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Huang Y, Yu Q, Liu Z, Feng Y, Yu J, Zhong H, Zhang Y, Zhang Z. Coherent control on the generation and annihilation of a pseudospin-induced optical vortex in a honeycomb photonic lattice. OPTICS LETTERS 2024; 49:3753-3756. [PMID: 38950259 DOI: 10.1364/ol.527186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2024] [Accepted: 06/07/2024] [Indexed: 07/03/2024]
Abstract
We experimentally investigate the coherently controllable generation and annihilation of a pseudospin-induced optical vortex in an optically induced honeycomb photonic lattice in a Λ-type 85Rb atomic vapor cell. Three Gaussian coupling beams are coupled into the atomic gases to form a hexagonal interference pattern, which can induce a honeycomb photonic lattice under electromagnetically induced transparency. Then, two probe beams interfere with each other to form periodical fringes and cover one set of sublattice in the honeycomb lattice, corresponding to excite the K or K' valleys in momentum space. By properly adjusting the experimental parameters, the generation and annihilation of the induced optical vortex can be effectively controlled. The theoretical simulations based on the Dirac and Schrödinger equations are performed to explore the underlying mechanisms, which will support the observations. The demonstrated properties of such controllable optical vortex may lay the foundation for the design of vortex-based optical devices with multidimensional tunability.
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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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3
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Yang L, Wang Y, Meng Y, Zhu Z, Xi X, Yan B, Lin S, Chen J, Shi BJ, Ge Y, Yuan SQ, Chen H, Sun HX, Liu GG, Yang Y, Gao Z. Observation of Dirac Hierarchy in Three-Dimensional Acoustic Topological Insulators. PHYSICAL REVIEW LETTERS 2022; 129:125502. [PMID: 36179186 DOI: 10.1103/physrevlett.129.125502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 08/24/2022] [Indexed: 06/16/2023]
Abstract
Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy comprising an eightfold bulk DC, a fourfold surface DC, and a twofold hinge DC, associated with a hierarchy of topological phases including first-order to third-order three-dimensional (3D) topological insulators, using the same 3D base lattice. Here, we report the first experimental observation of the Dirac hierarchy in 3D acoustic TIs. Using acoustic measurements, we unambiguously reveal that lifting of multifold DCs in each hierarchy can induce two-dimensional topological surface states with a fourfold DC in a first-order 3D TI, one-dimensional topological hinge states with a twofold DC in a second-order 3D TI, and zero-dimensional topological corner states in a third-order 3D TI. Our Letter not only expands the fundamental research scope of Dirac physics, but also opens up a new route for multidimensional robust wave manipulation.
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Affiliation(s)
- Linyun Yang
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yin Wang
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yan Meng
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Zhenxiao Zhu
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiang Xi
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bei Yan
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Shuxin Lin
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Jingming Chen
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Bin-Jie Shi
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Yong Ge
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Shou-Qi Yuan
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Hongsheng Chen
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
- ZJU-Hangzhou Global Science and Technology Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices and Smart Systems of Zhejiang, ZJU-UIUC Institute, Zhejiang University, Hangzhou 310027, China
| | - Hong-Xiang Sun
- Research Center of Fluid Machinery Engineering and Technology, School of Physics and Electronics Engineering, Jiangsu University, Zhenjiang 212013, China
- State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
| | - Gui-Geng Liu
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore
| | - Yihao Yang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
- ZJU-Hangzhou Global Science and Technology Innovation Center, Key Laboratory of Advanced Micro/Nano Electronic Devices and Smart Systems of Zhejiang, ZJU-UIUC Institute, Zhejiang University, Hangzhou 310027, China
| | - Zhen Gao
- Department of Electrical and Electronic Engineering, Southern University of Science and Technology, Shenzhen 518055, China
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4
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Tang XY, Zhang Y, Ding KH. Suppression of impurity magnetization by the saddle points. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:175301. [PMID: 35090141 DOI: 10.1088/1361-648x/ac4fe9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 01/28/2022] [Indexed: 06/14/2023]
Abstract
We study the localized magnetic states of an impurity in the semi-Dirac-like system where the saddle point (SP) is present. It is found that with increasing the saddle point energy (SPE), the impurity magnetization region diminishes greatly, and reaches a minimum at the SPE equal to the impurity energy. When continuing to increase the SPE, the impurity magnetization region rapidly becomes large. Correspondingly, an explicit decrease with the SPE close to the impurity energy is also observed in the magnetic moment of the impurity. This suppression behavior for the magnetization of the impurity can be understood from the SP induced mitigation of asymmetry on the density of state at impurity energy. In contrast, when the SP vanishes, due to the opening of the gap, the magnetic region exhibits a monotonous decay when the conduction band edge goes up through the impurity energy. The combined effect of the SP and the Coulomb interaction at the impurity on the local magnetization is also investigated.
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Affiliation(s)
- Xue-Yu Tang
- Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004, People's Republic of China
| | - Yun Zhang
- School of Mechanical Engineering, Hunan Industry Polytechnic, Changsha 410208, People's Republic of China
| | - Kai-He Ding
- Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004, People's Republic of China
- Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering, Changsha University of Science and Technology, Changsha 410076, People's Republic of China
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5
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Song Y, Monceaux Y, Bittner S, Chao K, Reynoso de la Cruz HM, Lafargue C, Decanini D, Dietz B, Zyss J, Grigis A, Checoury X, Lebental M. Möbius Strip Microlasers: A Testbed for Non-Euclidean Photonics. PHYSICAL REVIEW LETTERS 2021; 127:203901. [PMID: 34860038 DOI: 10.1103/physrevlett.127.203901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2020] [Accepted: 09/10/2021] [Indexed: 06/13/2023]
Abstract
We report on experiments with Möbius strip microlasers, which were fabricated with high optical quality by direct laser writing. A Möbius strip, i.e., a band with a half twist, exhibits the fascinating property that it has a single nonorientable surface and a single boundary. We provide evidence that, in contrast to conventional ring or disk resonators, a Möbius strip cavity cannot sustain whispering gallery modes (WGM). Comparison between experiments and 3D finite difference time domain (FDTD) simulations reveals that the resonances are localized on periodic geodesics.
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Affiliation(s)
- Yalei Song
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, 730000 Gansu, China
| | - Yann Monceaux
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
| | - Stefan Bittner
- Chair in Photonics, LMOPS EA-4423 Laboratory, CentraleSupélec and Université de Lorraine, 2 rue Edouard Belin, 57070 Metz, France
| | - Kimhong Chao
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
| | - Héctor M Reynoso de la Cruz
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
- Department of Physical Engineering, Academic Body of Statistical Mechanics, Science and Engineering Division of the University of Guanajuato, León, Gto. 36000, México
| | - Clément Lafargue
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
| | - Dominique Decanini
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120 Palaiseau, France
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, 730000 Gansu, China
| | - Joseph Zyss
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
| | - Alain Grigis
- Laboratoire d'Analyse, Géométrie et Applications, CNRS UMR 7539, Université Sorbonne Paris Cité, Université Paris 13, Institut Galilée, 99 avenue Jean-Baptiste Clément, 93430 Villetaneuse, France
| | - Xavier Checoury
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, 10 Boulevard Thomas Gobert, 91120 Palaiseau, France
| | - Melanie Lebental
- Laboratoire Lumière, Matière et Interfaces (LuMIn) CNRS, ENS Paris-Saclay, Université Paris-Saclay, CentraleSupélec, 91190 Gif-sur-Yvette, France
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6
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St-Jean P, Dauphin A, Massignan P, Real B, Jamadi O, Milicevic M, Lemaître A, Harouri A, Le Gratiet L, Sagnes I, Ravets S, Bloch J, Amo A. Measuring Topological Invariants in a Polaritonic Analog of Graphene. PHYSICAL REVIEW LETTERS 2021; 126:127403. [PMID: 33834841 DOI: 10.1103/physrevlett.126.127403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Revised: 09/08/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an important class of Hamiltonians corresponding to 2D lattices with time-reversal and chiral symmetry (e.g., graphene), the existence of edge states is linked to invariants that are not defined over the full 2D Brillouin zone, but on reduced 1D subspaces. Here, we demonstrate a novel scheme based on a combined real- and momentum-space measurement to directly access these 1D topological invariants in lattices of semiconductor microcavities confining exciton polaritons. We extract these invariants in arrays emulating the physics of regular and critically compressed graphene where Dirac cones have merged. Our scheme provides a direct evidence of the bulk-edge correspondence in these systems and opens the door to the exploration of more complex topological effects, e.g., involving disorder and interactions.
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Affiliation(s)
- P St-Jean
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Dauphin
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - P Massignan
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
- Departament de Física, Universitat Politècnica de Catalunya, Campus Nord B4-B5, 08034 Barcelona, Spain
| | - B Real
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - O Jamadi
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - M Milicevic
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Lemaître
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Harouri
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - L Le Gratiet
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - I Sagnes
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - S Ravets
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - J Bloch
- Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France
| | - A Amo
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
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7
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Real B, Jamadi O, Milićević M, Pernet N, St-Jean P, Ozawa T, Montambaux G, Sagnes I, Lemaître A, Le Gratiet L, Harouri A, Ravets S, Bloch J, Amo A. Semi-Dirac Transport and Anisotropic Localization in Polariton Honeycomb Lattices. PHYSICAL REVIEW LETTERS 2020; 125:186601. [PMID: 33196264 DOI: 10.1103/physrevlett.125.186601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Accepted: 09/16/2020] [Indexed: 06/11/2023]
Abstract
Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In particular, for a critical compression, a semi-Dirac cone is formed with massless and massive dispersions along perpendicular directions. Here we show direct evidence of the highly anisotropic transport of polaritons in a honeycomb lattice of coupled micropillars implementing a semi-Dirac cone. If we optically induce a vacancylike defect in the lattice, we observe an anisotropically localized polariton distribution in a single sublattice, a consequence of the semi-Dirac dispersion. Our work opens up new horizons for the study of transport and localization in lattices with chiral symmetry and exotic Dirac dispersions.
