1
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He J, Liu Z. Dirac cones in bipartite square-octagon lattice: A theoretical approach. J Chem Phys 2023; 159:044713. [PMID: 37522410 DOI: 10.1063/5.0160658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2023] [Accepted: 07/10/2023] [Indexed: 08/01/2023] Open
Abstract
Dirac cones are difficult to achieve in a square lattice with full symmetry. Here, we have theoretically investigated a bipartite tetragonal lattice composed of tetragons and octagons using both Tight-Binding (TB) model and density functional theory (DFT) calculations. The TB model predicts that the system exhibits nodal line semi-metallic properties when the on-site energies of all atoms are identical. When the on-site energies differ, the formation of an elliptical Dirac cone is predicted. Its physical properties (anisotropy, tilting, merging, and emerging) can be regulated by the hopping energies. An exact analytical formula is derived to determine the position of the Dirac point by the TB parameters, and a criterion for the existence of Dirac cones is obtained. The "divide-and-coupling" method is applied to understand the origin of the Dirac cone, which involves dividing the bands into several groups and examining the couplings among inter-groups and intra-groups. Various practical systems computed by DFT methods, e.g., t-BN, t-Si, 4,12,2-graphyne, and t-SiC, are also examined, and they all possess nodal lines or Dirac cones as predicted by the TB model. The results provide theoretical foundation for designing novel Dirac materials with tetragonal symmetry.
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Affiliation(s)
- Junwei He
- College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Zhirong Liu
- College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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2
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Rosenstein B, Shapiro BY. Two step I to II type transitions in layered Weyl semi-metals and their impact on superconductivity. Sci Rep 2023; 13:8450. [PMID: 37231114 DOI: 10.1038/s41598-023-35704-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2023] [Accepted: 05/22/2023] [Indexed: 05/27/2023] Open
Abstract
Novel "quasi two dimensional" typically layered (semi) metals offer a unique opportunity to control the density and even the topology of the electronic matter. Along with doping and gate voltage, a robust tuning is achieved by application of the hydrostatic pressure. In Weyl semi-metals the tilt of the dispersion relation cones, [Formula: see text] increases with pressure, so that one is able to reach type II ([Formula: see text]starting from the more conventional type I Weyl semi-metals [Formula: see text]. The microscopic theory of such a transition is constructed. It is found that upon increasing pressure the I to II transition occurs in two continuous steps. In the first step the cones of opposite chirality coalesce so that the chiral symmetry is restored, while the second transition to the Fermi surface extending throughout the Brillouin zone occurs at higher pressures. Flattening of the band leads to profound changes in Coulomb screening. Superconductivity observed recently in wide range of pressure and chemical composition in Weyl semi-metals of both types. The phonon theory of pairing including the Coulomb repulsion for a layered material is constructed and applied to recent extensive experiments on [Formula: see text].
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Affiliation(s)
- Baruch Rosenstein
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan, R.O.C
- Department of Physics, Institute of Superconductivity, Bar-Ilan University, 52900, Ramat Gan, Israel
| | - B Ya Shapiro
- Department of Physics, Institute of Superconductivity, Bar-Ilan University, 52900, Ramat Gan, Israel.
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3
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Chang YJ, Lu YH, Yang YY, Wang Y, Zhou WH, Wang XW, Jin XM. Inhibition and Reconstruction of Zener Tunneling in Photonic Honeycomb Lattices. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2110044. [PMID: 35306698 DOI: 10.1002/adma.202110044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2021] [Revised: 03/06/2022] [Indexed: 06/14/2023]
Abstract
Quantum coherence is the central element of particle states, and it characterizes the overall performance of various quantum materials. Bloch oscillation is a fundamental coherent behavior of particles under a static potential, which can be easily destroyed by Zener tunneling in multiband 2D lattice materials. The control of Zener tunneling therefore plays the key role in quantum engineering for complicated physical systems. Here, the inhibition and reconstruction of Zener tunneling in photonic honeycomb lattices are experimentally demonstrated. Deformed honeycomb lattices are integrated and an effective static potential is realized on the 2D lattice materials. Zener tunneling disappears in stretch-type lattices and wave packets stay in the dispersionless upper energy band. On the contrary, Zener tunneling is greatly enhanced in compression-type lattices and wave packets exhibit directional oscillations without branches, which manifest the preserved coherence of the wave packets. The results demonstrate the protection of photonic coherence by structurally controlling the Zener tunneling, representing a step toward flexible quantum engineering for large-scale artificial quantum materials.
