Higher-order topological insulators

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 Z ₂-classified. We provide the topological invariants for both cases. Furthermore, we show that SnTe as well as surface-modified Bi ₂TeI, 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:: 2018-06-01

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.  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, and Neupert, Titus. Fri .  
        "Higher-order topological insulators".  United States.  doi: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         = {2018},

  month        = {6}

}

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DOI: 10.1126/sciadv.aat0346

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Works referenced in this record:

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Similar Records

Title: Higher-order topological insulators

Abstract

Citation Formats

Generalized Gradient Approximation Made Simple journal, October 1996

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set journal, July 1996

Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1−xSbx journal, July 2008

Z2 Topological Order and the Quantum Spin Hall Effect journal, September 2005

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells journal, December 2006

Phase Transition in SnTe with Low Carrier Concentration journal, February 1975

Topological Insulators in Three Dimensions journal, March 2007

Topological crystalline insulators in the SnTe material class journal, January 2012

Topological field theory of time-reversal invariant insulators journal, November 2008

Generalized Gradient Approximation Made Simple
journal, October 1996

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996

Surface states and topological invariants in three-dimensional topological insulators: Application to ${Bi}_{1 - x} {Sb}_{x}$
journal, July 2008

$Z_{2}$ Topological Order and the Quantum Spin Hall Effect
journal, September 2005

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006

Phase Transition in SnTe with Low Carrier Concentration
journal, February 1975

Topological Insulators in Three Dimensions
journal, March 2007

Topological crystalline insulators in the SnTe material class
journal, January 2012

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journal, November 2008