Higher-Order Topology in Bismuth
By F. Schindler, Zhijun Wang, M. Vergniory, A. Cook, A. Murani, S. Sengupta, A. Kasumov, R. Deblock, Sangjun Jeon, I. Drozdov and 5 more. Nature Physics, 2018
772 citations recorded by the source corpus.
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. The study of the band structure and crystal symmetry of the semimetal bismuth indicates that this material is a higher-order topological insulator hosting robust one-dimensional metallic states on the hinges of the crystal.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/11de0e0f0388f747bc6e51aa935175fa48c1a218
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Citations in the corpus
- Gapless Surface Dirac Cone in Antiferromagnetic Topological Insulator MnBi2Te4 (2019, background): “While high-order topology and gapless hinge or edge states can be protected by symmetry operations like threefold axis [56], MxT , C3z, and C3zT are excluded in our following analysis because they do not support gapless E E F (e V ) A-type AFM (z)”
- Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases (2018, background): “The latter two symmetries are relevant for the semimetal Bi, which shows boundary states reminiscent of that of a second-order topological insulator [44].”