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Korshunov A, Hu H, Subires D, Jiang Y, Călugăru D, Feng X, Rajapitamahuni A, Yi C, Roychowdhury S, Vergniory MG, Strempfer J, Shekhar C, Vescovo E, Chernyshov D, Said AH, Bosak A, Felser C, Bernevig BA, Blanco-Canosa S. Softening of a flat phonon mode in the kagome ScV 6Sn 6. Nat Commun 2023; 14:6646. [PMID: 37863907 PMCID: PMC10589229 DOI: 10.1038/s41467-023-42186-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 09/29/2023] [Indexed: 10/22/2023] Open
Abstract
Geometrically frustrated kagome lattices are raising as novel platforms to engineer correlated topological electron flat bands that are prominent to electronic instabilities. Here, we demonstrate a phonon softening at the kz = π plane in ScV6Sn6. The low energy longitudinal phonon collapses at ~98 K and q = [Formula: see text] due to the electron-phonon interaction, without the emergence of long-range charge order which sets in at a different propagation vector qCDW = [Formula: see text]. Theoretical calculations corroborate the experimental finding to indicate that the leading instability is located at [Formula: see text] of a rather flat mode. We relate the phonon renormalization to the orbital-resolved susceptibility of the trigonal Sn atoms and explain the approximately flat phonon dispersion. Our data report the first example of the collapse of a kagome bosonic mode and promote the 166 compounds of kagomes as primary candidates to explore correlated flat phonon-topological flat electron physics.
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Affiliation(s)
- A Korshunov
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043, Grenoble, France
| | - H Hu
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, 20018, San Sebastián, Spain
| | - D Subires
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, 20018, San Sebastián, Spain
| | - Y Jiang
- Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - D Călugăru
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA
| | - X Feng
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, 20018, San Sebastián, Spain
- Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
| | - A Rajapitamahuni
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - C Yi
- Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
| | - S Roychowdhury
- Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
| | - M G Vergniory
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, 20018, San Sebastián, Spain
- Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
| | - J Strempfer
- Advanced Photon Source, Argonne National Laboratory, Lemont, IL, 60439, USA
| | - C Shekhar
- Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
| | - E Vescovo
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, NY, 11973, USA
| | - D Chernyshov
- Swiss-Norwegian BeamLines at European Synchrotron Radiation Facility, Grenoble, France
| | - A H Said
- Advanced Photon Source, Argonne National Laboratory, Lemont, IL, 60439, USA
| | - A Bosak
- European Synchrotron Radiation Facility (ESRF), BP 220, F-38043, Grenoble, France
| | - C Felser
- Max Planck Institute for Chemical Physics of Solids, 01187, Dresden, Germany
| | - B Andrei Bernevig
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, 20018, San Sebastián, Spain.
- Department of Physics, Princeton University, Princeton, NJ, 08544, USA.
- IKERBASQUE, Basque Foundation for Science, 48013, Bilbao, Spain.
| | - S Blanco-Canosa
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal, 20018, San Sebastián, Spain.
- IKERBASQUE, Basque Foundation for Science, 48013, Bilbao, Spain.
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2
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Sánchez-Barriga J, Clark OJ, Vergniory MG, Krivenkov M, Varykhalov A, Rader O, Schoop LM. Experimental Realization of a Three-Dimensional Dirac Semimetal Phase with a Tunable Lifshitz Transition in Au_{2}Pb. Phys Rev Lett 2023; 130:236402. [PMID: 37354399 DOI: 10.1103/physrevlett.130.236402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2022] [Revised: 03/02/2023] [Accepted: 04/28/2023] [Indexed: 06/26/2023]
Abstract
Three-dimensional Dirac semimetals are an exotic state of matter that continue to attract increasing attention due to the unique properties of their low-energy excitations. Here, by performing angle-resolved photoemission spectroscopy, we investigate the electronic structure of Au_{2}Pb across a wide temperature range. Our experimental studies on the (111)-cleaved surface unambiguously demonstrate that Au_{2}Pb is a three-dimensional Dirac semimetal characterized by the presence of a bulk Dirac cone projected off-center of the bulk Brillouin zone (BZ), in agreement with our theoretical calculations. Unusually, we observe that the bulk Dirac cone is significantly shifted by more than 0.4 eV to higher binding energies with reducing temperature, eventually going through a Lifshitz transition. The pronounced downward shift is qualitatively reproduced by our calculations indicating that an enhanced orbital overlap upon compression of the lattice, which preserves C_{4} rotational symmetry, is the main driving mechanism for the Lifshitz transition. These findings not only broaden the range of currently known materials exhibiting three-dimensional Dirac phases, but also show a viable mechanism by which it could be possible to switch on and off the contribution of the degeneracy point to electron transport without external doping.
