DOCSLIB.ORG

Dirac Fermions in Graphene and Graphite—A View from Angle

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Dirac Fermions in Graphene and Graphite—A View from Angle Dirac Fermions in Graphene and Graphite — a view from angle-resolved photoemission spectroscopy by Shuyun Zhou M.A. (UC Berkeley) 2005 B.S. (Tsinghua University) 2002 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor Alessandra Lanzara, Chair Professor Dung-Hai Lee Professor Oscar Dubon Fall 2007 The dissertation of Shuyun Zhou is approved. Chair Date Date Date University of California, Berkeley Fall 2007 Dirac Fermions in Graphene and Graphite — a view from angle-resolved photoemission spectroscopy Copyright c 2007 by Shuyun Zhou Abstract Dirac Fermions in Graphene and Graphite — a view from angle-resolved photoemission spectroscopy by Shuyun Zhou Doctor of Philosophy in Physics University of California, Berkeley Professor Alessandra Lanzara, Chair The research in graphene has exploded in the past few years, due to its intriguing physics as an emerging paradigm for relativistic condensed matter physics as well as its great promise for application in next gen- eration electronics. Understanding the low energy electronic structure of graphene is fundamental as most of the intriguing properties of graphene arise from its peculiar electronic dispersion, which resembles that of relativistic Dirac Fermions. This thesis presents a detailed study of the low energy electronic structure of graphene and its related three dimensional material - graphite - by using angle-resolved photoemission spectroscopy (ARPES), a direct probe of the electronic structure. In particular, the evolution of the Dirac Fermions in graphene and graphite as well as the effect of impurities is the focus of this thesis. This thesis is organized as follows. The first chapter is an introduction of the electronic structure of graphene and graphite, and the specialty of Dirac fermions compared to quasiparticles in conventional condensed matter systems. Chapter 2 is an introduction of the techniques used throughout this thesis - angle resolved photoemission spectroscopy (ARPES), X-ray photoemission spectroscopy (XPS) and low energy electron microscopy (LEEM). Chapter 3 discusses the growth and characterization of epitaxial graphene on SiC wafers. Chapters 4 and 5 present the ARPES results on epitaxial graphene, the evolution of the low energy electronic dynamics as a function of sample thickness and how to make graphene a finite band gap semi- conductor. More specifically, chapter 4 discusses how a gap is induced between the valence and conduction bands by graphene-substrate interaction and chapter 5 shows how a reversible metal-insulator transition can be possibly induced in epitaxial graphene by hole doping. Chapter 6 and 7 show the ARPES results on three dimensional graphite samples. Chapters 6 shows the coexistence of Dirac fermions with massive quasiparticles in different momentum space of single crys- talline graphite and the effect of impurity. Chapter 7 shows the surprising results of obtaining the band dispersions even in a partially polycrystalline graphite sample, the comparison with those obtained in sin- gle crystalline graphite, as well as the implication for ARPES study of partially polycrystalline samples in general. Professor Alessandra Lanzara Dissertation Committee Chair 1 Contents Abstract 1 Contents i Acknowledgements iii vitae vi 1 Introduction 1 1.1 Graphene - an emerging paradigm for relativistic condensed matter physics . 1 1.2 Electronic structure of graphene in the tight binding model . 3 1.3 Massless Dirac fermions and massive quasiparticles . 7 1.4 Electronic structure of infinite layer graphite . 8 2 Experimental techniques 10 2.1 Angle resolved photoemission spectroscopy (ARPES) . 10 2.1.1 ARPES and the photoelectric effect . 10 2.1.2 Three step model and sudden approximation . 13 2.1.3 Single particle spectral function description of ARPES . 15 2.1.4 Energy distribution curves (EDCs) and momentum distribution curves (MDCs) . 16 2.1.5 Electron mean free path and the probing depth of ARPES . 18 2.1.6 State of the art ARPES . 19 2.2 X-ray photoelectron spectroscopy (XPS) . 20 2.3 Low energy electron microscopy (LEEM) . 