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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 ( 1 1 ¯ 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 ( 1 1 ¯ 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:
Publication Date:
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

None, None. Topology on a new facet of bismuth. United States: N. p., 2019. Web. doi:10.1073/pnas.1900527116.
None, None. Topology on a new facet of bismuth. United States. doi:10.1073/pnas.1900527116.
None, None. Thu . "Topology on a new facet of bismuth". United States. doi:10.1073/pnas.1900527116.
@article{osti_1577614,
title = {Topology on a new facet of bismuth},
author = {None, None},
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 = {2019},
month = {6}
}

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Works referenced in this record:

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

  • Xu, Su-Yang; Liu, Chang; Alidoust, N.
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms2191

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

  • Yonezawa, Shingo; Tajiri, Kengo; Nakata, Suguru
  • Nature Physics, Vol. 13, Issue 2
  • DOI: 10.1038/nphys3907

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


Hourglass fermions
journal, April 2016

  • Wang, Zhijun; Alexandradinata, A.; Cava, R. J.
  • Nature, Vol. 532, Issue 7598
  • DOI: 10.1038/nature17410

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


Higher-order topological insulators
journal, June 2018

  • Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
  • Science Advances, Vol. 4, Issue 6
  • DOI: 10.1126/sciadv.aat0346

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

  • Mostofi, Arash A.; Yates, Jonathan R.; Lee, Young-Su
  • Computer Physics Communications, Vol. 178, Issue 9
  • DOI: 10.1016/j.cpc.2007.11.016

Topological phase transitions in thin films by tuning multivalley boundary-state couplings
journal, June 2017


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


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

  • Hsieh, D.; Qian, D.; Wray, L.
  • Nature, Vol. 452, Issue 7190, p. 970-974
  • DOI: 10.1038/nature06843

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

  • Dziawa, P.; Kowalski, B. J.; Dybko, K.
  • Nature Materials, Vol. 11, Issue 12
  • DOI: 10.1038/nmat3449

Signatures of Electron Fractionalization in Ultraquantum Bismuth
journal, September 2007


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


Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy
journal, October 2001


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

  • Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei
  • Nature Communications, Vol. 3, Article No. 982
  • DOI: 10.1038/ncomms1969

Topological crystalline insulator states in the Ca 2 As family
journal, December 2018


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

  • Matano, K.; Kriener, M.; Segawa, K.
  • Nature Physics, Vol. 12, Issue 9
  • DOI: 10.1038/nphys3781

Diagnosis for Nonmagnetic Topological Semimetals in the Absence of Spin-Orbital Coupling
journal, September 2018


Type-II Weyl semimetals
journal, November 2015

  • Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun
  • Nature, Vol. 527, Issue 7579
  • DOI: 10.1038/nature15768

Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1xSbx
journal, July 2008

  • Teo, Jeffrey C. Y.; Fu, Liang; Kane, C. L.
  • Physical Review B, Vol. 78, Issue 4, Article No. 045426
  • DOI: 10.1103/PhysRevB.78.045426

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

  • Liang, Tian; Gibson, Quinn; Xiong, Jun
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3696

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

  • Zeljkovic, Ilija; Okada, Yoshinori; Huang, Cheng-Yi
  • Nature Physics, Vol. 10, Issue 8
  • DOI: 10.1038/nphys3012

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

  • Xia, Y.; Qian, D.; Hsieh, D.
  • Nature Physics, Vol. 5, Issue 6, p. 398-402
  • DOI: 10.1038/nphys1274

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

  • Tanaka, Y.; Ren, Zhi; Sato, T.
  • Nature Physics, Vol. 8, Issue 11
  • DOI: 10.1038/nphys2442

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

  • Zhang, Haijun; Liu, Chao-Xing; Qi, Xiao-Liang
  • Nature Physics, Vol. 5, Issue 6, p. 438-442
  • DOI: 10.1038/nphys1270

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


Topological quantum chemistry
journal, July 2017

  • Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
  • Nature, Vol. 547, Issue 7663
  • DOI: 10.1038/nature23268

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


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

  • Feldman, Benjamin E.; Randeria, Mallika T.; Gyenis, András
  • Science, Vol. 354, Issue 6310
  • DOI: 10.1126/science.aag1715

