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Title: Higher-order topology in bismuth

Abstract

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.

Authors:
 [1]; ORCiD logo [2];  [3];  [1];  [4];  [5];  [6];  [4];  [7]; ORCiD logo [8];  [4];  [4]; ORCiD logo [7];  [9]; ORCiD logo [1]
  1. Univ. of Zurich (Switzerland). Dept. of Physics
  2. Princeton Univ., NJ (United States). Dept. of Physics
  3. 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)
  4. Univ. Paris-Sud, Orsay (France). Lab. of Solid Physics
  5. Univ. Paris-Sud, Orsay (France). Center for Nuclear Sciences and Matter Sciences (CSNSM)
  6. 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
  7. Princeton Univ., NJ (United States). Joseph Henry Lab. and Dept. of Physics
  8. Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
  9. 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)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); 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
OSTI Identifier:
1476292
Report Number(s):
BNL-209127-2018-JAAM
Journal ID: ISSN 1745-2473
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
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nature Physics
Additional Journal Information:
Journal Volume: 14; Journal Issue: 9; Journal ID: ISSN 1745-2473
Publisher:
Nature Publishing Group (NPG)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

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, and Neupert, Titus. Higher-order topology in bismuth. United States: N. p., 2018. Web. doi:10.1038/s41567-018-0224-7.
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. Higher-order topology in bismuth. United States. doi:10.1038/s41567-018-0224-7.
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, and Neupert, Titus. Mon . "Higher-order topology in bismuth". United States. doi:10.1038/s41567-018-0224-7.
@article{osti_1476292,
title = {Higher-order topology in bismuth},
author = {Schindler, Frank and Wang, Zhijun and Vergniory, Maia G. and Cook, Ashley M. and Murani, Anil and Sengupta, Shamashis and Kasumov, Alik Yu. and Deblock, Richard and Jeon, Sangjun and Drozdov, Ilya and Bouchiat, Hélène and Guéron, Sophie and Yazdani, Ali and Bernevig, B. Andrei and Neupert, Titus},
abstractNote = {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.},
doi = {10.1038/s41567-018-0224-7},
journal = {Nature Physics},
number = 9,
volume = 14,
place = {United States},
year = {Mon Jul 30 00:00:00 EDT 2018},
month = {Mon Jul 30 00:00:00 EDT 2018}
}

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