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Affiliation(s)
- Yi-Jun Chang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Yong-Heng Lu
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Ying-Yue Yang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Yao Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Wen-Hao Zhou
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Xiao-Wei Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy, State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, 200240, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui, 230026, China
- TuringQ Co., Ltd., Shanghai, 200240, China
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4
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Krivenkov M, Marchenko D, Sajedi M, Fedorov A, Clark OJ, Sánchez-Barriga J, Rienks EDL, Rader O, Varykhalov A. On the problem of Dirac cones in fullerenes on gold. NANOSCALE 2022; 14:9124-9133. [PMID: 35723255 DOI: 10.1039/d1nr07981f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Artificial graphene based on molecular networks enables the creation of novel 2D materials with unique electronic and topological properties. Landau quantization has been demonstrated by CO molecules arranged on the two-dimensional electron gas on Cu(111) and the observation of electron quantization may succeed based on the created gauge fields. Recently, it was reported that instead of individual manipulation of CO molecules, simple deposition of nonpolar C60 molecules on Cu(111) and Au(111) produces artificial graphene as evidenced by Dirac cones in photoemission spectroscopy. Here, we show that C60-induced Dirac cones on Au(111) have a different origin. We argue that those are related to umklapp diffraction of surface electronic bands of Au on the molecular grid of C60 in the final state of photoemission. We test this alternative explanation by precisely probing the dimensionality of the observed conical features in the photoemission spectra, by varying both the incident photon energy and the degree of charge doping via alkali adatoms. Using density functional theory calculations and spin-resolved photoemission we reveal the origin of the replicating Au(111) bands and resolve them as deep leaky surface resonances derived from the bulk Au sp-band residing at the boundary of its surface projection. We also discuss the manifold nature of these resonances which gives rise to an onion-like Fermi surface of Au(111).
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Affiliation(s)
- M Krivenkov
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - D Marchenko
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - M Sajedi
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - A Fedorov
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
- IFW Dresden, Helmholtzstr. 20, 01069 Dresden, Germany
- Joint Laboratory 'Functional Quantum Materials' at BESSY II, 12489, Berlin, Germany
| | - O J Clark
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - J Sánchez-Barriga
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - E D L Rienks
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - O Rader
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
| | - A Varykhalov
- Helmholtz-Zentrum Berlin für Materialien und Energie, BESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany.
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5
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Liu YG, Xu L, Li Z. Quantum phase transition in a non-Hermitian XYspin chain with global complex transverse field. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:295401. [PMID: 33984851 DOI: 10.1088/1361-648x/ac00dd] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 05/13/2021] [Indexed: 06/12/2023]
Abstract
In this work, we investigate the quantum phase transition in a non-HermitianXYspin chain. The phase diagram shows that the critical points of Ising phase transition expand into a critical transition zone after introducing a non-Hermitian effect. By analyzing the non-Hermitian gap and long-range correlation function, one can distinguish different phases by means of different gap features and decay properties of correlation function, a tricky problem in traditionalXYmodel. Furthermore, the results reveal the relationship among different regions of the phase diagram, non-Hermitian energy gap and long-range correlation function.
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Affiliation(s)
- Yu-Guo Liu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Lu Xu
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
- National Laboratory of Solid State Microstructures, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Zhi Li
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, People's Republic of China
- GPETR Center for Quantum Precision Measurement, South China Normal University, Guangzhou 510006, People's Republic of China
- Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, People's Republic of China
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6
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Zhang Q, Wu TC, Kuang G, Xie A, Lin N. Investigation of edge states in artificial graphene nano-flakes. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:225003. [PMID: 33607633 DOI: 10.1088/1361-648x/abe819] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2020] [Accepted: 02/19/2021] [Indexed: 06/12/2023]
Abstract
Graphene nano-flakes (GNFs) are predicted to host spin-polarized metallic edge states, which are envisioned for exploration of spintronics at the nanometer scale. To date, experimental realization of GNFs is only in its infancy because of the limitation of precise cutting or synthesizing methods at the nanometer scale. Here, we use low temperature scanning tunneling microscope to manipulate coronene molecules on a Cu(111) surface to build artificial triangular and hexagonal GNFs with either zigzag or armchair type of edges. We observe that an electronic state at the Dirac point emerges only in the GNFs with zigzag edges and localizes at the outmost lattice sites. The experimental results agree well with the tight-binding calculations. Our work renders an experimental confirmation of the predicated edge states of the GNFs.
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Affiliation(s)
- Qiushi Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, People's Republic of China
- Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, United States of America
| | - Tsz Chun Wu
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, People's Republic of China
| | - Guowen Kuang
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, People's Republic of China
| | - A'yu Xie
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, People's Republic of China
| | - Nian Lin
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, People's Republic of China
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7
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Hirata M, Kobayashi A, Berthier C, Kanoda K. Interacting chiral electrons at the 2D Dirac points: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2021; 84:036502. [PMID: 33059346 DOI: 10.1088/1361-6633/abc17c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 10/15/2020] [Indexed: 06/11/2023]
Abstract
The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)2I3, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)2I3. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)2I3, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)2I3. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.
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Affiliation(s)
- Michihiro Hirata
- Institute for Materials Research, Tohoku University, Aoba-ku, Sendai 980-8577, Japan
- MPA-Q, Los Alamos National Laboratory, NM 87545, United States of America
| | - Akito Kobayashi
- Department of Physics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
| | - Claude Berthier
- Laboratoire National des Champs Magnétiques Intenses, UPR 3228 CNRS, EMFL, UGA, UPS and INSA, Boite Postale 166, 38042 Grenoble Cedex 9, France
| | - Kazushi Kanoda
- Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
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8
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Gallerati A. Negative-curvature spacetime solutions for graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:135501. [PMID: 33412525 DOI: 10.1088/1361-648x/abd9a2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Accepted: 01/07/2021] [Indexed: 06/12/2023]
Abstract
We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.
