Topological states from topological crystals
Abstract
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.
- Authors:
-
[1];
[2];
[3];
[4];
[5]
- Chinese Academy of Sciences (CAS), Beijing (China). Beijing National Research Center for Condensed Matter Physics and Institute of Physics; Princeton Univ., NJ (United States). Dept. of Physics
- Univ. of Colorado, Boulder, CO (United States). Dept. of Physics; Univ. of Colorado, Boulder, CO (United States). Center for Theory of Quantum Matter
- Fudan Univ., Shanghai (China). Center for Field Theory and Particle Physics, Dept. of Physics; Fudan Univ., Shanghai (China). State Key Laboratory of Surface Physics; Collaborative Innovation Center of Advanced Microstructures, Nanjing (China)
- Chinese Academy of Sciences (CAS), Beijing (China). Beijing National Research Center for Condensed Matter Physics and Institute of Physics; CAS Center for Excellence in Topological Quantum Computation, Beijing (China)
- Univ. of Colorado, Boulder, CO (United States). Dept. of Physics; Univ. of Colorado, Boulder, CO (United States). Center for Theory of Quantum Matter
- Publication Date:
- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1626023
- Grant/Contract Number:
- SC0014415; 2016YFA0302400; 2016YFA0300600; 11674370; XXH13506-202; 2015CB921700
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Science Advances
- Additional Journal Information:
- Journal Volume: 5; Journal Issue: 12; Journal ID: ISSN 2375-2548
- Publisher:
- AAAS
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Science & Technology - Other Topics
Citation Formats
Song, Zhida, Huang, Sheng-Jie, Qi, Yang, Fang, Chen, and Hermele, Michael. Topological states from topological crystals. United States: N. p., 2019.
Web. doi:10.1126/sciadv.aax2007.
Song, Zhida, Huang, Sheng-Jie, Qi, Yang, Fang, Chen, & Hermele, Michael. Topological states from topological crystals. United States. https://doi.org/10.1126/sciadv.aax2007
Song, Zhida, Huang, Sheng-Jie, Qi, Yang, Fang, Chen, and Hermele, Michael. Wed .
"Topological states from topological crystals". United States. https://doi.org/10.1126/sciadv.aax2007. https://www.osti.gov/servlets/purl/1626023.
@article{osti_1626023,
title = {Topological states from topological crystals},
author = {Song, Zhida and Huang, Sheng-Jie and Qi, Yang and Fang, Chen and Hermele, Michael},
abstractNote = {We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry-protected topological states can be adiabatically deformed into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such that there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups. This enumeration gives topological crystalline insulators a full classification.},
doi = {10.1126/sciadv.aax2007},
journal = {Science Advances},
number = 12,
volume = 5,
place = {United States},
year = {Wed Dec 18 00:00:00 EST 2019},
month = {Wed Dec 18 00:00:00 EST 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 39 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Building crystalline topological phases from lower-dimensional states
journal, November 2017
- Huang, Sheng-Jie; Song, Hao; Huang, Yi-Ping
- Physical Review B, Vol. 96, Issue 20
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
Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator
journal, August 2013
- Okada, Y.; Serbyn, M.; Lin, H.
- Science, Vol. 341, Issue 6153
Anyon condensation and a generic tensor-network construction for symmetry-protected topological phases
journal, March 2017
- Jiang, Shenghan; Ran, Ying
- Physical Review B, Vol. 95, Issue 12
Twisted Equivariant Matter
journal, March 2013
- Freed, Daniel S.; Moore, Gregory W.
- Annales Henri Poincaré, Vol. 14, Issue 8
Classification of crystalline topological insulators and superconductors with point group symmetries
journal, February 2019
- Cornfeld, Eyal; Chapman, Adam
- Physical Review B, Vol. 99, Issue 7
Surface states and topological invariants in three-dimensional topological insulators: Application to
journal, July 2008
- Teo, Jeffrey C. Y.; Fu, Liang; Kane, C. L.
- Physical Review B, Vol. 78, Issue 4, Article No. 045426
Robust spin-polarized midgap states at step edges of topological crystalline insulators
journal, December 2016
- Sessi, P.; Di Sante, D.; Szczerbakow, A.
- Science, Vol. 354, Issue 6317
Robust spin-polarized midgap states at step edges of topological crystalline insulators
text, January 2016
- Sessi, P.; Di Sante, D.; Szczerbakow, A.
- American Association for the Advancement of Science
Hourglass fermions
journal, April 2016
- Wang, Zhijun; Alexandradinata, A.; Cava, R. J.