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Affiliation(s)
- J Sánchez-Barriga
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
- IMDEA Nanoscience, C/ Faraday 9, Campus de Cantoblanco, 28049 Madrid, Spain
| | - O J Clark
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
| | - M G Vergniory
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
- IMDEA Nanoscience, C/ Faraday 9, Campus de Cantoblanco, 28049 Madrid, Spain
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- Max Planck Institute for Chemical Physics of Solids, Dresden D-01187, Germany
- Department of Chemistry, Princeton University, Princeton, 08544 New Jersey, USA
| | - M Krivenkov
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
| | - A Varykhalov
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
| | - O Rader
- Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
| | - L M Schoop
- Department of Chemistry, Princeton University, Princeton, 08544 New Jersey, USA
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3
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Chen S, Leng PL, Konečná A, Modin E, Gutierrez-Amigo M, Vicentini E, Martín-García B, Barra-Burillo M, Niehues I, Maciel Escudero C, Xie XY, Hueso LE, Artacho E, Aizpurua J, Errea I, Vergniory MG, Chuvilin A, Xiu FX, Hillenbrand R. Real-space observation of ultraconfined in-plane anisotropic acoustic terahertz plasmon polaritons. Nat Mater 2023:10.1038/s41563-023-01547-8. [PMID: 37142739 DOI: 10.1038/s41563-023-01547-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Accepted: 03/31/2023] [Indexed: 05/06/2023]
Abstract
Thin layers of in-plane anisotropic materials can support ultraconfined polaritons, whose wavelengths depend on the propagation direction. Such polaritons hold potential for the exploration of fundamental material properties and the development of novel nanophotonic devices. However, the real-space observation of ultraconfined in-plane anisotropic plasmon polaritons (PPs)-which exist in much broader spectral ranges than phonon polaritons-has been elusive. Here we apply terahertz nanoscopy to image in-plane anisotropic low-energy PPs in monoclinic Ag2Te platelets. The hybridization of the PPs with their mirror image-by placing the platelets above a Au layer-increases the direction-dependent relative polariton propagation length and the directional polariton confinement. This allows for verifying a linear dispersion and elliptical isofrequency contour in momentum space, revealing in-plane anisotropic acoustic terahertz PPs. Our work shows high-symmetry (elliptical) polaritons on low-symmetry (monoclinic) crystals and demonstrates the use of terahertz PPs for local measurements of anisotropic charge carrier masses and damping.
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Affiliation(s)
- S Chen
- Terahertz Technology Innovation Research Institute, National Basic Science Center-Terahertz Science and Technology Frontier, Terahertz Precision Biomedical Discipline 111 Project, Shanghai Key Lab of Modern Optical System, University of Shanghai for Science and Technology, Shanghai, China
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
| | - P L Leng
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
| | - A Konečná
- Central European Institute of Technology, Brno University of Technology, Brno, Czech Republic
- Institute of Physical Engineering, Brno University of Technology, Brno, Czech Republic
| | - E Modin
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
| | - M Gutierrez-Amigo
- Materials Physics Center, CSIC-UPV/EHU, Donostia-San Sebastián, Spain
- Departamento de Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco (UPV/EHU), Bilbao, Spain
| | - E Vicentini
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
| | - B Martín-García
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | | | - I Niehues
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
| | - C Maciel Escudero
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
- Materials Physics Center, CSIC-UPV/EHU, Donostia-San Sebastián, Spain
| | - X Y Xie
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China
| | - L E Hueso
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - E Artacho
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Cambridge, UK
- Donostia International Physics Centre (DIPC), Donostia-San Sebastián, Spain
| | - J Aizpurua
- Materials Physics Center, CSIC-UPV/EHU, Donostia-San Sebastián, Spain
- Donostia International Physics Centre (DIPC), Donostia-San Sebastián, Spain
| | - I Errea
- Materials Physics Center, CSIC-UPV/EHU, Donostia-San Sebastián, Spain
- Donostia International Physics Centre (DIPC), Donostia-San Sebastián, Spain
- Departamento de Física Aplicada, Escuela de Ingeniería de Gipuzkoa, Universidad del País Vasco (UPV/EHU), Donostia-San Sebastián, Spain
| | - M G Vergniory
- Donostia International Physics Centre (DIPC), Donostia-San Sebastián, Spain
- Max Planck for Chemical Physics of Solids, Dresden, Germany
| | - A Chuvilin
- CIC nanoGUNE BRTA, Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain
| | - F X Xiu
- State Key Laboratory of Surface Physics and Department of Physics, Institute for Nanoelectronic Devices and Quantum Computing, Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China.
| | - R Hillenbrand
- IKERBASQUE, Basque Foundation for Science, Bilbao, Spain.