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Affiliation(s)
- B Real
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - O Jamadi
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
| | - M Milićević
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - N Pernet
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - P St-Jean
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - T Ozawa
- Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
- Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan
| | - G Montambaux
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405, Orsay, France
| | - I Sagnes
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Lemaître
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - L Le Gratiet
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Harouri
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - S Ravets
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - J Bloch
- Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120, Palaiseau, France
| | - A Amo
- Univ. Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers Atomes et Molécules, F-59000 Lille, France
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8
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Wu M, Peng R, Liu J, Zhao Q, Zhou J. Energy Band Attraction Effect in Non-Hermitian Systems. PHYSICAL REVIEW LETTERS 2020; 125:137703. [PMID: 33034479 DOI: 10.1103/physrevlett.125.137703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2020] [Accepted: 09/01/2020] [Indexed: 06/11/2023]
Abstract
The energy band attraction (EBA) caused by the nonorthogonal eigenvectors is a unique phenomenon in the non-Hermitian (NH) system. However, restricted by the required tight-binding approximation and meticulously engineered complex potentials, such an effect has never been experimentally demonstrated before. Here by a suitable design of all-dielectric Mie resonators in a parallel-plate transmission line, we for the first time verify the photonic analog of the EBA effects both theoretically and experimentally. The evolution of the EBA effect in a two-level NH system from gapped bands to gapless bands to flat bands is observed by precisely tuning the loss of the Mie resonators. The transmission spectra can be theoretically connected to the eigenvalues and eigenvectors of the NH Hamiltonian. Furthermore we extend our methods to a graphenelike two-dimensional NH system. Our works show a metamaterial approach toward NH topological photonics and foster a deeper understanding of band theory in open systems.
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Affiliation(s)
- Maopeng Wu
- Department of Engineering Physics, Tsinghua University, Beijing 100084, China
- State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
| | - Ruiguang Peng
- State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
| | - Jingquan Liu
- Department of Engineering Physics, Tsinghua University, Beijing 100084, China
| | - Qian Zhao
- State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
| | - Ji Zhou
- State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
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9
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Arnal M, Chatelain G, Martinez M, Dupont N, Giraud O, Ullmo D, Georgeot B, Lemarié G, Billy J, Guéry-Odelin D. Chaos-assisted tunneling resonances in a synthetic Floquet superlattice. SCIENCE ADVANCES 2020; 6:6/38/eabc4886. [PMID: 32948592 PMCID: PMC7500923 DOI: 10.1126/sciadv.abc4886] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 07/29/2020] [Indexed: 05/22/2023]
Abstract
The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. So far, most efforts in this domain have been directed to either fully regular or fully chaotic systems. Here, we focus on the intermediate regime, where regular orbits are surrounded by a large sea of chaotic trajectories. We observe a quantum chaos transport mechanism, called chaos-assisted tunneling, that translates in sharp resonances of the tunneling rate and provides previously unexplored possibilities for quantum simulation. More specifically, using Bose-Einstein condensates in a driven optical lattice, we experimentally demonstrate and characterize these resonances. Our work paves the way for quantum simulations with long-range transport and quantum control through complexity.
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Affiliation(s)
- M Arnal
- Laboratoire Collisions Agrégats Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - G Chatelain
- Laboratoire Collisions Agrégats Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - M Martinez
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - N Dupont
- Laboratoire Collisions Agrégats Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - O Giraud
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
| | - D Ullmo
- Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France
| | - B Georgeot
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - G Lemarié
- Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - J Billy
- Laboratoire Collisions Agrégats Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, France
| | - D Guéry-Odelin
- Laboratoire Collisions Agrégats Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, France.
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10
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Bellec M, Poli C, Kuhl U, Mortessagne F, Schomerus H. Observation of supersymmetric pseudo-Landau levels in strained microwave graphene. LIGHT, SCIENCE & APPLICATIONS 2020; 9:146. [PMID: 32864121 PMCID: PMC7438506 DOI: 10.1038/s41377-020-00351-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Revised: 06/04/2020] [Accepted: 06/16/2020] [Indexed: 06/11/2023]
Abstract
Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory. In particular, we resolve the full sublattice polarisation of the anomalous 0th pseudo-Landau level, which reveals a deep connection to zigzag edge states in the unstrained case.
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Affiliation(s)
- Matthieu Bellec
- Institut de Physique de Nice (INPHYNI), Université Côte d’Azur, CNRS, 06108 Nice, France
| | - Charles Poli
- Department of Physics, Lancaster University, Lancaster, LA1 4YB UK
| | - Ulrich Kuhl
- Institut de Physique de Nice (INPHYNI), Université Côte d’Azur, CNRS, 06108 Nice, France
| | - Fabrice Mortessagne
- Institut de Physique de Nice (INPHYNI), Université Côte d’Azur, CNRS, 06108 Nice, France
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11
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Pulse Reshaping in Double-zero-index Photonic Crystals with Dirac-like-cone Dispersion. Sci Rep 2020; 10:8416. [PMID: 32439891 PMCID: PMC7242388 DOI: 10.1038/s41598-020-65461-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2020] [Accepted: 05/04/2020] [Indexed: 11/26/2022] Open
Abstract
Triply-degenerate Dirac-like cone at the Brillouin zone center attracts much research interest in recent years. Whether the linear dispersion in such a Dirac-like cone reflects the same physics to Dirac cones at the Brillouin zone boundaries is still under investigation. In this manuscript, through microwave experiments and numerical simulations, we observe intriguing pulse reshaping phenomena in double-zero-index photonic crystals, which cannot be fully understood from their close-to-zero effective parameters. A reshaped pulse, with frequency components close to the Dirac frequency filtered, is propagating at a constant group velocity while part of these filtered frequencies appears at a much later time. In time domain measurements, we find a way to separate the effect between the linear dispersion and the extra flat band in Dirac-like cone to have a better understanding of the underneath physics. We succeed in obtaining the group velocity inside a double-zero-index photonic crystal and good consistence can be found between experiments, numerical simulations and band diagram calculations.
