Topological quantum chemistry
Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent succes...
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| Vydáno v: | Nature (London) Ročník 547; číslo 7663; s. 298 - 305 |
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| Hlavní autoři: | , , , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
London
Nature Publishing Group UK
20.07.2017
Nature Publishing Group |
| Témata: | |
| ISSN: | 0028-0836, 1476-4687, 1476-4687 |
| On-line přístup: | Získat plný text |
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| Abstract | Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more.
A complete electronic band theory is presented that describes the global properties of all possible band structures and materials, and can be used to predict new topological insulators and semimetals.
A quantum chemistry theory of electron bands
Chemists and physicists have traditionally fostered very different perspectives on energy band theory. Barry Bradlyn
et al
. have developed a new and complete theory to calculate electronic band structure with the unique feature that it can be used to determine for any material whether it is topologically trivial or not. The theory consists of several parts, joining up the conventional band structure approach, which considers electron properties in non-local, momentum space, with a local viewpoint of chemical bonding and interactions. The authors classify the band structures for all 230 symmetry groups and show how this can be used to search for previously undiscovered materials with interesting topological properties. |
|---|---|
| AbstractList | Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more.Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more. Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more. Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low number is indicative of the esoteric nature of topological insulators or of a fundamental problem with the current approaches to finding them. Here we propose a complete electronic band theory, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding. This theory of topological quantum chemistry provides a description of the universal (across materials), global properties of all possible band structures and (weakly correlated) materials, consisting of a graph-theoretic description of momentum (reciprocal) space and a complementary group-theoretic description in real space. For all 230 crystal symmetry groups, we classify the possible band structures that arise from local atomic orbitals, and show which are topologically non-trivial. Our electronic band theory sheds new light on known topological insulators, and can be used to predict many more. A complete electronic band theory is presented that describes the global properties of all possible band structures and materials, and can be used to predict new topological insulators and semimetals. A quantum chemistry theory of electron bands Chemists and physicists have traditionally fostered very different perspectives on energy band theory. Barry Bradlyn et al . have developed a new and complete theory to calculate electronic band structure with the unique feature that it can be used to determine for any material whether it is topologically trivial or not. The theory consists of several parts, joining up the conventional band structure approach, which considers electron properties in non-local, momentum space, with a local viewpoint of chemical bonding and interactions. The authors classify the band structures for all 230 symmetry groups and show how this can be used to search for previously undiscovered materials with interesting topological properties. Not provided. |
| Audience | Academic |
| Author | Cano, Jennifer Vergniory, M. G. Bradlyn, Barry Felser, C. Bernevig, B. Andrei Wang, Zhijun Aroyo, M. I. Elcoro, L. |
| Author_xml | – sequence: 1 givenname: Barry surname: Bradlyn fullname: Bradlyn, Barry organization: Princeton Center for Theoretical Science, Princeton University – sequence: 2 givenname: L. surname: Elcoro fullname: Elcoro, L. organization: Department of Condensed Matter Physics, University of the Basque Country UPV/EHU – sequence: 3 givenname: Jennifer surname: Cano fullname: Cano, Jennifer organization: Princeton Center for Theoretical Science, Princeton University – sequence: 4 givenname: M. G. surname: Vergniory fullname: Vergniory, M. G. organization: Donostia International Physics Center, Department of Applied Physics II, University of the Basque Country UPV/EHU, Max Planck Institute for Solid State Research – sequence: 5 givenname: Zhijun surname: Wang fullname: Wang, Zhijun organization: Department of Physics, Princeton University – sequence: 6 givenname: C. surname: Felser fullname: Felser, C. organization: Max Planck Institute for Chemical Physics of Solids – sequence: 7 givenname: M. I. surname: Aroyo fullname: Aroyo, M. I. organization: Department of Condensed Matter Physics, University of the Basque Country UPV/EHU – sequence: 8 givenname: B. Andrei surname: Bernevig fullname: Bernevig, B. Andrei email: bernevig@princeton.edu organization: Donostia International Physics Center, Department of Physics, Princeton University, Laboratoire Pierre Aigrain, Ecole Normale Supérieure-PSL Research University, CNRS, Université Pierre et Marie Curie-Sorbonne Universités, Université Paris Diderot-Sorbonne Paris Cité, Sorbonne Universités, UPMC Université Paris 06 |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/28726818$$D View this record in MEDLINE/PubMed https://www.osti.gov/biblio/1535042$$D View this record in Osti.gov |
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Lett. doi: 10.1103/PhysRevLett.117.096404 – reference: 28726842 - Nature. 2017 Jul 19;547(7663):257-258 – reference: 28726840 - Nature. 2017 Jul 19;547(7663):272-274 – reference: 28726825 - Nature. 2017 Jul 19;547(7663):287-288 – reference: 32472016 - Nature. 2020 May 29;: |
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| Title | Topological quantum chemistry |
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