- CIC nanoGUNE BRTA and Department of Electricity and Electronics, UPV/EHU, Donostia-San Sebastián, Spain.
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4
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Blanco de Paz M, Herrera MAJ, Arroyo Huidobro P, Alaeian H, Vergniory MG, Bradlyn B, Giedke G, García-Etxarri A, Bercioux D. Energy density as a probe of band representations in photonic crystals. J Phys Condens Matter 2022; 34:314002. [PMID: 35617944 DOI: 10.1088/1361-648x/ac73cf] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Accepted: 05/26/2022] [Indexed: 06/15/2023]
Abstract
Topological quantum chemistry (TQC) has recently emerged as an instrumental tool to characterize the topological nature of both fermionic and bosonic band structures. TQC is based on the study of band representations and the localization of maximally localized Wannier functions. In this article, we study various two-dimensional photonic crystal structures analyzing their topological character through a combined study of TQC, their Wilson-loop (WL) spectra and the electromagnetic energy density. Our study demonstrates that the analysis of the spatial localization of the energy density complements the study of the topological properties in terms of the spectrum of the WL operator and TQC.
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Affiliation(s)
- M Blanco de Paz
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- Instituto de Telecomunicações, Instituto Superior Tecnico-University of Lisbon, Avenida Rovisco Pais 1, Lisboa 1049-001, Portugal
| | - M A J Herrera
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, 20018 Donostia-San Sebastián, Basque Country, Spain
| | - P Arroyo Huidobro
- Instituto de Telecomunicações, Instituto Superior Tecnico-University of Lisbon, Avenida Rovisco Pais 1, Lisboa 1049-001, Portugal
| | - H Alaeian
- Elmore Family School of Electrical and Computer Engineering, Department of Physics and Astronomy, Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, United States of America
| | - M G Vergniory
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- Max Planck Institute for Chemical Physics of Solids, Dresden D-01187, Germany
| | - B Bradlyn
- Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, United States of America
| | - G Giedke
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Euskadi Plaza, 5, 48009 Bilbao, Spain
| | - A García-Etxarri
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Euskadi Plaza, 5, 48009 Bilbao, Spain
| | - D Bercioux
- Donostia International Physics Center, 20018 Donostia-San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, Euskadi Plaza, 5, 48009 Bilbao, Spain
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5
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Wang Z, Vergniory MG, Kushwaha S, Hirschberger M, Chulkov EV, Ernst A, Ong NP, Cava RJ, Bernevig BA. Publisher's Note: Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys [Phys. Rev. Lett. 117, 236401 (2016)]. Phys Rev Lett 2020; 124:239901. [PMID: 32603160 DOI: 10.1103/physrevlett.124.239901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Indexed: 06/11/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevLett.117.236401.
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6
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Vergniory MG, Elcoro L, Wang Z, Cano J, Felser C, Aroyo MI, Bernevig BA, Bradlyn B. Publisher's Note: Graph theory data for topological quantum chemistry [Phys. Rev. E 96, 023310 (2017)]. Phys Rev E 2020; 101:069902. [PMID: 32688549 DOI: 10.1103/physreve.101.069902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Indexed: 06/11/2023]
Abstract
This corrects the article DOI: 10.1103/PhysRevE.96.023310.
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7
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Vergniory MG, Elcoro L, Felser C, Regnault N, Bernevig BA, Wang Z. A complete catalogue of high-quality topological materials. Nature 2019; 566:480-485. [PMID: 30814710 DOI: 10.1038/s41586-019-0954-4] [Citation(s) in RCA: 181] [Impact Index Per Article: 36.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Accepted: 12/27/2018] [Indexed: 11/09/2022]
Abstract
Using a recently developed formalism called topological quantum chemistry, we perform a high-throughput search of 'high-quality' materials (for which the atomic positions and structure have been measured very accurately) in the Inorganic Crystal Structure Database in order to identify new topological phases. We develop codes to compute all characters of all symmetries of 26,938 stoichiometric materials, and find 3,307 topological insulators, 4,078 topological semimetals and no fragile phases. For these 7,385 materials we provide the electronic band structure, including some electronic properties (bandgap and number of electrons), symmetry indicators, and other topological information. Our results show that more than 27 per cent of all materials in nature are topological. We provide an open-source code that checks the topology of any material and allows other researchers to reproduce our results.