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Affiliation(s)
- Antonio Gallerati
- Politecnico di Torino, Dipartimento di Scienza Applicata e Tecnologia, corso Duca degli Abruzzi 24, 10129 Torino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Torino, via Pietro Giuria 1, 10125 Torino, Italy
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9
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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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10
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Pyrialakos GG, Schmitt N, Nye NS, Heinrich M, Kantartzis NV, Szameit A, Christodoulides DN. Symmetry-controlled edge states in the type-II phase of Dirac photonic lattices. Nat Commun 2020; 11:2074. [PMID: 32350272 PMCID: PMC7190735 DOI: 10.1038/s41467-020-15952-z] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Accepted: 03/30/2020] [Indexed: 11/09/2022] Open
Abstract
The exceptional properties exhibited by two-dimensional materials, such as graphene, are rooted in the underlying physics of the relativistic Dirac equation that describes the low energy excitations of such molecular systems. In this study, we explore a periodic lattice that provides access to the full solution spectrum of the extended Dirac Hamiltonian. Employing its photonic implementation of evanescently coupled waveguides, we indicate its ability to independently perturb the symmetries of the discrete model (breaking, also, the barrier towards the type-II phase) and arbitrarily define the location, anisotropy, and tilt of Dirac cones in the bulk. This unique aspect of topological control gives rise to highly versatile edge states, including an unusual class that emerges from the type-II degeneracies residing in the complex space of k. By probing these states, we investigate the topological nature of tilt and shed light on novel transport dynamics supported by Dirac configurations in two dimensions.
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Affiliation(s)
- Georgios G Pyrialakos
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece
| | - Nora Schmitt
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23, 18059, Rostock, Germany
| | - Nicholas S Nye
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece.,College of Optics & Photonics-CREOL, University of Central Florida, Orlando, FL, 2816, USA
| | - Matthias Heinrich
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23, 18059, Rostock, Germany
| | - Nikolaos V Kantartzis
- Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece
| | - Alexander Szameit
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23, 18059, Rostock, Germany
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11
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Kremer M, Biesenthal T, Maczewsky LJ, Heinrich M, Thomale R, Szameit A. Demonstration of a two-dimensional [Formula: see text]-symmetric crystal. Nat Commun 2019; 10:435. [PMID: 30683867 PMCID: PMC6347626 DOI: 10.1038/s41467-018-08104-x] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2018] [Accepted: 12/07/2018] [Indexed: 11/16/2022] Open
Abstract
With the discovery of [Formula: see text]-symmetric quantum mechanics, it was shown that even non-Hermitian systems may exhibit entirely real eigenvalue spectra. This finding did not only change the perception of quantum mechanics itself, it also significantly influenced the field of photonics. By appropriately designing one-dimensional distributions of gain and loss, it was possible to experimentally verify some of the hallmark features of [Formula: see text]-symmetry using electromagnetic waves. Nevertheless, an experimental platform to study the impact of [Formula: see text] -symmetry in two spatial dimensions has so far remained elusive. We break new grounds by devising a two-dimensional [Formula: see text]-symmetric system based on photonic waveguide lattices with judiciously designed refractive index landscape and alternating loss. With this system at hand, we demonstrate a non-Hermitian two-dimensional topological phase transition that is closely linked to the emergence of topological mid-gap edge states.
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Affiliation(s)
- Mark Kremer
- Institute for Physics, University of Rostock, Albert-Einstein-Straße 23, 18059 Rostock, Germany
| | - Tobias Biesenthal
- Institute for Physics, University of Rostock, Albert-Einstein-Straße 23, 18059 Rostock, Germany
| | - Lukas J. Maczewsky
- Institute for Physics, University of Rostock, Albert-Einstein-Straße 23, 18059 Rostock, Germany
| | - Matthias Heinrich
- Institute for Physics, University of Rostock, Albert-Einstein-Straße 23, 18059 Rostock, Germany
| | - Ronny Thomale
- Department of Physics and Astronomy, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
| | - Alexander Szameit
- Institute for Physics, University of Rostock, Albert-Einstein-Straße 23, 18059 Rostock, Germany
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12
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Liu X, Hersam MC. Interface Characterization and Control of 2D Materials and Heterostructures. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2018; 30:e1801586. [PMID: 30039558 DOI: 10.1002/adma.201801586] [Citation(s) in RCA: 58] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2018] [Revised: 04/09/2018] [Indexed: 05/28/2023]
Abstract
2D materials and heterostructures have attracted significant attention for a variety of nanoelectronic and optoelectronic applications. At the atomically thin limit, the material characteristics and functionalities are dominated by surface chemistry and interface coupling. Therefore, methods for comprehensively characterizing and precisely controlling surfaces and interfaces are required to realize the full technological potential of 2D materials. Here, the surface and interface properties that govern the performance of 2D materials are introduced. Then the experimental approaches that resolve surface and interface phenomena down to the atomic scale, as well as strategies that allow tuning and optimization of interfacial interactions in van der Waals heterostructures, are systematically reviewed. Finally, a future outlook that delineates the remaining challenges and opportunities for 2D material interface characterization and control is presented.
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Affiliation(s)
- Xiaolong Liu
- Applied Physics Graduate Program, Northwestern University, 2220 Campus Drive, Evanston, IL, 60208-3108, USA
| | - Mark C Hersam
- Applied Physics Graduate Program, Northwestern University, 2220 Campus Drive, Evanston, IL, 60208-3108, USA
- Department of Materials Science and Engineering, Department of Chemistry, Department of Medicine, Department of Electrical Engineering and Computer Science, Northwestern University, 2220 Campus Drive, Evanston, IL, 60208-3108, USA
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13
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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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14
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Tan X, Zhang DW, Liu Q, Xue G, Yu HF, Zhu YQ, Yan H, Zhu SL, Yu Y. Topological Maxwell Metal Bands in a Superconducting Qutrit. PHYSICAL REVIEW LETTERS 2018; 120:130503. [PMID: 29694203 DOI: 10.1103/physrevlett.120.130503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2017] [Revised: 01/01/2018] [Indexed: 06/08/2023]
Abstract
We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Threefold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.
