Topology on a new facet of bismuth

Hsu, Chuang-Han; Zhou, Xiaoting; Chang, Tay-Rong; Ma, Qiong; Gedik, Nuh; Bansil, Arun; Xu, Su-Yang; Lin, Hsin; Fu, Liang

doi:10.1073/pnas.1900527116

Title: Topology on a new facet of bismuth

Abstract

Bismuth-based materials have been instrumental in the development of topological physics, even though bulk bismuth itself has been long thought to be topologically trivial. A recent study has, however, shown that bismuth is in fact a higher-order topological insulator featuring one-dimensional (1D) topological hinge states protected by threefold rotational and inversion symmetries. In this paper, we uncover another hidden facet of the band topology of bismuth by showing that bismuth is also a first-order topological crystalline insulator protected by a twofold rotational symmetry. As a result, its (11¯0) surface exhibits a pair of gapless Dirac surface states. Remarkably, these surface Dirac cones are “unpinned” in the sense that they are not restricted to locate at specific k points in the (11¯0) surface Brillouin zone. These unpinned 2D Dirac surface states could be probed directly via various spectroscopic techniques. Our analysis also reveals the presence of a distinct, previously uncharacterized set of 1D topological hinge states protected by the twofold rotational symmetry. Our study thus provides a comprehensive understanding of the topological band structure of bismuth.

Authors:

^[1]; Zhou, Xiaoting ^[2]; Chang, Tay-Rong ^[3]; Ma, Qiong ^[4]; Gedik, Nuh ^[4]; Bansil, Arun ^[5]; Xu, Su-Yang ^[4];

^[6]; Fu, Liang ^[4]

National Univ. of Singapore (Singapore)
National Cheng Kung University, Tainan (Taiwan)
National Cheng Kung University, Tainan (Taiwan); Center for Quantum Frontiers of Research & Technology (QFort), Tainan (Taiwan)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Northeastern Univ., Boston, MA (United States)
Academia Sinica, Taipei (Taiwan)

Publication Date:: Thu Jun 13 00:00:00 EDT 2019

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Northeastern Univ., Boston, MA (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1577614

Grant/Contract Number:: AC02-05CH11231; FG02-07ER46352; SC0018945

Resource Type:: Accepted Manuscript

Journal Name:: Proceedings of the National Academy of Sciences of the United States of America

Additional Journal Information:: Journal Volume: 116; Journal Issue: 27; Journal ID: ISSN 0027-8424

Publisher:: National Academy of Sciences

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Science & Technology; Other Topics

Citation Formats


                    Hsu, Chuang-Han, Zhou, Xiaoting, Chang, Tay-Rong, Ma, Qiong, Gedik, Nuh, Bansil, Arun, Xu, Su-Yang, Lin, Hsin, and Fu, Liang. Topology on a new facet of bismuth.  United States: N. p., 2019. 
Web.  doi:10.1073/pnas.1900527116.

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                    Hsu, Chuang-Han, Zhou, Xiaoting, Chang, Tay-Rong, Ma, Qiong, Gedik, Nuh, Bansil, Arun, Xu, Su-Yang, Lin, Hsin, & Fu, Liang. Topology on a new facet of bismuth.  United States.  https://doi.org/10.1073/pnas.1900527116

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                    Hsu, Chuang-Han, Zhou, Xiaoting, Chang, Tay-Rong, Ma, Qiong, Gedik, Nuh, Bansil, Arun, Xu, Su-Yang, Lin, Hsin, and Fu, Liang. Thu .  
"Topology on a new facet of bismuth".  United States.  https://doi.org/10.1073/pnas.1900527116.  https://www.osti.gov/servlets/purl/1577614.