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Affiliation(s)
- M G Vergniory
- Donostia International Physics Center, San Sebastian, Spain.,IKERBASQUE, Basque Foundation for Science, Bilbao, Spain.,Applied Physics Department II, University of the Basque Country UPV/EHU, Bilbao, Spain
| | - L Elcoro
- Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Bilbao, Spain
| | - Claudia Felser
- Max Planck Institute for Chemical Physics of Solids, Dresden, Germany
| | - Nicolas Regnault
- Laboratoire de Physique de l'École Normale Supérieure, PSL University, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, Paris, France
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, NJ, USA. .,Physics Department, Freie Universität Berlin, Berlin, Germany. .,Max Planck Institute of Microstructure Physics, Halle, Germany.
| | - Zhijun Wang
- Department of Physics, Princeton University, Princeton, NJ, USA. .,Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing, China.
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8
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Cano J, Bradlyn B, Wang Z, Elcoro L, Vergniory MG, Felser C, Aroyo MI, Bernevig BA. Topology of Disconnected Elementary Band Representations. Phys Rev Lett 2018; 120:266401. [PMID: 30004773 DOI: 10.1103/physrevlett.120.266401] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2018] [Indexed: 06/08/2023]
Abstract
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples-one each in a symmorphic and a nonsymmorphic space group-of elementary band representations realized with an energy gap. In doing so, we explicitly construct a counterexample to a claim by Michel and Zak that single-valued elementary band representations in nonsymmorphic space groups with time-reversal symmetry are connected. For each example, we construct a topological invariant to explicitly demonstrate that the valence bands are nontrivial. We discover a new topological invariant: a movable but unremovable Dirac cone in the "Wilson Hamiltonian" and a bent-Z_{2} index.
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Affiliation(s)
- Jennifer Cano
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Barry Bradlyn
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Zhijun Wang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - L Elcoro
- Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - M G Vergniory
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Department of Applied Physics II, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain and Ikerbasque, Basque Foundation for Science, 48013 Bilbao, Spain
| | - C Felser
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - M I Aroyo
- Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France, Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris, France, and LPTMS, CNRS (UMR 8626), Université Paris-Saclay, 15 rue Georges Clémenceau, 91405 Orsay, France
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9
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Vergniory MG, Elcoro L, Wang Z, Cano J, Felser C, Aroyo MI, Bernevig BA, Bradlyn B. Graph theory data for topological quantum chemistry. Phys Rev E 2017; 96:023310. [PMID: 28950561 DOI: 10.1103/physreve.96.023310] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Indexed: 06/07/2023]
Abstract
Topological phases of noninteracting particles are distinguished by the global properties of their band structure and eigenfunctions in momentum space. On the other hand, group theory as conventionally applied to solid-state physics focuses only on properties that are local (at high-symmetry points, lines, and planes) in the Brillouin zone. To bridge this gap, we have previously [Bradlyn et al., Nature (London) 547, 298 (2017)NATUAS0028-083610.1038/nature23268] mapped the problem of constructing global band structures out of local data to a graph construction problem. In this paper, we provide the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs. Furthermore, we show how to apply these algorithms to certain "elementary" band structures highlighted in the aforementioned reference, and thus we identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures. Finally, we show how to use the newly developed bandrep program on the Bilbao Crystallographic Server to access the results of our computation.