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Affiliation(s)
- Xinsheng Tan
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Dan-Wei Zhang
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
| | - Qiang Liu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Guangming Xue
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hai-Feng Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Yan-Qing Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
| | - Hui Yan
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
| | - Shi-Liang Zhu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yang Yu
- National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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15
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Liu S, Shao LB, Hou QZ, Xue ZY. Quantum anomalous Hall phase in a one-dimensional optical lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:124001. [PMID: 29380747 DOI: 10.1088/1361-648x/aaab89] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We propose to simulate and detect quantum anomalous Hall phase with ultracold atoms in a one-dimensional optical lattice, with the other synthetic dimension being realized by modulating spin-orbit coupling. We show that the system manifests a topologically nontrivial phase with two chiral edge states which can be readily detected in this synthetic two-dimensional system. Moreover, it is interesting that at the phase transition point there is a flat energy band and this system can also be in a topologically nontrivial phase with two Fermi zero modes existing at the boundaries by considering the synthetic dimension as a modulated parameter. We also show how to measure these topological phases experimentally in ultracold atoms. Another model with a random Rashba and Dresselhaus spin-orbit coupling strength is also found to exhibit topological nontrivial phase, and the impact of the disorder to the system is revealed.
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Affiliation(s)
- Sheng Liu
- National Laboratory of Solid State Microstructures and School of Physics, Nanjing University, Nanjing 210093, People's Republic of China
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16
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Pyrialakos GG, Nye NS, Kantartzis NV, Christodoulides DN. Emergence of Type-II Dirac Points in Graphynelike Photonic Lattices. PHYSICAL REVIEW LETTERS 2017; 119:113901. [PMID: 28949222 DOI: 10.1103/physrevlett.119.113901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2017] [Indexed: 06/07/2023]
Abstract
We theoretically demonstrate that a type-II class of tilted Dirac cones can emerge in generalized two-dimensional anisotropic lattice arrangements. This is achieved by introducing a special set of graphynelike exchange bonds by means of which the complete spectrum of the underlying Weyl Hamiltonian can be realized. Our ab initio calculations demonstrate a unique class of eigensolutions corresponding to a type-II class of Dirac fermionic excitations. Based on our approach, one can systematically synthesize a wide range of strongly anisotropic band diagrams having tilted Dirac cones with variable location and orientation. Moreover, we show that asymmetric conical diffraction, as well as edge states, can arise in these configurations. Our results can provide a versatile platform to observe, for the first time, optical transport around type-II Dirac points in two-dimensional optical settings under linear, nonlinear, and non-Hermitian conditions.
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Affiliation(s)
- Georgios G Pyrialakos
- School of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece
| | - Nicholas S Nye
- College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816-270, USA
| | - Nikolaos V Kantartzis
- School of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece
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17
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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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18
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Tarnowski M, Nuske M, Fläschner N, Rem B, Vogel D, Freystatzky L, Sengstock K, Mathey L, Weitenberg C. Observation of Topological Bloch-State Defects and Their Merging Transition. PHYSICAL REVIEW LETTERS 2017; 118:240403. [PMID: 28665652 DOI: 10.1103/physrevlett.118.240403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2017] [Indexed: 06/07/2023]
Abstract
Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudospin texture. The topological defects appear as vortices in the azimuthal phase of this pseudospin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore, we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.
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Affiliation(s)
- Matthias Tarnowski
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Marlon Nuske
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Nick Fläschner
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Benno Rem
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
| | - Dominik Vogel
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
| | - Lukas Freystatzky
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Klaus Sengstock
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Ludwig Mathey
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
- Zentrum für Optische Quantentechnologien, Universität Hamburg, 22761 Hamburg, Germany
| | - Christof Weitenberg
- Institut für Laserphysik, Universität Hamburg, 22761 Hamburg, Germany
- The Hamburg Centre for Ultrafast Imaging, 22761 Hamburg, Germany
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19
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Weyl semimetals in optical lattices: moving and merging of Weyl points, and hidden symmetry at Weyl points. Sci Rep 2016; 6:33512. [PMID: 27644114 PMCID: PMC5028778 DOI: 10.1038/srep33512] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2015] [Accepted: 08/30/2016] [Indexed: 11/09/2022] Open
Abstract
We propose to realize Weyl semimetals in a cubic optical lattice. We find that there exist three distinct Weyl semimetal phases in the cubic optical lattice for different parameter ranges. One of them has two pairs of Weyl points and the other two have one pair of Weyl points in the Brillouin zone. For a slab geometry with (010) surfaces, the Fermi arcs connecting the projections of Weyl points with opposite topological charges on the surface Brillouin zone is presented. By adjusting the parameters, the Weyl points can move in the Brillouin zone. Interestingly, for two pairs of Weyl points, as one pair of them meet and annihilate, the originial two Fermi arcs coneect into one. As the remaining Weyl points annihilate further, the Fermi arc vanishes and a gap is opened. Furthermore, we find that there always exists a hidden symmetry at Weyl points, regardless of anywhere they located in the Brillouin zone. The hidden symmetry has an antiunitary operator with its square being −1.
