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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, Helene; Gueron, Sophie; Yazdani, Ali; Bernevig, B. Andrei; Neupert, Titus

NATURE PHYSICS
2018
VL / 14 - BP / 918 - EP / +
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. 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.

AccesS level

Green accepted, Green submitted

MENTIONS DATA