Higher-order topological insulators

Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.; Wang, Zhijun; Parkin, Stuart S.  P.; Bernevig, B. Andrei; Neupert, Titus

doi:10.1126/sciadv.aat0346

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:

^[1]; Cook, Ashley M. ^[1]; Vergniory, Maia G. ^[2];

^[3];

^[4];

^[5]; Neupert, Titus ^[1]

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:: Fri Jun 01 00:00:00 EDT 2018

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.

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                    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

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                    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.

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@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         = {Fri Jun 01 00:00:00 EDT 2018},

  month        = {Fri Jun 01 00:00:00 EDT 2018}

}

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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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DOI: 10.1103/physrevb.99.041301

Coupled-wire construction of static and Floquet second-order topological insulators
journal, January 2019

Bomantara, Raditya Weda; Zhou, Longwen; Pan, Jiaxin
Physical Review B, Vol. 99, Issue 4
DOI: 10.1103/physrevb.99.045441

Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
journal, February 2019

Okuma, Nobuyuki; Sato, Masatoshi; Shiozaki, Ken
Physical Review B, Vol. 99, Issue 8
DOI: 10.1103/physrevb.99.085127

Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
journal, March 2019

Ezawa, Motohiko
Physical Review B, Vol. 99, Issue 12
DOI: 10.1103/physrevb.99.121411

Three-dimensional superconductors with hybrid higher-order topology
journal, March 2019

Bultinck, Nick; Bernevig, B. Andrei; Zaletel, Michael P.
Physical Review B, Vol. 99, Issue 12
DOI: 10.1103/physrevb.99.125149

Boundary edge networks induced by bulk topology
journal, April 2019

Wang, Yan-Qi; Moore, Joel E.
Physical Review B, Vol. 99, Issue 15
DOI: 10.1103/physrevb.99.155102

Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
journal, May 2019

Peng, Yang; Xu, Yong
Physical Review B, Vol. 99, Issue 19
DOI: 10.1103/physrevb.99.195431

Symmetry representation approach to topological invariants in $C_{2 z} T$ -symmetric systems
journal, June 2019

Ahn, Junyeong; Yang, Bohm-Jung
Physical Review B, Vol. 99, Issue 23
DOI: 10.1103/physrevb.99.235125

Quantization of fractional corner charge in $C_{n}$ -symmetric higher-order topological crystalline insulators
journal, June 2019

Benalcazar, Wladimir A.; Li, Tianhe; Hughes, Taylor L.
Physical Review B, Vol. 99, Issue 24
DOI: 10.1103/physrevb.99.245151

High-Temperature Majorana Corner States
journal, October 2018

Wang, Qiyue; Liu, Cheng-Cheng; Lu, Yuan-Ming
Physical Review Letters, Vol. 121, Issue 18
DOI: 10.1103/physrevlett.121.186801

Second-Order Topological Superconductivity in $π$ -Junction Rashba Layers
journal, March 2019

Volpez, Yanick; Loss, Daniel; Klinovaja, Jelena
Physical Review Letters, Vol. 122, Issue 12
DOI: 10.1103/physrevlett.122.126402

Helical Hinge Majorana Modes in Iron-Based Superconductors
journal, May 2019

Zhang, Rui-Xing; Cole, William S.; Das Sarma, S.
Physical Review Letters, Vol. 122, Issue 18
DOI: 10.1103/physrevlett.122.187001

Non-Hermitian Sonic Second-Order Topological Insulator
journal, May 2019

Zhang, Zhiwang; Rosendo López, María; Cheng, Ying
Physical Review Letters, Vol. 122, Issue 19
DOI: 10.1103/physrevlett.122.195501

Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs
journal, June 2019

Chen, Xiao-Dong; Deng, Wei-Min; Shi, Fu-Long
Physical Review Letters, Vol. 122, Issue 23
DOI: 10.1103/physrevlett.122.233902

Splitting the Hinge Mode of Higher-Order Topological Insulators
journal, July 2019

Queiroz, Raquel; Stern, Ady
Physical Review Letters, Vol. 123, Issue 3
DOI: 10.1103/physrevlett.123.036802

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices
journal, August 2019

Zeng, Chuanchang; Stanescu, T. D.; Zhang, Chuanwei
Physical Review Letters, Vol. 123, Issue 6
DOI: 10.1103/physrevlett.123.060402

Higher-Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
journal, October 2019

Zhang, Rui-Xing; Cole, William S.; Wu, Xianxin
Physical Review Letters, Vol. 123, Issue 16
DOI: 10.1103/physrevlett.123.167001

Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides X Te 2 ( X = Mo , W )
journal, October 2019

Wang, Zhijun; Wieder, Benjamin J.; Li, Jian
Physical Review Letters, Vol. 123, Issue 18
DOI: 10.1103/physrevlett.123.186401

Higher-Order Topological Mott Insulators
journal, November 2019

Kudo, Koji; Yoshida, Tsuneya; Hatsugai, Yasuhiro
Physical Review Letters, Vol. 123, Issue 19
DOI: 10.1103/physrevlett.123.196402

Higher-Order Topological Insulator in Twisted Bilayer Graphene
journal, November 2019

Park, Moon Jip; Kim, Youngkuk; Cho, Gil Young
Physical Review Letters, Vol. 123, Issue 21
DOI: 10.1103/physrevlett.123.216803

Quantization in Chiral Higher Order Topological Insulators: Circular Dichroism and Local Chern Marker
journal, December 2019

Pozo, Oscar; Repellin, Cécile; Grushin, Adolfo G.
Physical Review Letters, Vol. 123, Issue 24
DOI: 10.1103/physrevlett.123.247401

Pfaffian Formalism for Higher-Order Topological Insulators
journal, January 2020

Li, Heqiu; Sun, Kai
Physical Review Letters, Vol. 124, Issue 3
DOI: 10.1103/physrevlett.124.036401