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@article{osti_1577614,

  title        = {Topology on a new facet of bismuth},

  author       = {Hsu, Chuang-Han and Zhou, Xiaoting and Chang, Tay-Rong and Ma, Qiong and Gedik, Nuh and Bansil, Arun and Xu, Su-Yang and Lin, Hsin and Fu, Liang},

  abstractNote = {Bismuth-based materials have been instrumental in the development of topological physics, even though bulk bismuth itself has been long thought to be topologically trivial. A recent study has, however, shown that bismuth is in fact a higher-order topological insulator featuring one-dimensional (1D) topological hinge states protected by threefold rotational and inversion symmetries. In this paper, we uncover another hidden facet of the band topology of bismuth by showing that bismuth is also a first-order topological crystalline insulator protected by a twofold rotational symmetry. As a result, its (11¯0) surface exhibits a pair of gapless Dirac surface states. Remarkably, these surface Dirac cones are “unpinned” in the sense that they are not restricted to locate at specific k points in the (11¯0) surface Brillouin zone. These unpinned 2D Dirac surface states could be probed directly via various spectroscopic techniques. Our analysis also reveals the presence of a distinct, previously uncharacterized set of 1D topological hinge states protected by the twofold rotational symmetry. Our study thus provides a comprehensive understanding of the topological band structure of bismuth.},

  doi          = {10.1073/pnas.1900527116},

  journal      = {Proceedings of the National Academy of Sciences of the United States of America},

  number       = 27,

  volume       = 116,

  place        = {United States},

  year         = {Thu Jun 13 00:00:00 EDT 2019},

  month        = {Thu Jun 13 00:00:00 EDT 2019}

}

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Hourglass Fermions
text, January 2016

Wang, Zhijun; Alexandradinata, A.; Cava, R. J.
arXiv
DOI: 10.48550/arxiv.1602.05585

Higher-Order Topological Insulators
text, January 2017

Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
arXiv
DOI: 10.48550/arxiv.1708.03636

Quantitative mappings between symmetry and topology in solids
text, January 2017

Song, Zhida; Zhang, Tiantian; Fang, Zhong
arXiv
DOI: 10.48550/arxiv.1711.11049

Connecting higher-order topological insulators to lower-dimensional topological insulators
text, January 2018

Matsugatani, Akishi; Watanabe, Haruki
arXiv
DOI: 10.48550/arxiv.1804.02794

Catalogue of Topological Electronic Materials
text, January 2018

Zhang, Tiantian; Jiang, Yi; Song, Zhida
arXiv
DOI: 10.48550/arxiv.1807.08756

Works referencing / citing this record:

Enhancement of the anisotropic thermoelectric power factor of topological crystalline insulator SnTe and related alloys via external perturbations
journal, January 2019

Yarmohammadi, Mohsen; Mirabbaszadeh, Kavoos
Journal of Materials Chemistry A, Vol. 7, Issue 44
DOI: 10.1039/c9ta08100c

Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides
journal, November 2019

Wang, Baokai; Singh, Bahadur; Ghosh, Barun
Physical Review B, Vol. 100, Issue 20
DOI: 10.1103/physrevb.100.205118

First Principles Calculations for Topological Quantum Materials
text, January 2020

Xiao, Jiewen; Yan, Binghai
arXiv
DOI: 10.48550/arxiv.2010.08371

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Similar Records

Title: Topology on a new facet of bismuth

Abstract

Citation Formats

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe journal, January 2012

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator journal, August 2013

Wannier center sheets in topological insulators journal, March 2014

Topological insulators and superconductors journal, October 2011

Manifestations of Berry's phase in molecules and condensed matter journal, February 2000

Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection journal, August 2011

Thermodynamic evidence for nematic superconductivity in CuxBi2Se3 journal, October 2016

Robust spin-polarized midgap states at step edges of topological crystalline insulators journal, December 2016

Robust spin-polarized midgap states at step edges of topological crystalline insulators text, January 2016

Hourglass fermions journal, April 2016

The surfaces of bismuth: Structural and electronic properties journal, January 2006

Higher-order topological insulators journal, June 2018

wannier90: A tool for obtaining maximally-localised Wannier functions journal, May 2008

Experimental Realization of a Three-Dimensional Topological Insulator, Bi2Te3 journal, June 2009

Wilson-loop characterization of inversion-symmetric topological insulators journal, April 2014

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

A pressure-induced topological phase with large Berry curvature in Pb 1− x Sn x Te journal, May 2017

Topological Crystalline Insulators journal, March 2011

Discovery of robust in-plane ferroelectricity in atomic-thick SnTe journal, July 2016

A tunable topological insulator in the spin helical Dirac transport regime text, January 2009

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

Band connectivity for topological quantum chemistry: Band structures as a graph theory problem journal, January 2018

