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Topological quantum chemistry

Author

Listed:
  • Barry Bradlyn

    (Princeton Center for Theoretical Science, Princeton University)

  • L. Elcoro

    (University of the Basque Country UPV/EHU)

  • Jennifer Cano

    (Princeton Center for Theoretical Science, Princeton University)

  • M. G. Vergniory

    (Donostia International Physics Center
    University of the Basque Country UPV/EHU
    Max Planck Institute for Solid State Research)

  • Zhijun Wang

    (Princeton University)

  • C. Felser

    (Max Planck Institute for Chemical Physics of Solids)

  • M. I. Aroyo

    (University of the Basque Country UPV/EHU)

  • B. Andrei Bernevig

    (Donostia International Physics Center
    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)

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.

Suggested Citation

  • Barry Bradlyn & L. Elcoro & Jennifer Cano & M. G. Vergniory & Zhijun Wang & C. Felser & M. I. Aroyo & B. Andrei Bernevig, 2017. "Topological quantum chemistry," Nature, Nature, vol. 547(7663), pages 298-305, July.
  • Handle: RePEc:nat:nature:v:547:y:2017:i:7663:d:10.1038_nature23268
    DOI: 10.1038/nature23268
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    Citations

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    Cited by:

    1. Jinyu Liu & Yinong Zhou & Sebastian Yepez Rodriguez & Matthew A. Delmont & Robert A. Welser & Triet Ho & Nicholas Sirica & Kaleb McClure & Paolo Vilmercati & Joseph W. Ziller & Norman Mannella & Javie, 2024. "Controllable strain-driven topological phase transition and dominant surface-state transport in HfTe5," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    2. Lei Chen & Fang Xie & Shouvik Sur & Haoyu Hu & Silke Paschen & Jennifer Cano & Qimiao Si, 2024. "Emergent flat band and topological Kondo semimetal driven by orbital-selective correlations," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    3. Sungjoon Park & Yoonseok Hwang & Hong Chul Choi & Bohm-Jung Yang, 2021. "Topological acoustic triple point," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    4. Robert-Jan Slager & Adrien Bouhon & F. Nur Ünal, 2024. "Non-Abelian Floquet braiding and anomalous Dirac string phase in periodically driven systems," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    5. Jonah Herzog-Arbeitman & B. Andrei Bernevig & Zhi-Da Song, 2024. "Interacting topological quantum chemistry in 2D with many-body real space invariants," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    6. Wuyang Ren & Wenhua Xue & Shuping Guo & Ran He & Liangzi Deng & Shaowei Song & Andrei Sotnikov & Kornelius Nielsch & Jeroen Brink & Guanhui Gao & Shuo Chen & Yimo Han & Jiang Wu & Ching-Wu Chu & Zhimi, 2023. "Vacancy-mediated anomalous phononic and electronic transport in defective half-Heusler ZrNiBi," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    7. M. dos Santos Dias & N. Biniskos & F. J. dos Santos & K. Schmalzl & J. Persson & F. Bourdarot & N. Marzari & S. Blügel & T. Brückel & S. Lounis, 2023. "Topological magnons driven by the Dzyaloshinskii-Moriya interaction in the centrosymmetric ferromagnet Mn5Ge3," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    8. Chunyu Guo & A. Alexandradinata & Carsten Putzke & Amelia Estry & Teng Tu & Nitesh Kumar & Feng-Ren Fan & Shengnan Zhang & Quansheng Wu & Oleg V. Yazyev & Kent R. Shirer & Maja D. Bachmann & Hailin Pe, 2021. "Temperature dependence of quantum oscillations from non-parabolic dispersions," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
    9. Wenting Cheng & Alexander Cerjan & Ssu-Ying Chen & Emil Prodan & Terry A. Loring & Camelia Prodan, 2023. "Revealing topology in metals using experimental protocols inspired by K-theory," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    10. N. Wagner & L. Crippa & A. Amaricci & P. Hansmann & M. Klett & E. J. König & T. Schäfer & D. Di Sante & J. Cano & A. J. Millis & A. Georges & G. Sangiovanni, 2023. "Mott insulators with boundary zeros," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    11. Julian Schulz & Jiho Noh & Wladimir A. Benalcazar & Gaurav Bahl & Georg von Freymann, 2022. "Photonic quadrupole topological insulator using orbital-induced synthetic flux," Nature Communications, Nature, vol. 13(1), pages 1-6, December.
    12. Ilia Komissarov & Tobias Holder & Raquel Queiroz, 2024. "The quantum geometric origin of capacitance in insulators," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    13. Tian Le & Ruihan Zhang & Changcun Li & Ruiyang Jiang & Haohao Sheng & Linfeng Tu & Xuewei Cao & Zhaozheng Lyu & Jie Shen & Guangtong Liu & Fucai Liu & Zhijun Wang & Li Lu & Fanming Qu, 2024. "Magnetic field filtering of the boundary supercurrent in unconventional metal NiTe2-based Josephson junctions," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    14. Kuan-Sen Lin & Giandomenico Palumbo & Zhaopeng Guo & Yoonseok Hwang & Jeremy Blackburn & Daniel P. Shoemaker & Fahad Mahmood & Zhijun Wang & Gregory A. Fiete & Benjamin J. Wieder & Barry Bradlyn, 2024. "Spin-resolved topology and partial axion angles in three-dimensional insulators," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    15. Frank Schindler & Stepan S. Tsirkin & Titus Neupert & B. Andrei Bernevig & Benjamin J. Wieder, 2022. "Topological zero-dimensional defect and flux states in three-dimensional insulators," Nature Communications, Nature, vol. 13(1), pages 1-18, December.
    16. Weixuan Zhang & Fengxiao Di & Xingen Zheng & Houjun Sun & Xiangdong Zhang, 2023. "Hyperbolic band topology with non-trivial second Chern numbers," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    17. Fa-Jie Wang & Zhen-Yu Xiao & Raquel Queiroz & B. Andrei Bernevig & Ady Stern & Zhi-Da Song, 2024. "Anderson critical metal phase in trivial states protected by average magnetic crystalline symmetry," Nature Communications, Nature, vol. 15(1), pages 1-13, December.
    18. Zhongyi Zhang & Zhenfei Wu & Chen Fang & Fu-chun Zhang & Jiangping Hu & Yuxuan Wang & Shengshan Qin, 2024. "Topological superconductivity from unconventional band degeneracy with conventional pairing," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    19. Abdulhakim Bake & Qi Zhang & Cong Son Ho & Grace L. Causer & Weiyao Zhao & Zengji Yue & Alexander Nguyen & Golrokh Akhgar & Julie Karel & David Mitchell & Zeljko Pastuovic & Roger Lewis & Jared H. Col, 2023. "Top-down patterning of topological surface and edge states using a focused ion beam," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    20. Jiabin Yu & Rui-Xing Zhang & Zhi-Da Song, 2021. "Dynamical symmetry indicators for Floquet crystals," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    21. Luis Elcoro & Benjamin J. Wieder & Zhida Song & Yuanfeng Xu & Barry Bradlyn & B. Andrei Bernevig, 2021. "Magnetic topological quantum chemistry," Nature Communications, Nature, vol. 12(1), pages 1-10, December.

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