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20
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Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field. ATOMS 2015. [DOI: 10.3390/atoms4010001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
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21
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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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22
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Dvorak M, Wu Z. Dirac point movement and topological phase transition in patterned graphene. NANOSCALE 2015; 7:3645-3650. [PMID: 25636026 DOI: 10.1039/c4nr06454b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The honeycomb lattice of graphene is characterized by linear dispersion and pseudospin chirality of fermions on the Dirac cones. If lattice anisotropy is introduced, the Dirac cones stay intact but move in reciprocal space. Dirac point movement can lead to a topological transition from semimetal to semiconductor when two inequivalent Dirac points merge, an idea that has attracted significant research interest. However, such movement normally requires unrealistically high lattice anisotropy. Here we show that anisotropic defects can break the C3 symmetry of graphene, leading to Dirac point drift in the Brillouin zone. Additionally, the long-range order in periodically patterned graphene can induce intervalley scattering between two inequivalent Dirac points, resulting in a semimetal-to-insulator topological phase transition. The magnitude and direction of Dirac point drift are predicted analytically, which are consistent with our first-principles electronic structure calculations. Thus, periodically patterned graphene can be used to study the fascinating physics associated with Dirac point movement and the corresponding phase transition.
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Affiliation(s)
- Marc Dvorak
- Department of Physics, Colorado School of Mines, Golden, CO, USA.
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23
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Walls JD, Hadad D. Suppressing Klein tunneling in graphene using a one-dimensional array of localized scatterers. Sci Rep 2015; 5:8435. [PMID: 25678400 PMCID: PMC4327422 DOI: 10.1038/srep08435] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2014] [Accepted: 01/19/2015] [Indexed: 11/28/2022] Open
Abstract
Graphene's unique physical and chemical properties make it an attractive platform for use in micro- and nanoelectronic devices. However, electrostatically controlling the flow of electrons in graphene can be challenging as a result of Klein tunneling, where electrons normally incident to a one-dimensional potential barrier of height V are perfectly transmitted even as V → ∞. In this study, theoretical and numerical calculations predict that the transmission probability for an electron wave normally incident to a one-dimensional array of localized scatterers can be significantly less than unity when the electron wavelength is smaller than the spacing between scatterers. In effect, placing periodic openings throughout a potential barrier can, somewhat counterintuitively, decrease transmission in graphene. Our results suggest that electrostatic potentials with spatial variations on the order of the electron wavelength can suppress Klein tunneling and could find applications in developing graphene electronic devices.
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Affiliation(s)
- Jamie D. Walls
- Department of Chemistry, University of Miami, Coral Gables, Florida 33124, USA
| | - Daniel Hadad
- Department of Chemistry, University of Miami, Coral Gables, Florida 33124, USA
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24
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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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25
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Liu MH, Rickhaus P, Makk P, Tóvári E, Maurand R, Tkatschenko F, Weiss M, Schönenberger C, Richter K. Scalable tight-binding model for graphene. PHYSICAL REVIEW LETTERS 2015; 114:036601. [PMID: 25659011 DOI: 10.1103/physrevlett.114.036601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2014] [Indexed: 06/04/2023]
Abstract
Artificial graphene consisting of honeycomb lattices other than the atomic layer of carbon has been shown to exhibit electronic properties similar to real graphene. Here, we reverse the argument to show that transport properties of real graphene can be captured by simulations using "theoretical artificial graphene." To prove this, we first derive a simple condition, along with its restrictions, to achieve band structure invariance for a scalable graphene lattice. We then present transport measurements for an ultraclean suspended single-layer graphene pn junction device, where ballistic transport features from complex Fabry-Pérot interference (at zero magnetic field) to the quantum Hall effect (at unusually low field) are observed and are well reproduced by transport simulations based on properly scaled single-particle tight-binding models. Our findings indicate that transport simulations for graphene can be efficiently performed with a strongly reduced number of atomic sites, allowing for reliable predictions for electric properties of complex graphene devices. We demonstrate the capability of the model by applying it to predict so-far unexplored gate-defined conductance quantization in single-layer graphene.
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Affiliation(s)
- Ming-Hao Liu
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Peter Rickhaus
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Péter Makk
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Endre Tóvári
- Department of Physics, Budapest University of Technology and Economics and Condensed Matter Research Group of the Hungarian Academy of Sciences, Budafoki ut 8, 1111 Budapest, Hungary
| | - Romain Maurand
- University Grenoble Alpes and CEA-INAC-SPSMS, F-38000 Grenoble, France
| | - Fedor Tkatschenko
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
| | - Markus Weiss
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Christian Schönenberger
- Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
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26
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Duca L, Li T, Reitter M, Bloch I, Schleier-Smith M, Schneider U. An Aharonov-Bohm interferometer for determining Bloch band topology. Science 2014; 347:288-92. [DOI: 10.1126/science.1259052] [Citation(s) in RCA: 185] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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27
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Wang ST, Deng DL, Duan LM. Probe of three-dimensional chiral topological insulators in an optical lattice. PHYSICAL REVIEW LETTERS 2014; 113:033002. [PMID: 25083642 DOI: 10.1103/physrevlett.113.033002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2014] [Indexed: 06/03/2023]
Abstract
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.
