DOI: 10.1016/j.scib.2021.06.024] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Revised: 06/16/2021] [Accepted: 06/21/2021] [Indexed: 01/20/2023]
Abstract
Metamaterials with higher-order topological band gaps that exhibit topological physics beyond the bulk-edge correspondence provide unique application values due to their ability of integrating topological boundary states at multiple dimensions in a single chip. On the other hand, in the past decade, micromechanical metamaterials are developing rapidly for various applications such as micro-piezoelectric-generators, intelligent micro-systems, on-chip sensing and self-powered micro-systems. To empower these cutting-edge applications with topological manipulations of elastic waves, higher-order topological mechanical systems working at high frequencies (MHz) with high quality-factors are demanded. The current realizations of higher-order topological mechanical systems, however, are still limited to systems with large scales (centimetres) and low frequencies (kHz). Here, we report the first experimental realization of an on-chip micromechanical metamaterial as the higher-order topological insulator for elastic waves at MHz. The higher-order topological phononic band gap is induced by the band inversion at the Brillouin zone corner which is achieved by configuring the orientations of the elliptic pillars etched on the silicon chip. With consistent experiments, theory and simulations, we demonstrate the emergence of coexisting topological edge and corner states in a single silicon chip as induced by the higher-order band topology. The experimental realization of on-chip micromechanical metamaterials with higher-order topology opens a new regime for materials and applications based on topological elastic waves.
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Affiliation(s)
- Ying Wu
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Mou Yan
- School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China
| | - Zhi-Kang Lin
- School of Physical Science and Technology & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
| | - Hai-Xiao Wang
- School of Physical Science and Technology, Guangxi Normal University, Guilin 541004, China
| | - Feng Li
- Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE) and School of Physics, Beijing Institute of Technology, Beijing 100081, China.
| | - Jian-Hua Jiang
- School of Physical Science and Technology & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China; Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China.
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19
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Yoshida T, Mizoguchi T, Hatsugai Y. Chiral edge modes in evolutionary game theory: A kagome network of rock-paper-scissors cycles. Phys Rev E 2021; 104:025003. [PMID: 34525642 DOI: 10.1103/physreve.104.025003] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2021] [Accepted: 07/13/2021] [Indexed: 11/07/2022]
Abstract
We theoretically demonstrate the realization of a chiral edge mode in a system beyond natural science. Specifically, we elucidate that a kagome network of rock-paper-scissors (K-RPS) hosts a chiral edge mode of the population density which is protected by the nontrivial topology in the bulk. The emergence of the chiral edge mode is demonstrated by numerically solving the Lotka-Volterra (LV) equation. This numerical result can be intuitively understood in terms of the cyclic motion of a single rock-paper-scissors cycle, which is analogous to the cyclotron motion of fermions. Furthermore, we point out that a linearized LV equation is mathematically equivalent to the Schrödinger equation describing quantum systems. This equivalence allows us to clarify the topological origin of the chiral edge mode in the K-RPS; a nonzero Chern number of the payoff matrix induces the chiral edge mode of the population density, which exemplifies the bulk-edge correspondence in two-dimensional systems described by evolutionary game theory.
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Affiliation(s)
- Tsuneya Yoshida
- Department of Physics, University of Tsukuba, Ibaraki 305-8571, Japan
| | | | - Yasuhiro Hatsugai
- Department of Physics, University of Tsukuba, Ibaraki 305-8571, Japan
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20
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Xie X, Dang J, Yan S, Zhang W, Hao H, Xiao S, Shi S, Zuo Z, Ni H, Niu Z, Zhang X, Wang C, Xu X. Optimization and robustness of the topological corner state in second-order topological photonic crystals. OPTICS EXPRESS 2021; 29:30735-30750. [PMID: 34614794 DOI: 10.1364/oe.438474] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2021] [Accepted: 08/20/2021] [Indexed: 06/13/2023]
Abstract
The second-order topological photonic crystal with the 0D corner state provides a new way to investigate cavity quantum electrodynamics and develop topological nanophotonic devices with diverse functionalities. Here, we report on the optimization and robustness of the topological corner state in the second-order topological photonic crystal both in theory and in experiment. The topological nanocavity is formed based on the 2D generalized Su-Schrieffer-Heeger model. The quality factor of the corner state is optimized theoretically and experimentally by changing the gap between two photonic crystals or just modulating the position or size of the airholes surrounding the corner. The fabricated quality factors are further optimized by the surface passivation treatment which reduces surface absorption. A maximum quality factor of the fabricated devices is about 6000, which is the highest value ever reported for the active topological corner state. Furthermore, we demonstrate the robustness of the corner state against strong disorders including the bulk defect, edge defect, and even corner defect. Our results lay a solid foundation for further investigations and applications of the topological corner state, such as the investigation of a strong coupling regime and the development of optical devices for topological nanophotonic circuitry.