22 3 Growth and characterization of epitaxial graphene 24 3.1 Growth of epitaxial graphene . 24 3.2 Characterization of epitaxial graphene . 26 3.2.1 Scanning electron microscopy (SEM) . 26 3.2.2 X-ray photoemission spectroscopy (XPS) . 27 i 3.2.3 Angle-resolved photoemission spectroscopy - ARPES . 29 3.2.4 Low energy electron microscopy (LEEM) . 30 4 Gap opening in epitaxial graphene 33 4.1 Dirac fermions in epitaxial graphene . 34 4.2 Departure from conical dispersion in single layer epitaxial graphene . 35 4.3 Gap interpretation vs many body interactions . 39 4.4 Thickness dependence of the gap and Dirac point energy . 40 4.5 Possible mechanisms of the gap . 44 4.5.1 Inter-Dirac-point scattering . 44 4.5.2 Quantum confinement . 44 4.5.3 Breaking of the sublattice symmetry due to graphene-substrate interaction . 46 4.6 Conclusions . 49 5 Metal-insulator transition in epitaxial graphene by molecular doping 50 5.1 Motivation . 50 5.2 Valence band of graphene with adsorption of nitrogen dioxide . 51 5.3 Gas adsorption and metal-insulator transition in bilayer graphene . 53 5.4 Metal-insulator transition in single layer graphene . 55 5.5 Conclusions . 57 6 Dirac fermions and effect of impurities in single crystalline graphite 59 6.1 Introduction . 59 6.2 Electronic structure of single crystal graphite . 60 6.2.1 Dispersions at H - massless Dirac fermions . 61 6.2.2 Dispersions at K - massive quasiparticles . 66 6.3 Effect of defect states . 67 6.4 Conclusions . 70 7 ARPES study of partially polycrystalline graphite: HOPG 71 7.1 Electronic structure of polycrystalline materials measured by ARPES . 71 7.2 ARPES study of the electronic structure of polycrystalline graphite . 73 7.3 Explanation of the paradoxical coexistence based on a density of states argument . 75 7.4 Dispersions along the surface normal direction . 77 7.5 Comparison of data taken from HOPG and single crystalline graphite . 79 7.5.1 Interlayer coupling . 79 7.5.2 Low energy dispersions and Dirac fermions . 80 7.5.3 Defect states . 81 ii 7.6 Conclusions and implication of this study . 86 Bibliography 87 List of Figures 96 iii Acknowledgements I am very lucky to work with a group of talented and kind people in my Ph.D., from whom I have benefited greatly. All the work presented here would not have been possible without them. First of all, my deepest thanks go to my advisor, Alessandra Lanzara. I am very lucky to have such an inspiring, creative and considerate advisor, who has made my Ph.D. fruitful and enjoyable. Besides the training, encouragement and support that she gave me in science, I also appreciate her willingness to care about students’ life beyond work. The past few years of working with her has been a fortune for me. Her endless enthusiasm for science, her open-mindedness and her wisdom to balance work and life, have set her as a role model for me. I could not ask for better colleagues than the people in Lanzara group. Dr. Gey-Hong Gweon taught me numerous things in my first three years, ranging from experimental skills to different physics topics. I appreciate his mentoring and the efforts that he has put in to make me a good experimentalist. Dr. Kyle McElroy taught me the importance of understanding the physics problems in different perspectives. Jeff Graf, Chris Jozwiak and I joined the group as the first generation graduate students and we shared the longest memories of our Ph.D. lives. Besides intelligent, they are the best colleagues who are always willing to share their knowledge and skills and provide immediate help whenever needed. Daniel Garcia’s talks are the most wonderful sound of the group and I appreciate his help to improve my speech skills, though I have to admit that I am not a fast learner in this aspect. David Siegel reminded me of the early years of my Ph.D. It is a pleasure to see that he has become very good at communications and experiments. The interaction with visitors Dr. Marco Portalupi and Dr. Andreas Bill, as well as undergrads Elizabeth Rollings, Annie Endozo and Max Watson, has also been very pleasant. The collaboration with many theorists has been quite beneficial and pleasant. Dung-Hai Lee is the longest theoretical collaborator. His deep physics insights and his enthusiasm for finding the most beautiful solutions