A topological Dirac insulator in a quantum spin Hall phase journal, April 2008

Topological crystalline insulator states in Pb1−xSnxSe journal, September 2012

Signatures of Electron Fractionalization in Ultraquantum Bismuth journal, September 2007

Higher-order topological insulators and superconductors protected by inversion symmetry journal, May 2018

Higher-order topology in bismuth text, January 2018

Symmetry-based indicators of band topology in the 230 space groups journal, June 2017

Building blocks of topological quantum chemistry: Elementary band representations journal, January 2018

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

Catalogue of topological electronic materials journal, February 2019

A tunable topological insulator in the spin helical Dirac transport regime journal, July 2009

Spin-rotation symmetry breaking in the superconducting state of CuxBi2Se3 journal, May 2016

Higher-order topological insulators text, January 2018

Type-II Weyl semimetals journal, November 2015

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

Topological insulators with inversion symmetry journal, July 2007

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator journal, March 2013

A complete catalogue of high-quality topological materials journal, February 2019

Colloquium: Topological insulators journal, November 2010

Evidence for massive bulk Dirac fermions in Pb1−xSnxSe from Nernst and thermopower experiments journal, November 2013

Higher-order topology in bismuth journal, July 2018

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi journal, January 2014

Mapping the unconventional orbital texture in topological crystalline insulators journal, July 2014

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface journal, May 2009

Experimental realization of a topological crystalline insulator in SnTe journal, September 2012

Quantitative mappings between symmetry and topology in solids journal, August 2018

Comprehensive search for topological materials using symmetry indicators journal, February 2019

Efficient topological materials discovery using symmetry indicators journal, February 2019

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface journal, May 2009

Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides journal, January 2014

Topological quantum chemistry journal, July 2017

Dirac semimetal and topological phase transitions in A 3 Bi ( A = Na , K, Rb) journal, May 2012

( d − 2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States journal, December 2017

Symmetry-enforced chiral hinge states and surface quantum anomalous Hall effect in the magnetic axion insulator Bi2–xSmxSe3 journal, March 2019

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets journal, May 2021

Wallpaper fermions and the nonsymmorphic Dirac insulator journal, July 2018

Phase Transitions of Dirac Electrons in Bismuth journal, July 2008

Observation of a nematic quantum Hall liquid on the surface of bismuth journal, October 2016

Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals journal, July 2016

Purely rotational symmetry-protected topological crystalline insulator $\alpha$ -Bi 4 Br 4 journal, May 2019

Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference journal, May 2018

The crystal structure of Bi and of solid solutions of Pb, Sn, Sb and Te in Bi journal, September 1962

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe text, January 2012

Experimental detection of α-particles from the radioactive decay of natural bismuth journal, April 2003

Experimental Detection of α-Particles from the Radioactive Decay of Natural Bismuth. journal, August 2003

Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy text, January 2001

Topological Crystalline Insulators text, January 2010

Topological crystalline insulator states in Pb(1-x)Sn(x)Se text, January 2012

Experimental realization of a topological crystalline insulator in SnTe text, January 2012

Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides text, January 2013

Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi text, January 2013

Wannier Center Sheets in Topological Insulators text, January 2013

Type-II Weyl Semimetals text, January 2015

Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals text, January 2016

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator text, January 2016

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe
journal, January 2012

Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator
journal, August 2013

Wannier center sheets in topological insulators
journal, March 2014

Topological insulators and superconductors
journal, October 2011

Manifestations of Berry's phase in molecules and condensed matter
journal, February 2000

Equivalent expression of $Z_{2}$ topological invariant for band insulators using the non-Abelian Berry connection
journal, August 2011

Thermodynamic evidence for nematic superconductivity in CuxBi2Se3
journal, October 2016

Robust spin-polarized midgap states at step edges of topological crystalline insulators
journal, December 2016

Robust spin-polarized midgap states at step edges of topological crystalline insulators
text, January 2016

Hourglass fermions
journal, April 2016

The surfaces of bismuth: Structural and electronic properties
journal, January 2006

Higher-order topological insulators
journal, June 2018

wannier90: A tool for obtaining maximally-localised Wannier functions
journal, May 2008

Experimental Realization of a Three-Dimensional Topological Insulator, Bi₂Te₃
journal, June 2009