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Affiliation(s)
- M G Vergniory
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Department of Applied Physics II, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
| | - L Elcoro
- Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - Zhijun Wang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Jennifer Cano
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - C Felser
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - M I Aroyo
- Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - B Andrei Bernevig
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, 24 rue Lhomond, 75231 Paris Cedex 05, France
- Sorbonne Universités, UPMC Université Paris 06, UMR 7589, LPTHE, F-75005 Paris, France
| | - Barry Bradlyn
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
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10
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Wang Z, Vergniory MG, Kushwaha S, Hirschberger M, Chulkov EV, Ernst A, Ong NP, Cava RJ, Bernevig BA. Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys. Phys Rev Lett 2016; 117:236401. [PMID: 27982662 DOI: 10.1103/physrevlett.117.236401] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2016] [Indexed: 06/06/2023]
Abstract
Weyl fermions have recently been observed in several time-reversal-invariant semimetals and photonics materials with broken inversion symmetry. These systems are expected to have exotic transport properties such as the chiral anomaly. However, most discovered Weyl materials possess a substantial number of Weyl nodes close to the Fermi level that give rise to complicated transport properties. Here we predict, for the first time, a new family of Weyl systems defined by broken time-reversal symmetry, namely, Co-based magnetic Heusler materials XCo_{2}Z (X=IVB or VB; Z=IVA or IIIA). To search for Weyl fermions in the centrosymmetric magnetic systems, we recall an easy and practical inversion invariant, which has been calculated to be -1, guaranteeing the existence of an odd number of pairs of Weyl fermions. These materials exhibit, when alloyed, only two Weyl nodes at the Fermi level-the minimum number possible in a condensed matter system. The Weyl nodes are protected by the rotational symmetry along the magnetic axis and separated by a large distance (of order 2π) in the Brillouin zone. The corresponding Fermi arcs have been calculated as well. This discovery provides a realistic and promising platform for manipulating and studying the magnetic Weyl physics in experiments.
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Affiliation(s)
- Zhijun Wang
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - M G Vergniory
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Department of Applied Physics II, Faculty of Science and Technology, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - S Kushwaha
- Department of Chemistry, Princeton University, Princeton, New Jersey 08540, USA
| | - Max Hirschberger
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - E V Chulkov
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
- Departamento de Física de Materiales, Universidad del País Vasco/Euskal Herriko Unibertsitatea UPV/EHU, 20080 Donostia-San Sebastián, Spain
- Saint Petersburg State University, 198504 Saint Petersburg, Russia
| | - A Ernst
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - N P Ong
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Robert J Cava
- Department of Chemistry, Princeton University, Princeton, New Jersey 08540, USA
| | - B Andrei Bernevig
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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11
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Bradlyn B, Cano J, Wang Z, Vergniory MG, Felser C, Cava RJ, Bernevig BA. Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals. Science 2016; 353:aaf5037. [DOI: 10.1126/science.aaf5037] [Citation(s) in RCA: 703] [Impact Index Per Article: 87.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2016] [Accepted: 07/05/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Barry Bradlyn
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
| | - Jennifer Cano
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544, USA
| | - Zhijun Wang
- Department of Physics, Princeton University, Princeton, NJ 08544, USA
| | - M. G. Vergniory
- Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018 Donostia-San Sebastián, Spain
| | - C. Felser
- Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
| | - R. J. Cava
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
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12
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Munoz F, Vergniory MG, Rauch T, Henk J, Chulkov EV, Mertig I, Botti S, Marques MAL, Romero AH. Topological Crystalline Insulator in a New Bi Semiconducting Phase. Sci Rep 2016; 6:21790. [PMID: 26905601 PMCID: PMC4764853 DOI: 10.1038/srep21790] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2015] [Accepted: 02/01/2016] [Indexed: 11/20/2022] Open
Abstract
Topological crystalline insulators are a type of topological insulators whose topological surface states are protected by a crystal symmetry, thus the surface gap can be tuned by applying strain or an electric field. In this paper we predict by means of ab initio calculations a new phase of Bi which is a topological crystalline insulator characterized by a mirror Chern number nM = −2, but not a strong topological insulator. This system presents an exceptional property: at the (001) surface its Dirac cones are pinned at the surface high-symmetry points. As a consequence they are also protected by time-reversal symmetry and can survive against weak disorder even if in-plane mirror symmetry is broken at the surface. Taking advantage of this dual protection, we present a strategy to tune the band-gap based on a topological phase transition unique to this system. Since the spin-texture of these topological surface states reduces the back-scattering in carrier transport, this effective band-engineering is expected to be suitable for electronic and optoelectronic devices with reduced dissipation.