- Nature, Vol. 532, Issue 7598
Breakdown of the topological classification for gapped phases of noninteracting fermions by quartic interactions
journal, September 2015
- Morimoto, Takahiro; Furusaki, Akira; Mudry, Christopher
- Physical Review B, Vol. 92, Issue 12
Topology of crystalline insulators and superconductors
journal, October 2014
- Shiozaki, Ken; Sato, Masatoshi
- Physical Review B, Vol. 90, Issue 16
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
journal, March 2015
- Ando, Yoichi; Fu, Liang
- Annual Review of Condensed Matter Physics, Vol. 6, Issue 1
Symmetry-Protected Topological Phases of Quantum Matter
journal, March 2015
- Senthil, T.
- Annual Review of Condensed Matter Physics, Vol. 6, Issue 1
Inversion-symmetric topological insulators
journal, June 2011
- Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
- Physical Review B, Vol. 83, Issue 24
Experimental realization of a topological crystalline insulator in SnTe
journal, September 2012
- Tanaka, Y.; Ren, Zhi; Sato, T.
- Nature Physics, Vol. 8, Issue 11
Topology of nonsymmorphic crystalline insulators and superconductors
journal, May 2016
- Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori
- Physical Review B, Vol. 93, Issue 19
Second-order topological insulators and superconductors with an order-two crystalline symmetry
journal, May 2018
- Geier, Max; Trifunovic, Luka; Hoskam, Max
- Physical Review B, Vol. 97, Issue 20
Quantitative mappings between symmetry and topology in solids
journal, August 2018
- Song, Zhida; Zhang, Tiantian; Fang, Zhong
- Nature Communications, Vol. 9, Issue 1
Topological Crystalline Insulators
journal, March 2011
- Fu, Liang
- Physical Review Letters, Vol. 106, Issue 10
Topological quantum chemistry
journal, July 2017
- Bradlyn, Barry; Elcoro, L.; Cano, Jennifer
- Nature, Vol. 547, Issue 7663
Classification of topological insulators and superconductors in three spatial dimensions
journal, November 2008
- Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira
- Physical Review B, Vol. 78, Issue 19
Topological Insulators in Three Dimensions
journal, March 2007
- Fu, Liang; Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 98, Issue 10, Article No. 106803
Topological crystalline insulator states in Pb1−xSnxSe
journal, September 2012
- Dziawa, P.; Kowalski, B. J.; Dybko, K.
- Nature Materials, Vol. 11, Issue 12
Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective
journal, March 2018
- Xiong, Charles Zhaoxi; Alexandradinata, A.
- Physical Review B, Vol. 97, Issue 11
-Dimensional Edge States of Rotation Symmetry Protected Topological States
journal, December 2017
- Song, Zhida; Fang, Zhong; Fang, Chen
- Physical Review Letters, Vol. 119, Issue 24
Higher-order topological insulators and superconductors protected by inversion symmetry
journal, May 2018
- Khalaf, Eslam
- Physical Review B, Vol. 97, Issue 20
Classification of topological quantum matter with symmetries
journal, August 2016
- Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P.
- Reviews of Modern Physics, Vol. 88, Issue 3
topology in nonsymmorphic crystalline insulators: Möbius twist in surface states
journal, April 2015
- Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori
- Physical Review B, Vol. 91, Issue 15
Symmetry-based indicators of band topology in the 230 space groups
journal, June 2017
- Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki
- Nature Communications, Vol. 8, Issue 1
Reactivity of prehydrated electrons toward nucleobases and nucleotides in aqueous solution
journal, December 2017
- Ma, Jun; Wang, Furong; Denisov, Sergey A.
- Science Advances, Vol. 3, Issue 12
Periodic table for topological insulators and superconductors
conference, January 2009
- Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
- ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
Wallpaper fermions and the nonsymmorphic Dirac insulator
journal, July 2018
- Wieder, Benjamin J.; Bradlyn, Barry; Wang, Zhijun
- Science, Vol. 361, Issue 6399
Weak topological insulators in PbTe/SnTe superlattices
journal, February 2014
- Yang, Gang; Liu, Junwei; Fu, Liang
- Physical Review B, Vol. 89, Issue 8
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
New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic
journal, April 2015
- Fang, Chen; Fu, Liang
- Physical Review B, Vol. 91, Issue 16
Topological invariants of time-reversal-invariant band structures
journal, March 2007
- Moore, J. E.; Balents, L.