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21
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Gong R, Zhang M, Li H, Lan Z. Topological photonic crystal fibers based on second-order corner modes. OPTICS LETTERS 2021; 46:3849-3852. [PMID: 34388757 DOI: 10.1364/ol.430579] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2021] [Accepted: 07/08/2021] [Indexed: 06/13/2023]
Abstract
Photonic crystal fibers represent one of the most active research fields in modern fiber optics. The recent advancements in topological photonics have inspired new fiber concepts and designs. Here, we demonstrate a new, to the best of our knowledge, type of topological photonic crystal fiber based on second-order photonic corner modes from the Su-Schrieffer-Heeger model. Different from previous works where the in-plane properties at kz=0 have been mainly studied, we find that in the fiber configuration of kz>0, a topological bandgap exists only when the propagation constant kz along the fiber axis is larger than a certain threshold and the emergent topological bandgap at large kz hosts two sets of corner fiber modes. We further investigate the propagation diagrams, propose a convenient way to tune the frequencies of the corner fiber modes within the topological bandgap, and envisage multi-frequency and multi-channel transmission capabilities of this new type of fiber. Our work will not only have practical importance, but could also open a new area for fiber exploration where many existing higher-order topological photonic modes could bring exciting new opportunities for fiber designs and applications.
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22
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Kang B, Lee W, Cho GY. Many-Body Invariants for Chern and Chiral Hinge Insulators. PHYSICAL REVIEW LETTERS 2021; 126:016402. [PMID: 33480785 DOI: 10.1103/physrevlett.126.016402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 12/03/2020] [Indexed: 06/12/2023]
Abstract
We construct new many-body invariants for 2D Chern and 3D chiral hinge insulators characterizing quantized pumping of bulk dipole and quadrupole moments. The many-body invariants are written entirely in terms of many-body ground state wave functions on a torus geometry with twisted boundary conditions and a set of unitary operators. We present a number of supporting arguments for the invariants via topological field theory interpretation, adiabatic pumping argument, and direct mapping to free-fermion band indices. Therefore, the invariants explicitly encircle several different pillars of theoretical descriptions of topological phases. Furthermore, our many-body invariants are written in forms which can be directly employed in various numerics including the exact diagonalization and the density-matrix renormalization group simulations. We finally confirm our invariants by numerical computations including an infinite density-matrix renormalization group on quasi-one-dimensional systems.
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Affiliation(s)
- Byungmin Kang
- School of Physics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Wonjun Lee
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
| | - Gil Young Cho
- Department of Physics, Pohang University of Science and Technology (POSTECH), Pohang 37673, Republic of Korea
- Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea
- Center for Artificial Low Dimensional Electronic Systems, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
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23
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Di Liberto M, Goldman N, Palumbo G. Non-Abelian Bloch oscillations in higher-order topological insulators. Nat Commun 2020; 11:5942. [PMID: 33230167 PMCID: PMC7684321 DOI: 10.1038/s41467-020-19518-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 10/13/2020] [Indexed: 11/09/2022] Open
Abstract
Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to a force. Observed in a wide range of synthetic systems, BOs are intrinsically related to geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry-phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties through the measurement of Berry phases and center-of-mass displacements.
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Affiliation(s)
- M Di Liberto
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium.
| | - N Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium
| | - G Palumbo
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, Brussels, B-1050, Belgium
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24
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Wang HX, Lin ZK, Jiang B, Guo GY, Jiang JH. Higher-Order Weyl Semimetals. PHYSICAL REVIEW LETTERS 2020; 125:146401. [PMID: 33064542 DOI: 10.1103/physrevlett.125.146401] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 09/04/2020] [Accepted: 09/08/2020] [Indexed: 06/11/2023]
Abstract
Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here, we report the theoretical discovery of higher-order Weyl semimetals and thereby the establishment of such an important connection. We demonstrate that higher-order Weyl semimetals can emerge in chiral materials such as chiral tetragonal crystals as the intermediate phase between the conventional Weyl semimetal and 3D higher-order topological phases. Higher-order Weyl semimetals manifest themselves uniquely by exhibiting concurrent chiral Fermi-arc surface states, topological hinge states, and the momentum-dependent fractional hinge charge, revealing a novel class of higher-order topological phases.
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Affiliation(s)
- Hai-Xiao Wang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, 1 Shizi Street, Suzhou 215006, China
- School of Physical Science and Technology, Guangxi Normal University, Guilin 541004, China
- Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 10617, Taiwan
- Physics Division, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan
| | - Zhi-Kang Lin
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, 1 Shizi Street, Suzhou 215006, China
| | - Bin Jiang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, 1 Shizi Street, Suzhou 215006, China
| | - Guang-Yu Guo
- Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 10617, Taiwan
- Physics Division, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan
| | - Jian-Hua Jiang
- School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, 1 Shizi Street, Suzhou 215006, China
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25
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Kim M, Jacob Z, Rho J. Recent advances in 2D, 3D and higher-order topological photonics. LIGHT, SCIENCE & APPLICATIONS 2020; 9:130. [PMID: 32704363 PMCID: PMC7371865 DOI: 10.1038/s41377-020-0331-y] [Citation(s) in RCA: 68] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Revised: 04/21/2020] [Accepted: 05/07/2020] [Indexed: 05/25/2023]
Abstract
Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.
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Affiliation(s)
- Minkyung Kim
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673 Republic of Korea
| | - Zubin Jacob
- School of Electrical and Computer Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47906 USA
| | - Junsuk Rho
- Department of Mechanical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673 Republic of Korea
- Department of Chemical Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 37673 Republic of Korea
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