Higher-order topology in bismuth

Schindler, Frank; Wang, Zhijun; Vergniory, Maia G.; Cook, Ashley M.; Murani, Anil; Sengupta, Shamashis; Kasumov, Alik Yu.; Deblock, Richard; Jeon, Sangjun; Drozdov, Ilya; Bouchiat, Hélène; Guéron, Sophie; Yazdani, Ali; Bernevig, B. Andrei; Neupert, Titus

doi:10.1038/s41567-018-0224-7

Title: Higher-order topology in bismuth

Journal Article · Mon Jul 30 00:00:00 EDT 2018 · Nature Physics

DOI:https://doi.org/10.1038/s41567-018-0224-7· OSTI ID:1476292

Schindler, Frank ^[1];

^[2]; Vergniory, Maia G. ^[3]; Cook, Ashley M. ^[1]; Murani, Anil ^[4]; Sengupta, Shamashis ^[5]; Kasumov, Alik Yu. ^[6]; Deblock, Richard ^[4]; Jeon, Sangjun ^[7];

^[8]; Bouchiat, Hélène ^[4]; Guéron, Sophie ^[4];

^[7]; Bernevig, B. Andrei ^[9];

^[1]

Univ. of Zurich (Switzerland). Dept. of Physics
Princeton Univ., NJ (United States). Dept. of Physics
Donostia International Physics Center (DIPC), Donostia (Spain); Univ. of the Basque Country, Bilbao (Spain). Dept. of Applied Physics II and Faculty of Science and Technology; Basque Foundation for Science (IKERBASQUE), Bilbao (Spain)
Univ. Paris-Sud, Orsay (France). Lab. of Solid Physics
Univ. Paris-Sud, Orsay (France). Center for Nuclear Sciences and Matter Sciences (CSNSM)
Univ. Paris-Sud, Orsay (France). Lab. of Solid Physics; Russian Academy of Sciences (RAS), Moscow (Russian Federation). Inst. of Microelectronics Technology and High Purity Materials
Princeton Univ., NJ (United States). Joseph Henry Lab. and Dept. of Physics
Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
Princeton Univ., NJ (United States). Joseph Henry Lab. and Dept. of Physics; Freie Univ., Berlin (Germany). Dept. of Physics; Max Planck Inst. of Microstructure Physics, Halle (Germany)

The mathematical field of topology has become a framework in which to describe the low-energy electronic structure of crystalline solids. Typical of a bulk insulating three-dimensional topological crystal are conducting two-dimensional surface states. This constitutes the topological bulk–boundary correspondence. We establish that the electronic structure of bismuth, an element consistently described as bulk topologically trivial, is in fact topological and follows a generalized bulk–boundary correspondence of higher-order: not the surfaces of the crystal, but its hinges host topologically protected conducting modes. These hinge modes are protected against localization by time-reversal symmetry locally, and globally by the three-fold rotational symmetry and inversion symmetry of the bismuth crystal. We support our claim theoretically and experimentally. Our theoretical analysis is based on symmetry arguments, topological indices, first-principles calculations, and the recently introduced framework of topological quantum chemistry. We provide supporting evidence from two complementary experimental techniques. With scanning-tunnelling spectroscopy, we probe the signatures of the rotational symmetry of the one-dimensional states located at the step edges of the crystal surface. With Josephson interferometry, we demonstrate their universal topological contribution to the electronic transport. Our work establishes bismuth as a higher-order topological insulator.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Swiss National Science Foundation (SNF); European Union (EU); Ministry of Economy and Competitiveness (MINECO) (Spain); National Science Foundation (NSF); National Research Agency (ANR) (France); US Army Research Office (ARO); Simons Foundation; Packard Foundation; Schmidt Fund

Grant/Contract Number:: SC0012704; 200021_169061; ERC-StG-Neupert-757867-PARATOP; IS2016-75862-P; DMR-142054; DMR-1608848; W911NF-12-1-046; sc0016239; DMR-1643312; ONR-N00014-14-1-0330; W911NF-12-1-0461; DMR-1420541

OSTI ID:: 1476292

Report Number(s):: BNL-209127-2018-JAAM

Journal Information:: Nature Physics, Vol. 14, Issue 9; ISSN 1745-2473

Publisher:: Nature Publishing Group (NPG)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 416 works

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Direct Observation of One-Dimensional Peierls-Type Charge Density Wave in Twin Boundaries of Monolayer MoTe$_2$ Wang, Li; Wu, Ying; Yu, Yayun arXiv https://doi.org/10.48550/arxiv.2007.07537	text	January 2020
Topological phases of amorphous matter Grushin, Adolfo G. arXiv https://doi.org/10.48550/arxiv.2010.02851	text	January 2020
Classical higher-order topological insulators Xie, Biye; Wang, Hai-Xiao; Zhang, Xiujuan arXiv https://doi.org/10.48550/arxiv.2010.05802	text	January 2020
First Principles Calculations for Topological Quantum Materials Xiao, Jiewen; Yan, Binghai arXiv https://doi.org/10.48550/arxiv.2010.08371	text	January 2020
Bulk and Edge Properties of Twisted Double-Bilayer Graphene Wang, Yimeng; Herzog-Arbeitman, Jonah; Burg, G. William arXiv https://doi.org/10.48550/arxiv.2101.03621	text	January 2021
Observation of higher-order non-Hermitian skin effect Zhang, Xiujuan; Tian, Yuan; Jiang, Jian-Hua arXiv https://doi.org/10.48550/arxiv.2102.09825	text	January 2021
Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices Olekhno, Nikita A.; Rozenblit, Alina D.; Kachin, Valerii I. arXiv https://doi.org/10.48550/arxiv.2103.08980	preprint	January 2021
IrRep: Symmetry eigenvalues and irreducible representations of ab initio band structures Mikel, Iraola,; L., Mañes, Juan; Barry, Bradlyn, Elsevier https://doi.org/10.5167/uzh-219129	text	January 2022

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