- Physical Review B, Vol. 75, Issue 12, Article No. 121306(R)
Classification of topological insulators and superconductors in the presence of reflection symmetry
journal, August 2013
- Chiu, Ching-Kai; Yao, Hong; Ryu, Shinsei
- Physical Review B, Vol. 88, Issue 7
Entanglement and inversion symmetry in topological insulators
journal, December 2010
- Turner, Ari M.; Zhang, Yi; Vishwanath, Ashvin
- Physical Review B, Vol. 82, Issue 24
Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe
text, January 2012
- Xu, Su-Yang; Liu, Chang; Alidoust, N.
- Nature Publishing Group
Generalized Wen-Zee terms
journal, May 2019
- Han, Bo; Wang, Huajia; Ye, Peng
- Physical Review B, Vol. 99, Issue 20
Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010
- Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira
- New Journal of Physics, Vol. 12, Issue 6
Classification of topological insulators and superconductors in three spatial dimensions
text, January 2008
- Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira
- arXiv
Periodic table for topological insulators and superconductors
text, January 2009
- Kitaev, Alexei
- arXiv
Inversion Symmetric Topological Insulators
text, January 2010
- Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
- arXiv
Topological crystalline insulator states in Pb(1-x)Sn(x)Se
text, January 2012
- Dziawa, P.; Kowalski, B. J.; Dybko, K.
- arXiv
Experimental realization of a topological crystalline insulator in SnTe
text, January 2012
- Tanaka, Y.; Ren, Zhi; Sato, T.
- arXiv
Classification of topological insulators and superconductors in the presence of reflection symmetry
text, January 2013
- Chiu, Ching-Kai; Yao, Hong; Ryu, Shinsei
- arXiv
Weak Topological Insulators in PbTe/SnTe Superlattices
text, January 2013
- Yang, Gang; Liu, Junwei; Fu, Liang
- arXiv
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
text, January 2015
- Ando, Yoichi; Fu, Liang
- arXiv
Classification of topological quantum matter with symmetries
text, January 2015
- Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P.
- arXiv
Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
text, January 2016
- Jiang, Shenghan; Ran, Ying
- arXiv
Symmetry-based Indicators of Band Topology in the 230 Space Groups
text, January 2017
- Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki
- arXiv
Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
text, January 2017
- Xiong, Charles Zhaoxi; Alexandradinata, A.
- arXiv
Quantitative mappings between symmetry and topology in solids
text, January 2017
- Song, Zhida; Zhang, Tiantian; Fang, Zhong
- arXiv
Higher-order topological insulators and superconductors protected by inversion symmetry
text, January 2018
- Khalaf, Eslam
- arXiv
Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
text, January 2018
- Cornfeld, Eyal; Chapman, Adam
- arXiv
Topological invariants of time-reversal-invariant band structures
text, January 2006
- Moore, J. E.; Balents, L.
- arXiv
Topological Insulators in Three Dimensions
text, January 2006
- Fu, Liang; Kane, C. L.; Mele, E. J.
- arXiv
Correction: Corrigendum: Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe
journal, August 2016
- Xu, Su-Yang; Liu, Chang; Alidoust, N.
- Nature Communications, Vol. 7, Issue 1
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
Erratum: Symmetry-based indicators of band topology in the 230 space groups
journal, October 2017
- Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki
- Nature Communications, Vol. 8, Issue 1
Reactivity of prehydrated electrons toward nucleobases and nucleotides in aqueous solution
journal, December 2017
- Ma, Jun; Wang, Furong; Denisov, Sergey A.
- Science Advances, Vol. 3, Issue 12
Robust spin-polarized midgap states at step edges of topological crystalline insulators
journal, December 2016
- Sessi, P.; Di Sante, D.; Szczerbakow, A.
- Science, Vol. 354, Issue 6317
Wallpaper fermions and the nonsymmorphic Dirac insulator
journal, July 2018
- Wieder, Benjamin J.; Bradlyn, Barry; Wang, Zhijun
- Science, Vol. 361, Issue 6399
Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
text, January 2013
- Okada, Yoshinori; Serbyn, Maksym; Lin, Hsin
- arXiv
Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
text, January 2015
- Morimoto, Takahiro; Furusaki, Akira; Mudry, Christopher
- arXiv
Gauging spatial symmetries and the classification of topological crystalline phases
text, January 2016
- Thorngren, Ryan; Else, Dominic V.
- arXiv
Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
text, January 2017
- Xiong, Charles Zhaoxi; Alexandradinata, A.
- arXiv
Quantitative mappings between symmetry and topology in solids
text, January 2017
- Song, Zhida; Zhang, Tiantian; Fang, Zhong
- arXiv