are very inspiring. The collaboration with A.N. Castro Neto, F. Guinea S.G. Louie and C.D. Spataru has been a great pleasure. Alexei Fedorov has collaborated in most of the research work presented here. His assistance in the experiments and his support for trying new experiments is highly appreciated. I am grateful to Andreas Schmid and Farid El Gably for providing extensive help with the LEEM measurements at the most critical time. John Pepper is very talented in machining and I thank him for making modifications to accommodate the needs of some challenging experiments. I thank Prof. P. N. First and Prof. W. A. de Heer for providing the graphene samples at the beginning of this project. I thank Prof. Oscar Dubon and Prof. Michael F. Crommie for serving as my committee members for the qualifying exam. J. T. Robinson and J. W. Beeman have been very nice to help me with substrate treatment. I thank the friendly and helpful people on the ALS floor: X. J. Zhou, W. L. Yang, N. Manella, K. Tanaka, S.-K. Mo, Y.-D. Chuang, J. H. Guo, B. K. Freelon, B. S. Mun. The LBL security people have been very kind to escort me to work and to home in many late nights. My personal interaction with other physicists also helps me greatly.
Load more

Recommended publications
  • Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene M
    Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene M. Milićević, G. Montambaux, T. Ozawa, O. Jamadi, B. Real, I. Sagnes, A. Lemaitre, L. Le Gratiet, A. Harouri, J. Bloch, et al. To cite this version: M. Milićević, G. Montambaux, T. Ozawa, O. Jamadi, B. Real, et al.. Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene. Physical Review X, American Physical Society, 2019, 9 (3), 10.1103/PhysRevX.9.031010. hal-02335931 HAL Id: hal-02335931 https://hal.archives-ouvertes.fr/hal-02335931 Submitted on 28 Oct 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. PHYSICAL REVIEW X 9, 031010 (2019) Featured in Physics Type-III and Tilted Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene M. Milićević,1 G. Montambaux,2 T. Ozawa,3 O. Jamadi,4 B. Real,4 I. Sagnes,1 A. Lemaître,1 L. Le Gratiet,1 A. Harouri,1 J. Bloch,1 and A. Amo4 1Centre de Nanosciences et de Nanotechnologies (C2N), CNRS Universit´e Paris-Sud/Paris-Saclay, Palaiseau, France 2Laboratoire de Physique des Solides,
    [Show full text]
  • Landau Quantization of Dirac Fermions in Graphene and Its Multilayers
    Front. Phys. 12(4), 127208 (2017) DOI 10.1007/s11467-016-0655-5 REVIEW ARTICLE Landau quantization of Dirac fermions in graphene and its multilayers Long-jing Yin (殷隆晶), Ke-ke Bai (白珂珂), Wen-xiao Wang (王文晓), Si-Yu Li (李思宇), Yu Zhang (张钰), Lin He (何林)ǂ The Center for Advanced Quantum Studies, Department of Physics, Beijing Normal University, Beijing 100875, China Corresponding author. E-mail: ǂ[email protected] Received December 28, 2016; accepted January 26, 2017 When electrons are confined in a two-dimensional (2D) system, typical quantum–mechanical phenomena such as Landau quantization can be detected. Graphene systems, including the single atomic layer and few-layer stacked crystals, are ideal 2D materials for studying a variety of quantum–mechanical problems. In this article, we review the experimental progress in the unusual Landau quantized behaviors of Dirac fermions in monolayer and multilayer graphene by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Through STS measurement of the strong magnetic fields, distinct Landau-level spectra and rich level-splitting phenomena are observed in different graphene layers. These unique properties provide an effective method for identifying the number of layers, as well as the stacking orders, and investigating the fundamentally physical phenomena of graphene. Moreover, in the presence of a strain and charged defects, the Landau quantization of graphene can be significantly modified, leading to unusual spectroscopic and electronic properties. Keywords Landau quantization, graphene, STM/STS, stacking order, strain and defect PACS numbers Contents 1 Introduction ....................................................................................................................... 2 2 Landau quantization in graphene monolayer, Bernal bilayer, and Bernal trilayer ...........
