Aperiodic topological crystalline insulators
Abstract
Topological crystalline insulators (TCIs) are normally described with topological protection imposed by the crystalline symmetry. In general, yet, the existence of TCI states does not necessitate the periodicity of crystals as long as an essential lattice symmetry can be identified. Here we demonstrate the compatibility of TCIs with aperiodic systems, as exemplified by an octagonal quasicrystal. The aperiodic TCIs we proposed are attributed to a band inversion mechanism, which inverts states with the same parity but opposite eigenvalues of a specific symmetry (such as mirror reflection). The nontrivial topology is characterized by a nonzero integer "mirror Bott index". Furthermore, we demonstrate that the topological edge states and quantized conductance of the aperiodic TCI, which are robust against disorder, can be effectively manipulated by external electric fields. Our findings not only provide a better understanding of electronic topology in relation to symmetry but also extend the experimental realization of topological states to much broader material categories beyond crystals.
- Authors:
-
[1]
- Univ. of Utah, Salt Lake City, UT (United States)
- Univ. of Utah, Salt Lake City, UT (United States); Fudan Univ., Shanghai (China)
- Publication Date:
- Research Org.:
- Univ. of Utah, Salt Lake City, UT (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1581164
- Grant/Contract Number:
- FG02-04ER46148
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 4; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Huang, Huaqing, Wu, Yong-Shi, and Liu, Feng. Aperiodic topological crystalline insulators. United States: N. p., 2020.
Web. doi:10.1103/PhysRevB.101.041103.
Huang, Huaqing, Wu, Yong-Shi, & Liu, Feng. Aperiodic topological crystalline insulators. United States. https://doi.org/10.1103/PhysRevB.101.041103
Huang, Huaqing, Wu, Yong-Shi, and Liu, Feng. Mon .
"Aperiodic topological crystalline insulators". United States. https://doi.org/10.1103/PhysRevB.101.041103. https://www.osti.gov/servlets/purl/1581164.
@article{osti_1581164,
title = {Aperiodic topological crystalline insulators},
author = {Huang, Huaqing and Wu, Yong-Shi and Liu, Feng},
abstractNote = {Topological crystalline insulators (TCIs) are normally described with topological protection imposed by the crystalline symmetry. In general, yet, the existence of TCI states does not necessitate the periodicity of crystals as long as an essential lattice symmetry can be identified. Here we demonstrate the compatibility of TCIs with aperiodic systems, as exemplified by an octagonal quasicrystal. The aperiodic TCIs we proposed are attributed to a band inversion mechanism, which inverts states with the same parity but opposite eigenvalues of a specific symmetry (such as mirror reflection). The nontrivial topology is characterized by a nonzero integer "mirror Bott index". Furthermore, we demonstrate that the topological edge states and quantized conductance of the aperiodic TCI, which are robust against disorder, can be effectively manipulated by external electric fields. Our findings not only provide a better understanding of electronic topology in relation to symmetry but also extend the experimental realization of topological states to much broader material categories beyond crystals.},
doi = {10.1103/PhysRevB.101.041103},
journal = {Physical Review B},
number = 4,
volume = 101,
place = {United States},
year = {2020},
month = {1}
}
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Works referenced in this record:
Topological Crystalline Insulators in Transition Metal Oxides
journal, April 2013
- Kargarian, Mehdi; Fiete, Gregory A.
- Physical Review Letters, Vol. 110, Issue 15
Topological Phases without Crystalline Counterparts
journal, November 2019
- Varjas, Dániel; Lau, Alexander; Pöyhönen, Kim
- Physical Review Letters, Vol. 123, Issue 19
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
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
The ℤ 2 index of disordered topological insulators with time reversal symmetry
journal, February 2016
- Katsura, Hosho; Koma, Tohru
- Journal of Mathematical Physics, Vol. 57, Issue 2
Topological insulators and superconductors
journal, October 2011
- Qi, Xiao-Liang; Zhang, Shou-Cheng
- Reviews of Modern Physics, Vol. 83, Issue 4
Time-reversal symmetry protected chiral interface states between quantum spin and quantum anomalous Hall insulators
journal, August 2015
- Huang, Huaqing; Wang, Zhaoyou; Luo, Nannan
- Physical Review B, Vol. 92, Issue 7
Theory of spin Bott index for quantum spin Hall states in nonperiodic systems
journal, September 2018
- Huang, Huaqing; Liu, Feng
- Physical Review B, Vol. 98, Issue 12
Non-commutative tools for topological insulators
journal, June 2010
- Prodan, Emil
- New Journal of Physics, Vol. 12, Issue 6
Theory of the Topological Anderson Insulator
journal, November 2009
- Groth, C. W.; Wimmer, M.; Akhmerov, A. R.
- Physical Review Letters, Vol. 103, Issue 19
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
Topological Crystalline Insulator Phase in Graphene Multilayers
journal, June 2015
- Kindermann, M.