Wilson-loop characterization of inversion-symmetric topological insulators
journal, April 2014

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

A pressure-induced topological phase with large Berry curvature in Pb _{1− x} Sn _x Te
journal, May 2017

Topological Crystalline Insulators
journal, March 2011

Discovery of robust in-plane ferroelectricity in atomic-thick SnTe
journal, July 2016

A tunable topological insulator in the spin helical Dirac transport regime
text, January 2009

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

Band connectivity for topological quantum chemistry: Band structures as a graph theory problem
journal, January 2018

A topological Dirac insulator in a quantum spin Hall phase
journal, April 2008

Topological crystalline insulator states in Pb1−xSnxSe
journal, September 2012

Signatures of Electron Fractionalization in Ultraquantum Bismuth
journal, September 2007

Higher-order topological insulators and superconductors protected by inversion symmetry
journal, May 2018

Higher-order topology in bismuth
text, January 2018

Symmetry-based indicators of band topology in the 230 space groups
journal, June 2017

Building blocks of topological quantum chemistry: Elementary band representations
journal, January 2018

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

Catalogue of topological electronic materials
journal, February 2019

A tunable topological insulator in the spin helical Dirac transport regime
journal, July 2009

Spin-rotation symmetry breaking in the superconducting state of CuxBi2Se3
journal, May 2016

Higher-order topological insulators
text, January 2018

Type-II Weyl semimetals
journal, November 2015

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

Topological insulators with inversion symmetry
journal, July 2007

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
journal, March 2013

A complete catalogue of high-quality topological materials
journal, February 2019

Colloquium: Topological insulators
journal, November 2010

Evidence for massive bulk Dirac fermions in Pb1−xSnxSe from Nernst and thermopower experiments
journal, November 2013

Higher-order topology in bismuth
journal, July 2018

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi
journal, January 2014

Mapping the unconventional orbital texture in topological crystalline insulators
journal, July 2014

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
journal, May 2009

Experimental realization of a topological crystalline insulator in SnTe
journal, September 2012

Quantitative mappings between symmetry and topology in solids
journal, August 2018

Comprehensive search for topological materials using symmetry indicators
journal, February 2019

Efficient topological materials discovery using symmetry indicators
journal, February 2019

Topological insulators in Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ with a single Dirac cone on the surface
journal, May 2009

Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides
journal, January 2014

Topological quantum chemistry
journal, July 2017

Dirac semimetal and topological phase transitions in $A_{3}$ Bi ( $A = Na$ , K, Rb)
journal, May 2012

$(d - 2)$ -Dimensional Edge States of Rotation Symmetry Protected Topological States
journal, December 2017

Symmetry-enforced chiral hinge states and surface quantum anomalous Hall effect in the magnetic axion insulator Bi2–xSmxSe3
journal, March 2019

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets
journal, May 2021

Wallpaper fermions and the nonsymmorphic Dirac insulator
journal, July 2018

Phase Transitions of Dirac Electrons in Bismuth
journal, July 2008

Observation of a nematic quantum Hall liquid on the surface of bismuth
journal, October 2016

Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
journal, July 2016

Purely rotational symmetry-protected topological crystalline insulator $\alpha$ -Bi 4 Br 4
journal, May 2019

Ferroelectric quantum Hall phase revealed by visualizing Landau level wavefunction interference
journal, May 2018

The crystal structure of Bi and of solid solutions of Pb, Sn, Sb and Te in Bi
journal, September 1962

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe
text, January 2012

Experimental detection of α-particles from the radioactive decay of natural bismuth
journal, April 2003

Experimental Detection of α-Particles from the Radioactive Decay of Natural Bismuth.
journal, August 2003

Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy
text, January 2001

Topological Crystalline Insulators
text, January 2010

Topological crystalline insulator states in Pb(1-x)Sn(x)Se
text, January 2012

Experimental realization of a topological crystalline insulator in SnTe
text, January 2012

Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides
text, January 2013

Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi
text, January 2013

Wannier Center Sheets in Topological Insulators
text, January 2013

Type-II Weyl Semimetals
text, January 2015

Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
text, January 2016

Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
text, January 2016

Symmetry-based Indicators of Band Topology in the 230 Space Groups
text, January 2017

Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
text, January 2017

Quantitative mappings between symmetry and topology in solids
text, January 2017