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Affiliation(s)
- S-T Wang
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA and Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - D-L Deng
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA and Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
| | - L-M Duan
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA and Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, People's Republic of China
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28
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Tao HS, Chen YH, Lin HF, Liu HD, Liu WM. Layer anti-ferromagnetism on bilayer honeycomb lattice. Sci Rep 2014; 4:5367. [PMID: 24947369 PMCID: PMC4064339 DOI: 10.1038/srep05367] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2013] [Accepted: 05/29/2014] [Indexed: 11/09/2022] Open
Abstract
Bilayer honeycomb lattice, with inter-layer tunneling energy, has a parabolic dispersion relation, and the inter-layer hopping can cause the charge imbalance between two sublattices. Here, we investigate the metal-insulator and magnetic phase transitions on the strongly correlated bilayer honeycomb lattice by cellular dynamical mean-field theory combined with continuous time quantum Monte Carlo method. The procedures of magnetic spontaneous symmetry breaking on dimer and non-dimer sites are different, causing a novel phase transition between normal anti-ferromagnet and layer anti-ferromagnet. The whole phase diagrams about the magnetism, temperature, interaction and inter-layer hopping are obtained. Finally, we propose an experimental protocol to observe these phenomena in future optical lattice experiments.
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Affiliation(s)
- Hong-Shuai Tao
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yao-Hua Chen
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Heng-Fu Lin
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hai-Di Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Wu-Ming Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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29
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Veselago lensing with ultracold atoms in an optical lattice. Nat Commun 2014; 5:3327. [PMID: 24525693 DOI: 10.1038/ncomms4327] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Accepted: 01/27/2014] [Indexed: 11/08/2022] Open
Abstract
Veselago pointed out that electromagnetic wave theory allows for materials with a negative index of refraction, in which most known optical phenomena would be reversed. A slab of such a material can focus light by negative refraction, an imaging technique strikingly different from conventional positive refractive index optics, where curved surfaces bend the rays to form an image of an object. Here we demonstrate Veselago lensing for matter waves, using ultracold atoms in an optical lattice. A relativistic, that is, photon-like, dispersion relation for rubidium atoms is realized with a bichromatic optical lattice potential. We rely on a Raman π-pulse technique to transfer atoms between two different branches of the dispersion relation, resulting in a focusing that is completely analogous to the effect described by Veselago for light waves. Future prospects of the demonstrated effects include novel sub-de Broglie wavelength imaging applications.
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30
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Bellec M, Kuhl U, Montambaux G, Mortessagne F. Topological transition of Dirac points in a microwave experiment. PHYSICAL REVIEW LETTERS 2013; 110:033902. [PMID: 23373925 DOI: 10.1103/physrevlett.110.033902] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2012] [Indexed: 06/01/2023]
Abstract
By means of a microwave tight-binding analogue experiment of a graphenelike lattice, we observe a topological transition between a phase with a pointlike band gap characteristic of massless Dirac fermions and a gapped phase. By applying a controlled anisotropy on the structure, we investigate the transition directly via density of states measurements. The wave function associated with each eigenvalue is mapped and reveals new states at the Dirac point, localized on the armchair edges. We find that with increasing anisotropy, these new states are more and more localized at the edges.
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Affiliation(s)
- Matthieu Bellec
- Laboratoire Physique de la Matière Condensée, CNRS UMR 7336, Université Nice-Sophia Antipolis, Nice, France
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31
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Gamayun OV, Gorbar EV, Gusynin VP. Magnetic field driven instability in the planar NJL model in the real-time formalism. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.86.065021] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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32
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Vishveshwara S. A glimpse of quantum phenomena in optical lattices. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2012; 370:2916-2929. [PMID: 22615468 DOI: 10.1098/rsta.2011.0248] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the non-specialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.
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Affiliation(s)
- Smitha Vishveshwara
- Department of Physics, Loomis Laboratories, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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Boada O, Celi A, Latorre JI, Lewenstein M. Quantum simulation of an extra dimension. PHYSICAL REVIEW LETTERS 2012; 108:133001. [PMID: 22540696 DOI: 10.1103/physrevlett.108.133001] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Indexed: 05/22/2023]
Abstract
We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest nontrivial realization of a fourth dimension corresponds to the creation of a bi-volume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.
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Affiliation(s)
- O Boada
- Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, 647 Diagonal, 08028 Barcelona, Spain
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34
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Tarruell L, Greif D, Uehlinger T, Jotzu G, Esslinger T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 2012; 483:302-5. [PMID: 22422263 DOI: 10.1038/nature10871] [Citation(s) in RCA: 712] [Impact Index Per Article: 59.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2011] [Accepted: 01/17/2012] [Indexed: 11/09/2022]
Abstract
Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.
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Affiliation(s)
- Leticia Tarruell
- Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland
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35
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Designer Dirac fermions and topological phases in molecular graphene. Nature 2012; 483:306-10. [PMID: 22422264 DOI: 10.1038/nature10941] [Citation(s) in RCA: 195] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2011] [Accepted: 02/09/2012] [Indexed: 11/09/2022]
Abstract
The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.
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36
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Neupert T, Santos L, Ryu S, Chamon C, Mudry C. Topological Hubbard model and its high-temperature quantum Hall effect. PHYSICAL REVIEW LETTERS 2012; 108:046806. [PMID: 22400877 DOI: 10.1103/physrevlett.108.046806] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2011] [Indexed: 05/31/2023]
Abstract
The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.
