Journal
NATURE PHYSICS
Volume 14, Issue 9, Pages 918-+Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41567-018-0224-7
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Funding
- Swiss National Science Foundation [200021_169061]
- European Union's Horizon 2020 research and innovation programme [ERC-StG-Neupert-757867-PARATOP]
- Spanish MINECO [IS2016-75862-P]
- National Science Foundation [NSF PHY-1125915]
- ANR grant DIRACFORMAG
- ANR grant MAGMA
- ANR grant JETS
- NSF-MRSEC programmes through the Princeton Center for Complex Materials [DMR-142054, NSF-DMR-1608848]
- ARO-MURI programme [W911NF-12-1-046]
- Department of Energy [de-sc0016239]
- Simons Investigator Award
- Packard Foundation
- Schmidt Fund for Innovative Research
- NSF EAGER grant [DMR-1643312, ONR-N00014-14-1-0330]
- ARO MURI [W911NF-12-1-0461]
- NSF-MRSEC [DMR-1420541]
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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. Here, 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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