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12
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Xu Y, Jiang G, Miotkowski I, Biswas RR, Chen YP. Tuning Insulator-Semimetal Transitions in 3D Topological Insulator thin Films by Intersurface Hybridization and In-Plane Magnetic Fields. PHYSICAL REVIEW LETTERS 2019; 123:207701. [PMID: 31809081 DOI: 10.1103/physrevlett.123.207701] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2019] [Revised: 09/23/2019] [Indexed: 05/28/2023]
Abstract
A pair of Dirac points (analogous to a vortex-antivortex pair) associated with opposite topological numbers (with ±π Berry phases) can be merged together through parameter tuning and annihilated to gap the Dirac spectrum, offering a canonical example of a topological phase transition. Here, we report transport studies on thin films of BiSbTeSe_{2}, which is a 3D topological insulator that hosts spin-helical gapless (semimetallic) Dirac fermion surface states for sufficiently thick samples, with an observed resistivity close to h/4e^{2} at the charge neutral point. When the sample thickness is reduced to below ∼10 nm thick, we observe a transition from metallic to insulating behavior, consistent with the expectation that the Dirac cones from the top and bottom surfaces hybridize (analogous to a "merging" in the real space) to give a trivial gapped insulator. Furthermore, we observe that an in-plane magnetic field can drive the system again towards a metallic behavior, with a prominent negative magnetoresistance (up to ∼-95%) and a temperature-insensitive resistivity close to h/2e^{2} at the charge neutral point. The observation is consistent with a predicted effect of an in-plane magnetic field to reduce the hybridization gap (which, if small enough, may be smeared by disorder and give rise to a metallic behavior). A sufficiently strong magnetic field is predicted to restore and split again the Dirac points in the momentum space, inducing a distinct 2D topological semimetal phase with two single-fold Dirac cones of opposite spin-momentum windings.
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Affiliation(s)
- Yang Xu
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
| | - Guodong Jiang
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Ireneusz Miotkowski
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Rudro R Biswas
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Yong P Chen
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
- School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA
- WPI-AIMR International Research Center for Materials Sciences, Tohoku University, Sendai 980-8577, Japan
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13
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Guo R, Nečada M, Hakala TK, Väkeväinen AI, Törmä P. Lasing at K Points of a Honeycomb Plasmonic Lattice. PHYSICAL REVIEW LETTERS 2019; 122:013901. [PMID: 31012715 DOI: 10.1103/physrevlett.122.013901] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2018] [Indexed: 05/10/2023]
Abstract
We study lasing at the high-symmetry points of the Brillouin zone in a honeycomb plasmonic lattice. We use symmetry arguments to define singlet and doublet modes at the K points of the reciprocal space. We experimentally demonstrate lasing at the K points that is based on plasmonic lattice modes and two-dimensional feedback. By comparing polarization properties to T-matrix simulations, we identify the lasing mode as one of the singlets with an energy minimum at the K point enabling feedback. Our results offer prospects for studies of topological lasing in radiatively coupled systems.
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Affiliation(s)
- R Guo
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - M Nečada
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - T K Hakala
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
- Institute of Photonics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
| | - A I Väkeväinen
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - P Törmä
- Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
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14
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Montambaux G, Lim LK, Fuchs JN, Piéchon F. Winding Vector: How to Annihilate Two Dirac Points with the Same Charge. PHYSICAL REVIEW LETTERS 2018; 121:256402. [PMID: 30608851 DOI: 10.1103/physrevlett.121.256402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2018] [Indexed: 06/09/2023]
Abstract
The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite (+- scenario) or identical (++ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the same winding number emerge under appropriate distortion (interaction, etc.), following the ++ scenario. Under further distortion, these Dirac points merge following the +- scenario, that is corresponding to opposite winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.
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Affiliation(s)
- Gilles Montambaux
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
| | - Lih-King Lim
- Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Jean-Noël Fuchs
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France
| | - Frédéric Piéchon
- Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, F-91405 Orsay, France
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15
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Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces. Nat Commun 2018; 9:2194. [PMID: 29875384 PMCID: PMC5989260 DOI: 10.1038/s41467-018-03982-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2017] [Accepted: 03/27/2018] [Indexed: 11/13/2022] Open
Abstract
Pseudorelativistic Dirac quasiparticles have emerged in a plethora of artificial graphene systems that mimic the underlying honeycomb symmetry of graphene. However, it is notoriously difficult to manipulate their properties without modifying the lattice structure. Here we theoretically investigate polaritons supported by honeycomb metasurfaces and, despite the trivial nature of the resonant elements, we unveil rich Dirac physics stemming from a non-trivial winding in the light–matter interaction. The metasurfaces simultaneously exhibit two distinct species of massless Dirac polaritons, namely type-I and type-II. By modifying only the photonic environment via an enclosing cavity, one can manipulate the location of the type-II Dirac points, leading to qualitatively different polariton phases. This enables one to alter the fundamental properties of the emergent Dirac polaritons while preserving the lattice structure—a unique scenario which has no analog in real or artificial graphene systems. Exploiting the photonic environment will thus give rise to unexplored Dirac physics at the subwavelength scale. Manipulating the properties of artificial graphene systems without changing the lattice has proven difficult. Here, Mann et al. theoretically show that changing the photonic environment alone can modify the fundamental properties of emergent massless Dirac polaritons in honeycomb metasurfaces.
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16
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Zhan X, Xiao L, Bian Z, Wang K, Qiu X, Sanders BC, Yi W, Xue P. Detecting Topological Invariants in Nonunitary Discrete-Time Quantum Walks. PHYSICAL REVIEW LETTERS 2017; 119:130501. [PMID: 29341719 DOI: 10.1103/physrevlett.119.130501] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Indexed: 05/27/2023]
Abstract
We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.
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Affiliation(s)
- Xiang Zhan
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Lei Xiao
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Zhihao Bian
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Kunkun Wang
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Xingze Qiu
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China
- Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, CAS, Hefei 230026, China
| | - Barry C Sanders
- Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, CAS, Hefei 230026, China
- Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, CAS, Hefei 230026, China
- Institute for Quantum Science and Technology, University of Calgary, Alberta T2N 1N4, Canada
- Program in Quantum Information Science, Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1, Canada
| | - Wei Yi
- Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei 230026, China
- Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, CAS, Hefei 230026, China
| | - Peng Xue
- Department of Physics, Southeast University, Nanjing 211189, China
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
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17
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Naumis GG, Barraza-Lopez S, Oliva-Leyva M, Terrones H. Electronic and optical properties of strained graphene and other strained 2D materials: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2017; 80:096501. [PMID: 28540862 DOI: 10.1088/1361-6633/aa74ef] [Citation(s) in RCA: 119] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.
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Affiliation(s)
- Gerardo G Naumis
- Depto. de Sistemas Complejos, Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, Mexico City 01000, Mexico
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18
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Downing CA, Portnoi ME. Localization of massless Dirac particles via spatial modulations of the Fermi velocity. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:315301. [PMID: 28685706 DOI: 10.1088/1361-648x/aa7884] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.
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Affiliation(s)
- C A Downing
- Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000 Strasbourg, France
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19
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Yu SY, Sun XC, Ni X, Wang Q, Yan XJ, He C, Liu XP, Feng L, Lu MH, Chen YF. Surface phononic graphene. NATURE MATERIALS 2016; 15:1243-1247. [PMID: 27595348 DOI: 10.1038/nmat4743] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Accepted: 07/25/2016] [Indexed: 06/06/2023]
Abstract
Strategic manipulation of wave and particle transport in various media is the key driving force for modern information processing and communication. In a strongly scattering medium, waves and particles exhibit versatile transport characteristics such as localization, tunnelling with exponential decay, ballistic, and diffusion behaviours due to dynamical multiple scattering from strong scatters or impurities. Recent investigations of graphene have offered a unique approach, from a quantum point of view, to design the dispersion of electrons on demand, enabling relativistic massless Dirac quasiparticles, and thus inducing low-loss transport either ballistically or diffusively. Here, we report an experimental demonstration of an artificial phononic graphene tailored for surface phonons on a LiNbO3 integrated platform. The system exhibits Dirac quasiparticle-like transport, that is, pseudo-diffusion at the Dirac point, which gives rise to a thickness-independent temporal beating for transmitted pulses, an analogue of Zitterbewegung effects. The demonstrated fully integrated artificial phononic graphene platform here constitutes a step towards on-chip quantum simulators of graphene and unique monolithic electro-acoustic integrated circuits.
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Affiliation(s)
- Si-Yuan Yu
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Xiao-Chen Sun
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Xu Ni
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Qing Wang
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Xue-Jun Yan
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Cheng He
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
| | - Xiao-Ping Liu
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Liang Feng
- Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, New York 14260, USA
| | - Ming-Hui Lu
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
| | - Yan-Feng Chen
- National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
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20
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Keil R, Poli C, Heinrich M, Arkinstall J, Weihs G, Schomerus H, Szameit A. Universal Sign Control of Coupling in Tight-Binding Lattices. PHYSICAL REVIEW LETTERS 2016; 116:213901. [PMID: 27284657 DOI: 10.1103/physrevlett.116.213901] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Indexed: 06/06/2023]
Abstract
We present a method of locally inverting the sign of the coupling term in tight-binding systems, by means of inserting a judiciously designed ancillary site and eigenmode matching of the resulting vertex triplet. Our technique can be universally applied to all lattice configurations, as long as the individual sites can be detuned. We experimentally verify this method in laser-written photonic lattices and confirm both the magnitude and the sign of the coupling by interferometric measurements. Based on these findings, we demonstrate how such universal sign-flipped coupling links can be embedded into extended lattice structures to impose a Z_{2}-gauge transformation. This opens a new avenue for investigations on topological effects arising from magnetic fields with aperiodic flux patterns or in disordered systems.
