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Title: Higher-order topology in bismuth

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.
 [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:
Report Number(s):
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
Accepted Manuscript
Journal Name:
Nature Physics
Additional Journal Information:
Journal Volume: 14; Journal Issue: 9; Journal ID: ISSN 1745-2473
Nature Publishing Group (NPG)
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
Country of Publication:
United States
OSTI Identifier: