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Title: 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:
ORCiD logo [1];  [1];  [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [5];  [1]
  1. Univ. of Zurich (Switzerland)
  2. Donostia International Physics Center (Spain); University of the Basque Country Universidad del País Vasco, Bilbao (Spain)
  3. Princeton Univ., NJ (United States)
  4. Max Planck Institute of Microstructure Physics, Halle (Germany)
  5. 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. https://doi.org/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. https://doi.org/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. https://doi.org/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}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 203 works
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Figures / Tables:

Fig. 1. 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 » are the planes invariant under the mirror symmetries M̂xy and M̂x$\bar{y}$ that protect the hinge states. (C) By supplementing each surface of the chiral HOTI in (A) with a Chern insulator with Hall conductivity σxy = ± e2/h, the number of chiral hinge modes can be changed by 2. The Hall conductivities of the additional Chern insulator layers alternate (blue for + e2/h, red for −e2/h) to comply with the Ĉ$^z_4$T̂ symmetry. The topology is therefore $\mathbb{Z}$2-classified.« less

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