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Affiliation(s)
- Robert Keil
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - Charles Poli
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Matthias Heinrich
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Jake Arkinstall
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Gregor Weihs
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
| | - Henning Schomerus
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Alexander Szameit
- Institute of Applied Physics, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
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21
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Diebel F, Leykam D, Kroesen S, Denz C, Desyatnikov AS. Conical Diffraction and Composite Lieb Bosons in Photonic Lattices. PHYSICAL REVIEW LETTERS 2016; 116:183902. [PMID: 27203324 DOI: 10.1103/physrevlett.116.183902] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Indexed: 06/05/2023]
Abstract
Pseudospin describes how waves are distributed between different "internal" degrees of freedom or microscopic states, such as polarizations, sublattices, or layers. Here, we experimentally demonstrate and explain wave dynamics in a photonic Lieb lattice, which hosts an integer pseudospin s=1 conical intersection. We study the most striking differences displayed by integer pseudospin states: pseudospin-dependent conical diffraction and the generation of higher charged optical vortices.
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Affiliation(s)
- Falko Diebel
- Institut für Angewandte Physik and Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Daniel Leykam
- Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Sebastian Kroesen
- Institut für Angewandte Physik and Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Cornelia Denz
- Institut für Angewandte Physik and Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Anton S Desyatnikov
- Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia
- Department of Physics, Nazarbayev University, 53 Kabanbay Batyr Avenue, Astana 010000, Kazakhstan
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22
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Dietz B, Klaus T, Miski-Oglu M, Richter A, Wunderle M, Bouazza C. Spectral Properties of Dirac Billiards at the van Hove Singularities. PHYSICAL REVIEW LETTERS 2016; 116:023901. [PMID: 26824540 DOI: 10.1103/physrevlett.116.023901] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2015] [Indexed: 06/05/2023]
Abstract
We study distributions of the ratios of level spacings of rectangular and Africa-shaped superconducting microwave resonators containing circular scatterers on a triangular grid, so-called Dirac billiards (DBs). The high-precision measurements allowed the determination of, respectively, all 1651 and 1823 eigenfrequencies in the first two bands. The resonance densities are similar to that of graphene. They exhibit two sharp peaks at the van Hove singularities which separate the band structure into regions with a linear and a quadratic dispersion relation, respectively. In the vicinity of the van Hove singularities we observe rapid changes in, e.g., the wave function structure. Accordingly, we question whether the spectral properties are there still determined by the shapes of the DBs. The commonly used statistical measures are no longer applicable; however, we demonstrate in this Letter that the ratio distributions provide suitable measures.
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Affiliation(s)
- B Dietz
- Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany
| | - T Klaus
- Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany
| | - M Miski-Oglu
- Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany
| | - A Richter
- Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany
| | - M Wunderle
- Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany
| | - C Bouazza
- Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstrasse 9, D-64289 Darmstadt, Germany
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23
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Hou JM, Chen W. Hidden symmetry and protection of Dirac points on the honeycomb lattice. Sci Rep 2015; 5:17571. [PMID: 26639178 PMCID: PMC4671008 DOI: 10.1038/srep17571] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2015] [Accepted: 11/02/2015] [Indexed: 11/29/2022] Open
Abstract
The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on the honeycomb lattice, can also be perfectly explained by the parameter dependent evolution of the hidden symmetry.
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Affiliation(s)
- Jing-Min Hou
- Department of Physics, Southeast University, Nanjing 211189, China
| | - Wei Chen
- College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
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24
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Dietz B, Richter A. Quantum and wave dynamical chaos in superconducting microwave billiards. CHAOS (WOODBURY, N.Y.) 2015; 25:097601. [PMID: 26428554 DOI: 10.1063/1.4915527] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.
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Affiliation(s)
- B Dietz
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - A Richter
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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25
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Li Y, Mei J. Double Dirac cones in two-dimensional dielectric photonic crystals. OPTICS EXPRESS 2015; 23:12089-12099. [PMID: 25969297 DOI: 10.1364/oe.23.012089] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
By exploiting the accidental degeneracy of the doubly-degenerate dipolar and quadrupolar modes, we show that a two-dimensional dielectric photonic crystal (PC) can exhibit the double Dirac cone dispersion relation at the Γ point. Using a perturbation method and group theory, we demonstrate that the double cone is composed of two identical and overlapping Dirac cones with predictable linear slopes, and the linearity of the dispersion is guaranteed by the spatial symmetry of the Bloch eigenstates. Numerical simulations including wave-front shaping, unidirectional transmission and perfect tunneling show that the corresponding PC structure can be characterized by a zero effective refractive index.