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Affiliation(s)
- Titus Neupert
- Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
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37
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Yang HT. Strain induced shift of Dirac points and the pseudo-magnetic field in graphene. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:505502. [PMID: 22119780 DOI: 10.1088/0953-8984/23/50/505502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We prove that the strain induced shift of the Dirac points in graphene is a curl field if the strain is nonuniform. This curl field provides a geometrical explanation of the strain induced pseudo-magnetic field. We also prove that the Dirac points must be confined within two triangles, each one having one-eighth the area of the Brillouin zone.
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Affiliation(s)
- Hua Tong Yang
- Center for Advanced Optoelectronic Functional Materials Research, Key Laboratory for UV-Emitting Materials and Technology of Ministry of Education, and School of Physics, Northeast Normal University, Changchun 130024, People's Republic of China.
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38
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Alba E, Fernandez-Gonzalvo X, Mur-Petit J, Pachos JK, Garcia-Ripoll JJ. Seeing topological order in time-of-flight measurements. PHYSICAL REVIEW LETTERS 2011; 107:235301. [PMID: 22182096 DOI: 10.1103/physrevlett.107.235301] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2011] [Revised: 08/31/2011] [Indexed: 05/31/2023]
Abstract
In this Letter, we provide a general methodology to directly measure topological order in cold atom systems. As an application, we propose the realization of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentum-space Skyrmions.
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Affiliation(s)
- E Alba
- Instituto de Física Fundamental, IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
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39
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Chen Z, Wu B. Bose-Einstein condensate in a honeycomb optical lattice: fingerprint of superfluidity at the Dirac point. PHYSICAL REVIEW LETTERS 2011; 107:065301. [PMID: 21902335 DOI: 10.1103/physrevlett.107.065301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2011] [Revised: 07/06/2011] [Indexed: 05/31/2023]
Abstract
Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adiabaticity by interaction of arbitrary small strength.
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Affiliation(s)
- Zhu Chen
- Institute of Physics, Chinese Academy of Sciences, Beijing, China
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40
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Wüster S, Eisfeld A, Rost JM. Conical intersections in an ultracold gas. PHYSICAL REVIEW LETTERS 2011; 106:153002. [PMID: 21568550 DOI: 10.1103/physrevlett.106.153002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2010] [Indexed: 05/30/2023]
Abstract
We find that energy surfaces of more than two atoms or molecules interacting via transition dipole-dipole potentials generically possess conical intersections (CIs). Typically only few atoms participate strongly in such an intersection. For the fundamental case, a circular trimer, we show how the CI affects adiabatic excitation transport via electronic decoherence or geometric phase interference. These phenomena may be experimentally accessible if the trimer is realized by light alkali atoms in a ring trap, whose interactions are induced by off-resonant dressing with Rydberg states. Such a setup promises a direct probe of the full many-body density dynamics near a CI.
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Affiliation(s)
- S Wüster
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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41
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Sun GY, Kou SP. Possible anomalous spin dynamics of the Hubbard model on a honeycomb lattice. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:045603. [PMID: 21406891 DOI: 10.1088/0953-8984/23/4/045603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
In this paper, the Hubbard model on a honeycomb lattice is investigated by using an O(3) nonlinear σ model. A possible candidate for a quantum non-magnetic insulator in a narrow parameter region is found near the metal-insulator transition. After studying the magnetic properties of the quantum non-magnetic insulator, anomalous spin dynamics is shown. In addition, we find that this region could be widened by hole doping.
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Affiliation(s)
- Gao-Yong Sun
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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42
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Bermudez A, Mazza L, Rizzi M, Goldman N, Lewenstein M, Martin-Delgado MA. Wilson fermions and axion electrodynamics in optical lattices. PHYSICAL REVIEW LETTERS 2010; 105:190404. [PMID: 21231153 DOI: 10.1103/physrevlett.105.190404] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2010] [Revised: 09/03/2010] [Indexed: 05/28/2023]
Abstract
We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.
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Affiliation(s)
- A Bermudez
- Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
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43
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Yu Y, Yang K. Simulating the Wess-Zumino supersymmetry model in optical lattices. PHYSICAL REVIEW LETTERS 2010; 105:150605. [PMID: 21230884 DOI: 10.1103/physrevlett.105.150605] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2010] [Revised: 09/11/2010] [Indexed: 05/30/2023]
Abstract
We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.
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Affiliation(s)
- Yue Yu
- Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100190, China
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44
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Bahat-Treidel O, Peleg O, Grobman M, Shapira N, Segev M, Pereg-Barnea T. Klein tunneling in deformed honeycomb lattices. PHYSICAL REVIEW LETTERS 2010; 104:063901. [PMID: 20366822 DOI: 10.1103/physrevlett.104.063901] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2009] [Revised: 09/17/2009] [Indexed: 05/29/2023]
Abstract
We study the scattering of waves off a potential step in deformed honeycomb lattices. For deformations below a critical value, perfect Klein tunneling is obtained; i.e., a potential step transmits waves at normal incidence with nonresonant unit-transmission probability. Beyond the critical deformation a gap forms in the spectrum, and a potential step perpendicular to the deformation direction reflects all normally incident waves, exhibiting a dramatic transition form unit transmission to total reflection. These phenomena are generic to honeycomb lattices and apply to electromagnetic waves in photonic lattices, quasiparticles in graphene, and cold atoms in optical lattices.