    [Show full text]
  • Borophosphene: a New Anisotropic Dirac Cone Monolayer with High
    Borophosphene: a New Anisotropic Dirac Cone Monolayer with High Fermi Velocity and Unique Feature of Self-doping Yang Zhang,†,‡ Jun Kang,‡ Fan Zheng,‡ Peng-Fei Gao,† Sheng-Li Zhang,† and Lin-Wang Wang*,‡ †Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Department of Applied Physics, School of Science, Xi'an Jiaotong University, Xi'an 710049, China ‡Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA ABSTRACT: Two-dimensional (2D) Dirac cone materials exhibit linear energy dispersion at the Fermi level, where the effective masses of carriers are very close to zero and the Fermi velocity is ultrahigh, only 2 ~ 3 orders of magnitude lower than the light velocity. Such the Dirac cone materials have great promise in high-performance electronic devices. Herein, we have employed the genetic algorithms methods combining with first-principles calculations to propose a new 2D anisotropic Dirac cone material, that is, orthorhombic boron phosphide (BP) monolayer named as borophosphene. Molecular dynamics simulation and phonon dispersion have been used to evaluate the dynamic and thermal stability of borophosphene. Because of the unique arrangements of B-B and P-P dimers, the mechanical and electronic properties are highly anisotropic. Of great interest is that the Dirac cone of the borophosphene is robust, independent of in-plane biaxial and uniaxial strains, and can also be observed in its one-dimensional (1D) zigzag nanoribbons and armchair nanotubes. The Fermi velocities are ~ 105 m/s, the same order of magnitude with that of graphene. By using a tight-binding model, the origin of the Dirac cone of borophosphene is analyzed.
    [Show full text]
  • Optical Studies on Dirac and Weyl Semimetals
    Optical Studies on Dirac and Weyl Semimetals Von der Fakult¨at Mathematik und Physik der Universit¨at Stuttgart zur Erlangung der Wurde¨ eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung vorgelegt von Micha Benjamin Schilling aus Gunzburg¨ Hauptberichter: Prof. Dr. Martin Dressel Mitberichter: Dr. Jurgen Smet Tag der mundlichen¨ Prufung:¨ 19.11.2018 Prufungsvorsitzende:¨ Prof. Dr. Maria Daghofer 1. Physikalisches Institut der Universit¨at Stuttgart 2018 Wer die Grenzen akzeptiert, der ist grenzenlos beschr¨ankt! Paul Hartmut Wurdig¨ (Sido) in 'Grenzenlos' - Sido feat. Marius Muller-Westernhagen¨ (2013) To God and all creation Abstract This thesis presents the results of optical spectroscopy measurements on various Dirac materials, including the nodal line semimetal ZrSiS, the topologically non- trivial half-Heusler compounds YbPtBi and GdPtBi, and the anisotropic Dirac semimetals CaMnBi2 and SrMnBi2. Generally, optical studies of this kind access the low-energy excitation spectra of the materials. In case of Dirac materials, optics probes the dynamics of Dirac and Weyl fermions, as well as other exotic quasiparticles emerging in these quantum materials. The major results, obtained in this work can be summarized as follows. In ZrSiS, the response of the nodal line Dirac fermions is revealed by a frequency- independent optical conductivity σ1(!), which arises from the effectively reduced dimensionality of the linearly dispersing bands [1,2]. This is consistent with band structure calculations [3] and verified by a theoretical model for the optical response of nodal line semimetals [2]. From our optical fits, we derive the length k0 of the nodal line in the reciprocal space and an upper limit for the energy gap ∆ induced by spin-orbit coupling.