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26
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Poli C, Bellec M, Kuhl U, Mortessagne F, Schomerus H. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat Commun 2015; 6:6710. [PMID: 25833814 PMCID: PMC4396359 DOI: 10.1038/ncomms7710] [Citation(s) in RCA: 110] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Accepted: 02/19/2015] [Indexed: 11/17/2022] Open
Abstract
The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including couplers, rectifiers and lasers. At interfaces between systems with topologically distinct band structure, robust symmetry protected states emerge. Here, Poli et al. control such states in a coupled dielectric resonator chain with parity-time symmetry and exploit their topological nature to protect them from absorptive losses.
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Affiliation(s)
- Charles Poli
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | - Matthieu Bellec
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université Nice Sophia Antipolis, 06100 Nice, France
| | - Ulrich Kuhl
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université Nice Sophia Antipolis, 06100 Nice, France
| | - Fabrice Mortessagne
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université Nice Sophia Antipolis, 06100 Nice, France
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Böhm J, Bellec M, Mortessagne F, Kuhl U, Barkhofen S, Gehler S, Stöckmann HJ, Foulger I, Gnutzmann S, Tanner G. Microwave experiments simulating quantum search and directed transport in artificial graphene. PHYSICAL REVIEW LETTERS 2015; 114:110501. [PMID: 25839247 DOI: 10.1103/physrevlett.114.110501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2014] [Indexed: 06/04/2023]
Abstract
A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to √N, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density-namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.
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Affiliation(s)
- Julian Böhm
- Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France
| | - Matthieu Bellec
- Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France
| | - Fabrice Mortessagne
- Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France
| | - Ulrich Kuhl
- Laboratoire de Physique de la Matière Condensée, UMR 7336, Université Nice Sophia Antipolis, CNRS, Parc Valrose, 06100 Nice, France
| | - Sonja Barkhofen
- AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany
- Applied Physics, University of Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany
| | - Stefan Gehler
- AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany
- Department of Energy Management and Power System Operation, University of Kassel, D-34121 Kassel, Germany
| | - Hans-Jürgen Stöckmann
- AG Quantenchaos, Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany
| | - Iain Foulger
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Sven Gnutzmann
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Gregor Tanner
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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He WY, Chan CT. The emergence of Dirac points in photonic crystals with mirror symmetry. Sci Rep 2015; 5:8186. [PMID: 25640993 PMCID: PMC4650825 DOI: 10.1038/srep08186] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2014] [Accepted: 01/07/2015] [Indexed: 11/20/2022] Open
Abstract
We show that Dirac points can emerge in photonic crystals possessing mirror symmetry when band gap closes. The mechanism of generating Dirac points is discussed in a two-dimensional photonic square lattice, in which four Dirac points split out naturally after the touching of two bands with different parity. The emergence of such nodal points, characterized by vortex structure in momentum space, is attributed to the unavoidable band crossing protected by mirror symmetry. The Dirac nodes can be unbuckled through breaking the mirror symmetry and a photonic analog of Chern insulator can be achieved through time reversal symmetry breaking. Breaking time reversal symmetry can lead to unidirectional helical edge states and breaking mirror symmetry can reduce the band gap to amplify the finite size effect, providing ways to engineer helical edge states.
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Affiliation(s)
- Wen-Yu He
- Department of Physics and Institute for Advanced Study, the Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
| | - C T Chan
- Department of Physics and Institute for Advanced Study, the Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China
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Abstract
Abstract
Inspired by the great development of graphene, more and more research has been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition-metal oxides (VO2)n/(TiO2)m and (CrO2)n/(TiO2)m, organic and organometallic crystals, so-MoS2, and artificial lattices (electron gases and ultracold atoms). Their structural and electronic properties are summarized. We also investigate how Dirac points emerge, move, and merge in these systems. The von Neumann–Wigner theorem is used to explain the scarcity of Dirac cones in 2D systems, which leads to rigorous requirements on the symmetry, parameters, Fermi level, and band overlap of materials to achieve Dirac cones. Connections between existence of Dirac cones and the structural features are also discussed.
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Affiliation(s)
- Jinying Wang
- Center for Nanochemstry, Colledge of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Shibin Deng
- Center for Nanochemstry, Colledge of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Zhongfan Liu
- Center for Nanochemstry, Colledge of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Zhirong Liu
- Center for Nanochemstry, Colledge of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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Lim LK, Fuchs JN, Montambaux G. Mass and chirality inversion of a Dirac cone pair in Stückelberg interferometry. PHYSICAL REVIEW LETTERS 2014; 112:155302. [PMID: 24785046 DOI: 10.1103/physrevlett.112.155302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2013] [Indexed: 06/03/2023]
Abstract
We show that a Stückelberg interferometer made of two massive Dirac cones can reveal information on band eigenstates such as the chirality and mass sign of the cones. For a given spectrum with two gapped cones, we propose several low-energy Hamiltonians differing by their eigenstates properties. The corresponding interband transition probability is affected by such differences in its interference fringes being shifted by a new phase of geometrical origin. This phase can be a useful bulk probe for topological band structures realized with artificial crystals.