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Affiliation(s)
- Omri Bahat-Treidel
- Department of Physics, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
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45
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Goldman N, Kubasiak A, Bermudez A, Gaspard P, Lewenstein M, Martin-Delgado MA. Non-Abelian optical lattices: anomalous quantum Hall effect and Dirac fermions. PHYSICAL REVIEW LETTERS 2009; 103:035301. [PMID: 19659289 DOI: 10.1103/physrevlett.103.035301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2009] [Revised: 05/29/2009] [Indexed: 05/28/2023]
Abstract
We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular, we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
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Affiliation(s)
- N Goldman
- Center for Nonlinear Phenomena and Complex Systems-Université Libre de Bruxelles (U.L.B.), Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
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46
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Zhu SL, Zhang DW, Wang ZD. Delocalization of relativistic dirac particles in disordered one-dimensional systems and its implementation with cold atoms. PHYSICAL REVIEW LETTERS 2009; 102:210403. [PMID: 19519087 DOI: 10.1103/physrevlett.102.210403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2008] [Indexed: 05/27/2023]
Abstract
We study theoretically the localization of relativistic particles in disordered one-dimensional chains. It is found that the relativistic particles tend to delocalization in comparison with the nonrelativistic particles with the same disorder strength. More intriguingly, we reveal that the massless Dirac particles are entirely delocalized for any energy due to the inherent chiral symmetry, leading to a well-known result that particles are always localized in one-dimensional systems for arbitrary weak disorders to break down. Furthermore, we propose a feasible scheme to detect the delocalization feature of the Dirac particles with cold atoms in a light-induced gauge field.
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Affiliation(s)
- Shi-Liang Zhu
- Laboratory of Quantum Information Technology, SPTE, South China Normal University, Guangzhou, China
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47
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Park CH, Louie SG. Making massless Dirac fermions from a patterned two-dimensional electron gas. NANO LETTERS 2009; 9:1793-7. [PMID: 19338276 DOI: 10.1021/nl803706c] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
Analysis of the electronic structure of an ordinary two-dimensional electron gas (2DEG) under an appropriate external periodic potential of hexagonal symmetry reveals that massless Dirac fermions are generated near the corners of the supercell Brillouin zone. The required potential parameters are found to be achievable under or close to laboratory conditions. Moreover, the group velocity is tunable by changing either the effective mass of the 2DEG or the lattice parameter of the external potential, and it is insensitive to the potential amplitude. The finding should provide a new class of systems other than graphene for investigating and exploiting massless Dirac fermions using 2DEGs in semiconductors.
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Affiliation(s)
- Cheol-Hwan Park
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
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48
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Shao LB, Zhu SL, Sheng L, Xing DY, Wang ZD. Realizing and detecting the quantum Hall effect without landau levels by using ultracold atoms. PHYSICAL REVIEW LETTERS 2008; 101:246810. [PMID: 19113652 DOI: 10.1103/physrevlett.101.246810] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2008] [Indexed: 05/27/2023]
Abstract
We design an ingenious scheme to realize Haldane's quantum Hall model without Landau levels by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on site energies in two sublattices required in the model can be implemented through tuning the phase of one laser beam. The staggered magnetic field is generated from the light-induced Berry phase. Moreover, we establish a relation between the Hall conductivity and the atomic density, enabling us to detect the Chern number with the typical density-profile-measurement technique.
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Affiliation(s)
- L B Shao
- Institute for Condensed Matter Physics and Department of Physics, South China Normal University, Guangzhou, China
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49
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Bahat-Treidel O, Peleg O, Segev M. Symmetry breaking in honeycomb photonic lattices. OPTICS LETTERS 2008; 33:2251-2253. [PMID: 18830368 DOI: 10.1364/ol.33.002251] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We study the phenomena associated with symmetry breaking in honeycomb photonic lattices. As the honeycomb structure is gradually deformed, conical diffraction around its diabolic points becomes elliptic and eventually no longer occurs. As the deformation is further increased, a gap opens between the first two bands, and the lattice can support a gap soliton. The existence of the gap soliton serves as a means to detect the symmetry breaking and provide an estimate of the size of the gap.
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Affiliation(s)
- Omri Bahat-Treidel
- Department of Physics and Solid State Institute, Technion-Israel Institute of Technology, Haifa, Israel
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50
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Vaishnav JY, Clark CW. Observing Zitterbewegung with ultracold atoms. PHYSICAL REVIEW LETTERS 2008; 100:153002. [PMID: 18518102 DOI: 10.1103/physrevlett.100.153002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2007] [Indexed: 05/26/2023]
Abstract
We propose an optical lattice scheme which would permit the experimental observation of Zitterbewegung (ZB) with ultracold, neutral atoms. A four-level tripod variant of the setup for stimulated Raman adiabatic passage (STIRAP) has previously been proposed for generating non-Abelian gauge fields. Dirac-like Hamiltonians, which exhibit ZB, are simple examples of such non-Abelian gauge fields; we show how a variety of them can arise, and how ZB can be observed, in a tripod system. We predict that the ZB should occur at experimentally accessible frequencies and amplitudes.
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Affiliation(s)
- J Y Vaishnav
- Joint Quantum Institute, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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