    [Show full text]
  • Introduction to Dirac Materials and Topological Insulators Jérome Cayssol
    Introduction to Dirac materials and topological insulators Jérome Cayssol To cite this version: Jérome Cayssol. Introduction to Dirac materials and topological insulators. Comptes Rendus Physique, Centre Mersenne, 2013, 14 (9-10), pp.760-778. 10.1016/j.crhy.2013.09.012. hal-00942955 HAL Id: hal-00942955 https://hal.archives-ouvertes.fr/hal-00942955 Submitted on 1 Mar 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial| 4.0 International License Topological insulators/Isolants topologiques Introduction to Dirac materials and topological insulators Introduction aux matériaux de Dirac et aux isolants topologiques ∗ Jérôme Cayssol a,b, a Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany b LOMA (UMR 5798), CNRS and University Bordeaux-1, 33045 Talence, France article info abstract Keywords: We present a short pedagogical introduction to the physics of Dirac materials, restricted Dirac fermions to graphene and two-dimensional topological insulators. We start with a brief reminder of Graphene the Dirac and Weyl equations in the particle physics context. Turning to condensed matter Topological insulators systems, semimetallic graphene and various Dirac insulators are introduced, including the Edge modes Haldane and the Kane–Mele topological insulators.
    [Show full text]
  • The Rare Two-Dimensional Materials with Dirac Cones
    The Rare Two-Dimensional Materials with Dirac Cones Jinying Wang, Shibin Deng, Zhongfan Liu, and Zhirong Liu* 1 Center for Nanochemstry, Colledge of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China *Email address: [email protected] Note: This manuscript has been published as Natl. Sci. Rev. 2 (1), 22-39 (2015), refer to: http://nsr.oxfordjournals.org/content/2/1/22.full Keywords: graphene, silicene, graphyne, two-dimensional, Dirac cone, Dirac materials ABSTRACT Inspired by the great development of graphene, more and more works have 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
    [Show full text]
  • Manipulating Type-I and Type-II Dirac Polaritons in Cavity-Embedded Honeycomb Metasurfaces
    ORE Open Research Exeter TITLE Manipulating Type-I and Type-II Dirac Polaritons in Cavity-Embedded Honeycomb Metasurfaces AUTHORS Mann, C-R; Sturges, TJ; Weick, G; et al. JOURNAL Nature Communications DEPOSITED IN ORE 21 March 2018 This version available at http://hdl.handle.net/10871/33238 COPYRIGHT AND REUSE Open Research Exeter makes this work available in accordance with publisher policies. A NOTE ON VERSIONS The version presented here may differ from the published version. If citing, you are advised to consult the published version for pagination, volume/issue and date of publication ARTICLE DOI: 10.1038/s41467-018-03982-7 OPEN Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces Charlie-Ray Mann 1, Thomas J. Sturges 1, Guillaume Weick2, William L. Barnes 1 & Eros Mariani1 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. 1234567890():,; 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.