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Affiliation(s)
- F Munoz
- Departamento de Física, Facultad de Ciencias, Universidad de Chile &Centro para el Desarrollo de la Nanociencia y la Nanotecnologia, CEDENNA, Santiago, Chile
| | - M G Vergniory
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain
| | - T Rauch
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
| | - J Henk
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
| | - E V Chulkov
- Donostia International Physics Center, 20018 Donostia-San Sebastian, Spain.,Tomsk State University, Tomsk, Russia.,Departamento de Fisica de materiales, Facultad de Ciencias Quimicas, UPV/EHU and Centro de Fisica de Materiales, Centro Mixto CSIC-UPV/EHU, San Sebastian, Spain.,St. Petersburg State University, St. Petersburg, Russia
| | - I Mertig
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany.,Max Planck Institute of Microstructure Physics, Halle, Germany
| | - S Botti
- Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität Jena, Jena, Germany.,Institut Lumière Matière (UMR5306), Université Lyon 1-CNRS, Université de Lyon, F-69622 Villeurbanne Cedex, France
| | - M A L Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany.,Institut Lumière Matière (UMR5306), Université Lyon 1-CNRS, Université de Lyon, F-69622 Villeurbanne Cedex, France
| | - A H Romero
- Physics Department, West Virginia University, Morgantown, USA
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13
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Roy S, Meyerheim HL, Ernst A, Mohseni K, Tusche C, Vergniory MG, Menshchikova TV, Otrokov MM, Ryabishchenkova AG, Aliev ZS, Babanly MB, Kokh KA, Tereshchenko OE, Chulkov EV, Schneider J, Kirschner J. Tuning the Dirac point position in Bi(2)Se(3)(0001) via surface carbon doping. Phys Rev Lett 2014; 113:116802. [PMID: 25259997 DOI: 10.1103/physrevlett.113.116802] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2014] [Indexed: 06/03/2023]
Abstract
Angular resolved photoemission spectroscopy in combination with ab initio calculations show that trace amounts of carbon doping of the Bi_{2}Se_{3} surface allows the controlled shift of the Dirac point within the bulk band gap. In contrast to expectation, no Rashba-split two-dimensional electron gas states appear. This unique electronic modification is related to surface structural modification characterized by an expansion of the top Se-Bi spacing of ≈11% as evidenced by surface x-ray diffraction. Our results provide new ways to tune the surface band structure of topological insulators.
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Affiliation(s)
- Sumalay Roy
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - H L Meyerheim
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - A Ernst
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany and Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Linnéstraße 2, 04103 Leipzig, Germany
| | - K Mohseni
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - C Tusche
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
| | - M G Vergniory
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany and Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Spain
| | - T V Menshchikova
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany and Tomsk State University, 634050 Tomsk, Russia
| | - M M Otrokov
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany and Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Spain and Tomsk State University, 634050 Tomsk, Russia
| | | | - Z S Aliev
- Baku State University, General and Inorganic Chemistry Department, AZ1148 Baku, Azerbaijan
| | - M B Babanly
- Baku State University, General and Inorganic Chemistry Department, AZ1148 Baku, Azerbaijan
| | - K A Kokh
- Institute of Geology and Mineralogy SB RAS, 630090 Novosibirsk, Russia
| | - O E Tereshchenko
- Institute of Semiconductor Physics SB RAS, and Novosibirsk State University, 630090 Novosibirsk, Russia
| | - E V Chulkov
- Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Spain and Departamento de Física de Materiales UPV/EHU, Centro de Física de Materiales CFM-MPC and Centro Mixto CSIC-UPV/EHU, 20080 San Sebastián/Donostia, Spain
| | - J Schneider
- Department für Geowissenschaften Ludwig-Maximilians Universität München, D-80333 München, Germany
| | - J Kirschner
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany and Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany
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14
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Vergniory MG, Marques MAL, Botti S, Amsler M, Goedecker S, Chulkov EV, Ernst A, Romero AH. Comment on "Topological insulators in ternary compounds with a honeycomb lattice". Phys Rev Lett 2013; 110:129701. [PMID: 25166853 DOI: 10.1103/physrevlett.110.129701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2012] [Indexed: 06/03/2023]
Abstract
A Comment on the Letter by Zhang et al., Phys. Rev. Lett. 106, 156402 (2011).
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Affiliation(s)
- M G Vergniory
- Max Planck Institute of Microstructure Physics, Halle 06120, Germany
| | - M A L Marques
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne cedex, France
| | - S Botti
- Institut Lumière Matière, UMR5306 Université Lyon 1-CNRS, Université de Lyon, 69622 Villeurbanne cedex, France
| | - M Amsler
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - S Goedecker
- Department of Physics, Universität Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - E V Chulkov
- Donostia International Physics Center, Donostia/San Sebastian 20018, Spain
| | - A Ernst
- Max Planck Institute of Microstructure Physics, Halle 06120, Germany
| | - A H Romero
- Max Planck Institute of Microstructure Physics, Halle 06120, Germany
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