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


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

  • de Marcillac, Pierre; Coron, Noël; Dambier, Gérard
  • Nature, Vol. 422, Issue 6934
  • DOI: 10.1038/nature01541

    Works referencing / citing this record:

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

    • Mostofi, Arash A.; Yates, Jonathan R.; Lee, Young-Su
    • Computer Physics Communications, Vol. 178, Issue 9
    • DOI: 10.1016/j.cpc.2007.11.016

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


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

    • de Marcillac, Pierre; Coron, Noël; Dambier, Gérard
    • Nature, Vol. 422, Issue 6934
    • DOI: 10.1038/nature01541

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

    • Hsieh, D.; Qian, D.; Wray, L.
    • Nature, Vol. 452, Issue 7190, p. 970-974
    • DOI: 10.1038/nature06843

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


    Type-II Weyl semimetals
    journal, November 2015

    • Soluyanov, Alexey A.; Gresch, Dominik; Wang, Zhijun
    • Nature, Vol. 527, Issue 7579
    • DOI: 10.1038/nature15768

    Hourglass fermions
    journal, April 2016

    • Wang, Zhijun; Alexandradinata, A.; Cava, R. J.
    • Nature, Vol. 532, Issue 7598
    • DOI: 10.1038/nature17410

    Topological quantum chemistry
    journal, July 2017

    • Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
    • Nature, Vol. 547, Issue 7663
    • DOI: 10.1038/nature23268

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

    • Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei
    • Nature Communications, Vol. 3, Article No. 982
    • DOI: 10.1038/ncomms1969

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

    • Xu, Su-Yang; Liu, Chang; Alidoust, N.
    • Nature Communications, Vol. 3, Issue 1
    • DOI: 10.1038/ncomms2191

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

    • Liang, Tian; Gibson, Quinn; Xiong, Jun
    • Nature Communications, Vol. 4, Issue 1
    • DOI: 10.1038/ncomms3696

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

    • Dziawa, P.; Kowalski, B. J.; Dybko, K.
    • Nature Materials, Vol. 11, Issue 12
    • DOI: 10.1038/nmat3449

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

    • Zhang, Haijun; Liu, Chao-Xing; Qi, Xiao-Liang
    • Nature Physics, Vol. 5, Issue 6, p. 438-442
    • DOI: 10.1038/nphys1270

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

    • Xia, Y.; Qian, D.; Hsieh, D.
    • Nature Physics, Vol. 5, Issue 6, p. 398-402
    • DOI: 10.1038/nphys1274

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

    • Tanaka, Y.; Ren, Zhi; Sato, T.
    • Nature Physics, Vol. 8, Issue 11
    • DOI: 10.1038/nphys2442

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

    • Zeljkovic, Ilija; Okada, Yoshinori; Huang, Cheng-Yi
    • Nature Physics, Vol. 10, Issue 8
    • DOI: 10.1038/nphys3012

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

    • Matano, K.; Kriener, M.; Segawa, K.
    • Nature Physics, Vol. 12, Issue 9
    • DOI: 10.1038/nphys3781

    Thermodynamic evidence for nematic superconductivity in CuxBi2Se3
    journal, October 2016

    • Yonezawa, Shingo; Tajiri, Kengo; Nakata, Suguru
    • Nature Physics, Vol. 13, Issue 2
    • DOI: 10.1038/nphys3907

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


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


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


    Higher-order topology in bismuth
    journal, July 2018


    Efficient topological materials discovery using symmetry indicators
    journal, February 2019


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


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


    Catalogue of topological electronic materials
    journal, February 2019


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


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


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


    Connecting higher-order topological insulators to lower-dimensional topological insulators
    journal, November 2018


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


    Higher-order topological insulators
    journal, June 2018

    • Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G.
    • Science Advances, Vol. 4, Issue 6
    • DOI: 10.1126/sciadv.aat0346

    Signatures of Electron Fractionalization in Ultraquantum Bismuth
    journal, September 2007


    Phase Transitions of Dirac Electrons in Bismuth
    journal, July 2008


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


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


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


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


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


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


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

    • Feldman, Benjamin E.; Randeria, Mallika T.; Gyenis, András
    • Science, Vol. 354, Issue 6310
    • DOI: 10.1126/science.aag1715

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


    Wallpaper fermions and the nonsymmorphic Dirac insulator
    journal, July 2018