    [Show full text]
  • Landau Quantization of Topological Surface States in Bi2se3
    Selected for a Viewpoint in Physics week ending PRL 105, 076801 (2010) PHYSICAL REVIEW LETTERS 13 AUGUST 2010 Landau Quantization of Topological Surface States in Bi2Se3 Peng Cheng,1 Canli Song,1 Tong Zhang,1,2 Yanyi Zhang,1 Yilin Wang,2 Jin-Feng Jia,1 Jing Wang,1 Yayu Wang,1 Bang-Fen Zhu,1 Xi Chen,1,* Xucun Ma,2,† Ke He,2 Lili Wang,2 Xi Dai,2 Zhong Fang,2 Xincheng Xie,2 Xiao-Liang Qi,3,4 Chao-Xing Liu,4,5 Shou-Cheng Zhang,4 and Qi-Kun Xue1,2 1Department of Physics, Tsinghua University, Beijing 100084, China 2Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China 3Microsoft Research, Station Q, University of California, Santa Barbara, California 93106, USA 4Department of Physics, Stanford University, Stanford California 94305, USA 5Physikalisches Institut, Universita¨tWu¨rzburg, D-97074 Wu¨rzburg, Germany (Received 25 May 2010; published 9 August 2010) We report the direct observation of Landau quantization in Bi2Se3 thin films by using a low-temperature scanning tunneling microscope. In particular, we discovered the zeroth Landau level, which is predicted to give rise to the half-quantized Hall effect for the topological surface states. The existence of the discrete Landau levels (LLs) and the suppression of LLs by surface impurities strongly support the 2D nature of the topological states. These observations may eventually lead to the realization of quantum Hall effect in topological insulators. DOI: 10.1103/PhysRevLett.105.076801 PACS numbers: 73.20.Àr, 68.37.Ef, 71.70.Di, 72.25.Dc The recent theoretical prediction and experimental real- 0:03 =cm and thickness of 0.1 mm.
    [Show full text]
  • Dirac Material Graphene
    Dirac Material Graphene Elena Sheka Russian Peoples’ Friendship University of Russia Moscow, 117198 Russia [email protected] Abstract. The paper presents author’s view on spin-rooted properties of graphene supported by numerous experimental and calculation evidences. Correlation of odd pz electrons of the honeycomb lattice meets a strict demand “different orbitals for different spins”, which leads to spin polarization of electronic states, on the one hand, and generation of an impressive pool of local spins distributed over the lattice, on the other. These features characterize graphene as a peculiar semimetal with Dirac cone spectrum at particular points of Brillouin zone. However, spin-orbit coupling (SOC), though small but available, supplemented by dynamic SOC caused by electron correlation, transforms graphene-semimetal into graphene-topological insulator (TI). The consequent topological non-triviality and local spins are proposed to discuss such peculiar properties of graphene as high temperature ferromagnetism and outstanding chemical behavior. The connection of these new findings with difficulties met at attempting to convert graphene-TI into semiconductor one is discussed. Key words: graphene, Dirac fermions, quasi-relativistic description, hexagonal honeycomb structure, local spins, open-shell molecules, spin-orbital coupling, quantum spin Hall insulator, high temperature ferromagnetism, chemical activity. 1. Introduction Presented in the current paper concerns three main issues laying the foundation of spin features of graphene: (1) a significant correlation of pz odd electrons, exhibited in terms of spin peculiarities of the unrestricted Hartree-Fock (UHF) solutions, (2) spin-orbital coupling (SOC) and (3) the crucial role of the C=C bond length distribution over the body in exhibiting the spin- based features.
    [Show full text]
  • Dirac Cone, Flat Band and Saddle Point in Kagome Magnet Ymn6sn6
    ARTICLE https://doi.org/10.1038/s41467-021-23536-8 OPEN Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6 Man Li 1, Qi Wang1, Guangwei Wang2, Zhihong Yuan2, Wenhua Song1, Rui Lou3,4,5, Zhengtai Liu 6, ✉ ✉ ✉ ✉ Yaobo Huang7, Zhonghao Liu6,8 , Hechang Lei 1 , Zhiping Yin 2 & Shancai Wang 1 Kagome-lattices of 3d-transition metals hosting Weyl/Dirac fermions and topological flat bands exhibit non-trivial topological characters and novel quantum phases, such as the 1234567890():,; anomalous Hall effect and fractional quantum Hall effect. With consideration of spin–orbit coupling and electron correlation, several instabilities could be induced. The typical char- acters of the electronic structure of a kagome lattice, i.e., the saddle point, Dirac-cone, and flat band, around the Fermi energy (EF) remain elusive in magnetic kagome materials. We present the experimental observation of the complete features in ferromagnetic kagome layers of YMn6Sn6 helically coupled along the c-axis, by using angle-resolved photoemission spectroscopy and band structure calculations. We demonstrate a Dirac dispersion near EF, which is predicted by spin-polarized theoretical calculations, carries an intrinsic Berry cur- vature and contributes to the anomalous Hall effect in transport measurements. In addition, a flat band and a saddle point with a high density of states near EF are observed. These multi- sets of kagome features are of orbital-selective origin and could cause multi-orbital mag- netism. The Dirac fermion, flat band and saddle point in the vicinity of EF open an opportunity in manipulating the topological properties in magnetic materials. 1 Department of Physics and Beijing Key Laboratory of Opto-Electronic Functional Materials & Micro-Nano Devices, Renmin University of China, Beijing, China.
