Higher-order topological insulators
Abstract
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk but conducting surface states that are topologically protected by time-reversal (or spatial) symmetries. We extend the notion of three-dimensional topological insulators to systems that host no gapless surface states but exhibit topologically protected gapless hinge states. Their topological character is protected by spatiotemporal symmetries of which we present two cases: (i) Chiral higher-order topological insulators protected by the combination of time-reversal and a fourfold rotation symmetry. Their hinge states are chiral modes, and the bulk topology is Embedded Image-classified. (ii) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs, and the bulk topology is Z2-classified. We provide the topological invariants for both cases. Furthermore, we show that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.
- Authors:
-
[1];
[3];
[4];
[5];
- Univ. of Zurich (Switzerland)
- Donostia International Physics Center (Spain); University of the Basque Country Universidad del País Vasco, Bilbao (Spain)
- Princeton Univ., NJ (United States)
- Max Planck Institute of Microstructure Physics, Halle (Germany)
- Princeton Univ., NJ (United States); Donostia International Physics Center (Spain); Laboratoire Pierre Aigrain, Ecole Normale Supérieure–Paris Sciences & Lettres Research University, CNRS, Université Pierre et Marie Curie–Sorbonne Universités, Université Paris Diderot–Sorbonne Paris Cité (France)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1499926
- Grant/Contract Number:
- SC0016239
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Science Advances
- Additional Journal Information:
- Journal Volume: 4; Journal Issue: 6; Journal ID: ISSN 2375-2548
- Publisher:
- AAAS
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Schindler, Frank, Cook, Ashley M., Vergniory, Maia G., Wang, Zhijun, Parkin, Stuart S. P., Bernevig, B. Andrei, and Neupert, Titus. Higher-order topological insulators. United States: N. p., 2018.
Web. doi:10.1126/sciadv.aat0346.
Schindler, Frank, Cook, Ashley M., Vergniory, Maia G., Wang, Zhijun, Parkin, Stuart S. P., Bernevig, B. Andrei, & Neupert, Titus. Higher-order topological insulators. United States. doi:10.1126/sciadv.aat0346.
Schindler, Frank, Cook, Ashley M., Vergniory, Maia G., Wang, Zhijun, Parkin, Stuart S. P., Bernevig, B. Andrei, and Neupert, Titus. Fri .
"Higher-order topological insulators". United States. doi:10.1126/sciadv.aat0346. https://www.osti.gov/servlets/purl/1499926.
@article{osti_1499926,
title = {Higher-order topological insulators},
author = {Schindler, Frank and Cook, Ashley M. and Vergniory, Maia G. and Wang, Zhijun and Parkin, Stuart S. P. and Bernevig, B. Andrei and Neupert, Titus},
abstractNote = {Three-dimensional topological (crystalline) insulators are materials with an insulating bulk but conducting surface states that are topologically protected by time-reversal (or spatial) symmetries. We extend the notion of three-dimensional topological insulators to systems that host no gapless surface states but exhibit topologically protected gapless hinge states. Their topological character is protected by spatiotemporal symmetries of which we present two cases: (i) Chiral higher-order topological insulators protected by the combination of time-reversal and a fourfold rotation symmetry. Their hinge states are chiral modes, and the bulk topology is Embedded Image-classified. (ii) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs, and the bulk topology is Z2-classified. We provide the topological invariants for both cases. Furthermore, we show that SnTe as well as surface-modified Bi2TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.},
doi = {10.1126/sciadv.aat0346},
journal = {Science Advances},
number = 6,
volume = 4,
place = {United States},
year = {2018},
month = {6}
}
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Figures / Tables:
Fig. 1. : Topologically protected hinge excitations of second-order 3D TIs. (A) Time-reversal breaking model with chiral hinge currents running along the corners of a Ĉ$^z_4$-preserving bulk termination where periodic boundary conditions in z direction are assumed. (B) Time-reversal invariant model with antipropagating Kramers pairs of hingemodes. Highlighted in graymore »
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journal, March 2020
- Takahashi, Ryo; Tanaka, Yutaro; Murakami, Shuichi
- Physical Review Research, Vol. 2, Issue 1
Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators
journal, September 2018
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- Physical Review X, Vol. 8, Issue 3
Structure and topology of band structures in the 1651 magnetic space groups
journal, August 2018
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