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Affiliation(s)
- Lih-King Lim
- Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, 91405 Orsay, France and Laboratoire Charles Fabry, Institut d'Optique, CNRS, Université Paris-Sud, 2 avenue Augustin Fresnel, F-91127 Palaiseau cedex, France
| | - Jean-Noël Fuchs
- Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, 91405 Orsay, France and Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris, France
| | - Gilles Montambaux
- Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, 91405 Orsay, France
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Plotnik Y, Rechtsman MC, Song D, Heinrich M, Zeuner JM, Nolte S, Lumer Y, Malkova N, Xu J, Szameit A, Chen Z, Segev M. Observation of unconventional edge states in 'photonic graphene'. NATURE MATERIALS 2014; 13:57-62. [PMID: 24193661 DOI: 10.1038/nmat3783] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2012] [Accepted: 09/18/2013] [Indexed: 06/02/2023]
Abstract
Graphene, a two-dimensional honeycomb lattice of carbon atoms, has been attracting much interest in recent years. Electrons therein behave as massless relativistic particles, giving rise to strikingly unconventional phenomena. Graphene edge states are essential for understanding the electronic properties of this material. However, the coarse or impure nature of the graphene edges hampers the ability to directly probe the edge states. Perhaps the best example is given by the edge states on the bearded edge that have never been observed-because such an edge is unstable in graphene. Here, we use the optical equivalent of graphene-a photonic honeycomb lattice-to study the edge states and their properties. We directly image the edge states on both the zigzag and bearded edges of this photonic graphene, measure their dispersion properties, and most importantly, find a new type of edge state: one residing on the bearded edge that has never been predicted or observed. This edge state lies near the Van Hove singularity in the edge band structure and can be classified as a Tamm-like state lacking any surface defect. The mechanism underlying its formation may counterintuitively appear in other crystalline systems.
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Affiliation(s)
- Yonatan Plotnik
- 1] Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel [2]
| | - Mikael C Rechtsman
- 1] Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel [2]
| | - Daohong Song
- 1] The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physical School and School of Physics, Nankai University, Tianjin 300457, China [2]
| | - Matthias Heinrich
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Julia M Zeuner
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Stefan Nolte
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Yaakov Lumer
- Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel
| | - Natalia Malkova
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Jingjun Xu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physical School and School of Physics, Nankai University, Tianjin 300457, China
| | - Alexander Szameit
- Institute of Applied Physics, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany
| | - Zhigang Chen
- 1] The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physical School and School of Physics, Nankai University, Tianjin 300457, China [2] Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Mordechai Segev
- Technion-Israel Institute of Technology, Technion City 32000, Haifa, Israel
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Breitkreiz M, Brouwer PW. Semiclassical theory of speckle correlations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062905. [PMID: 24483529 DOI: 10.1103/physreve.88.062905] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2013] [Indexed: 06/03/2023]
Abstract
Coherent wave propagation in random media results in a characteristic speckle pattern, with spatial intensity correlations with short-range and long-range behavior. Here, we show how the speckle correlation function can be obtained from a ray picture for two representative geometries, namely a chaotic cavity and a random waveguide. Our calculation allows us to study the crossover between a "ray limit" and a "wave limit," in which the Ehrenfest time τ(E) is larger or smaller than the typical transmission time τ(D), respectively. Remarkably, long-range speckle correlations persist in the ray limit τ(E)≫τ(D).
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Affiliation(s)
- Maxim Breitkreiz
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
| | - Piet W Brouwer
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, 14195 Berlin, Germany
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33
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Franco-Villafañe JA, Sadurní E, Barkhofen S, Kuhl U, Mortessagne F, Seligman TH. First experimental realization of the Dirac oscillator. PHYSICAL REVIEW LETTERS 2013; 111:170405. [PMID: 24206466 DOI: 10.1103/physrevlett.111.170405] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2013] [Indexed: 06/02/2023]
Abstract
We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yield the spectrum of the one-dimensional Dirac oscillator with and without a mass term. The flexibility of the experimental setup allows the implementation of other one-dimensional Dirac-type equations.
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Affiliation(s)
- J A Franco-Villafañe
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Avenida Universidad s/n, 62210 Cuernavaca, México
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Assili M, Haddad S. Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:365503. [PMID: 23941870 DOI: 10.1088/0953-8984/25/36/365503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.
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Affiliation(s)
- M Assili
- Département de Physique, Faculté des Sciences de Tunis, Université Tunis El Manar, Campus universitaire 1060 Tunis, Tunisia
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35
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Polini M, Guinea F, Lewenstein M, Manoharan HC, Pellegrini V. Artificial honeycomb lattices for electrons, atoms and photons. NATURE NANOTECHNOLOGY 2013; 8:625-633. [PMID: 24002076 DOI: 10.1038/nnano.2013.161] [Citation(s) in RCA: 111] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2013] [Accepted: 07/17/2013] [Indexed: 06/02/2023]
Abstract
Artificial honeycomb lattices offer a tunable platform for studying massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band-structure engineering and cooperative effects leads to spectacular manifestations in tunnelling and optical spectroscopies.
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Affiliation(s)
- Marco Polini
- NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy.
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