    [Show full text]
  • Arxiv:1707.04503V2 [Physics.Optics] 4 Mar 2018 2
    Manipulating Type-I and Type-II Dirac Polaritons in Cavity-Embedded Honeycomb Metasurfaces Charlie-Ray Mann,1 Thomas J. Sturges,1 Guillaume Weick,2 William L. Barnes,1 and Eros Mariani1 1EPSRC Centre for Doctoral Training in Metamaterials (XM2), Department of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, United Kingdom. 2Universite´ de Strasbourg, CNRS, Institut de Physique et Chimie des Materiaux´ de Strasbourg, UMR 7504, F-67000 Strasbourg, France. 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. A new kind of type-II Dirac point emerges which simultaneously exists with its conventional type-I counterpart. By modifying only the photonic environment via an enclosing cavity, one can manipulate the location of the type-II Dirac points, leading to distinct polariton phases. This enables one to alter the fundamental properties of the emergent Dirac polaritons while preserv- ing the lattice structure—a unique scenario which has no analog in real or artificial graphene systems so far. Exploiting the photonic environment will thus give rise to unexplored Dirac physics at the subwavelength scale. arXiv:1707.04503v2 [physics.optics] 4 Mar 2018 2 The groundbreaking discovery of monolayer graphene [1] has inspired an extensive quest to emulate massless Dirac quasi- particles in a myriad of distinct artificial graphene systems [2–11], ranging from ultracold atoms in optical lattices [3] to evanescently coupled photonic waveguide arrays [4].
    [Show full text]
  • Tilted and Type-III Dirac Cones Emerging from Flat Bands in Photonic Orbital Graphene
    Tilted and type-III Dirac cones emerging from flat bands in photonic orbital graphene M. Milicevic 1, G. Montambaux 2, T. Ozawa 3, I. Sagnes 1, A. Lemaître 1, L. Le Gratiet 1, A. Harouri 1, J. Bloch 1, A. Amo 4* 1Centre de Nanosciences et de Nanotechnologies, CNRS, Univ. Paris-Sud, Université Paris-Saclay, C2N- Marcoussis, 91460 Marcoussis, France 2Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, France 3 Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan 4Univ. Lille, CNRS, UMR 8523 – PhLAM – Physique des Lasers Atomes et Molécules, F-59000 Lille, France *[email protected] The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, the emergence of intricate transport phenomena has been predicted, such as modified Klein tunnelling, intrinsic anomalous Hall effects and ferrimagnetism. However, Dirac materials are rare, particularly with tilted Dirac cones. Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of exotic Dirac dispersions. Here we take advantage of the orbital structure of photonic resonators arranged in a honeycomb lattice to implement photonic lattices with semi- Dirac, tilted and, most interestingly, type-III Dirac cones that combine flat and linear dispersions. The tilted cones emerge from the touching of a flat and a parabolic band with a non-trivial topological charge. These results open the way to the synthesis of orbital Dirac matter with unconventional transport properties and, in combination with polariton nonlinearities, to the study of topological and Dirac superfluids in photonic lattices.
    [Show full text]