- Physical Review Letters, Vol. 114, Issue 22
Colloquium : Topological band theory
journal, June 2016
- Bansil, A.; Lin, Hsin; Das, Tanmoy
- Reviews of Modern Physics, Vol. 88, Issue 2
Topological Phases Protected by Point Group Symmetry
journal, February 2017
- Song, Hao; Huang, Sheng-Jie; Fu, Liang
- Physical Review X, Vol. 7, Issue 1
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006
- Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C.
- Science, Vol. 314, Issue 5806, p. 1757-1761
Topological Crystalline Insulators
journal, March 2011
- Fu, Liang
- Physical Review Letters, Vol. 106, Issue 10
Direct observation of domains and discommensurations in Mn-Si-Al octagonal quasicrystal by transmission electron microscopy
journal, September 1991
- Jiang, J. C.; Wang, N.; Fung, K. K.
- Physical Review Letters, Vol. 67, Issue 10
Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
journal, September 2018
- Huang, Huaqing; Liu, Feng
- Physical Review Letters, Vol. 121, Issue 12
Two-dimensional Topological Crystalline Insulator Phase in Sb/Bi Planar Honeycomb with Tunable Dirac Gap
journal, January 2016
- Hsu, Chia-Hsiu; Huang, Zhi-Quan; Crisostomo, Christian P.
- Scientific Reports, Vol. 6, Issue 1
Topological crystalline insulator states in Pb1−xSnxSe
journal, September 2012
- Dziawa, P.; Kowalski, B. J.; Dybko, K.
- Nature Materials, Vol. 11, Issue 12
Emerging topological states in quasi-two-dimensional materials: Emerging topological states in quasi-2D materials
journal, December 2016
- Huang, Huaqing; Xu, Yong; Wang, Jianfeng
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 7, Issue 4
Entanglement spectrum classification of -invariant noninteracting topological insulators in two dimensions
journal, January 2013
- Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
- Physical Review B, Vol. 87, Issue 3
Electronic and vibrational spectra of two-dimensional quasicrystals
journal, February 1986
- Odagaki, T.; Nguyen, D.
- Physical Review B, Vol. 33, Issue 4
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
Topological Crystalline Materials of J = 3 / 2 Electrons: Antiperovskites, Dirac Points, and High Winding Topological Superconductivity
journal, November 2018
- Kawakami, Takuto; Okamura, Tetsuya; Kobayashi, Shingo
- Physical Review X, Vol. 8, Issue 4
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
Two types of Dirac-cone surface states on the (111) surface of the topological crystalline insulator SnTe
journal, December 2013
- Tanaka, Y.; Shoman, T.; Nakayama, K.
- Physical Review B, Vol. 88, Issue 23
Comparison of quantum spin Hall states in quasicrystals and crystals
journal, August 2019
- Huang, Huaqing; Liu, Feng
- Physical Review B, Vol. 100, Issue 8
Electric Field Tuning of the Rashba Effect in the Polar Perovskite Structures
journal, February 2014
- Shanavas, K. V.; Satpathy, S.
- Physical Review Letters, Vol. 112, Issue 8
Elastic properties of semiconductors using universal tight-binding parameters
journal, October 1991
- Kitamura, Michihide; Harrison, Walter A.
- Physical Review B, Vol. 44, Issue 15
Robust dual topological character with spin-valley polarization in a monolayer of the Dirac semimetal
journal, February 2017
- Niu, Chengwang; Buhl, Patrick M.; Bihlmayer, Gustav
- Physical Review B, Vol. 95, Issue 7
Theory of the multicenter bond
journal, February 1986
- van Schilfgaarde, Mark; Harrison, Walter A.
- Physical Review B, Vol. 33, Issue 4
Catalogue of topological electronic materials
journal, February 2019
- Zhang, Tiantian; Jiang, Yi; Song, Zhida
- Nature, Vol. 566, Issue 7745
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
New tight-binding parameters for covalent solids obtained using Louie peripheral states
journal, November 1981
- Harrison, W. A.
- Physical Review B, Vol. 24, Issue 10
Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)
journal, May 1984
- Sancho, M. P. Lopez; Sancho, J. M. Lopez; Rubio, J.
- Journal of Physics F: Metal Physics, Vol. 14, Issue 5
Anyons in an exactly solved model and beyond
journal, January 2006
- Kitaev, Alexei
- Annals of Physics, Vol. 321, Issue 1
Disordered topological insulators via C * -algebras
journal, December 2010
- Loring, T. A.; Hastings, M. B.
- EPL (Europhysics Letters), Vol. 92, Issue 6
s p -band tight-binding model for the Bychkov-Rashba effect in a two-dimensional electron system including nearest-neighbor contributions from an electric field
journal, August 2012
- Ast, Christian R.; Gierz, Isabella
- Physical Review B, Vol. 86, Issue 8
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
Topological classification with additional symmetries from Clifford algebras
journal, September 2013
- Morimoto, Takahiro; Furusaki, Akira
- Physical Review B, Vol. 88, Issue 12
Invariants of almost commuting unitaries
journal, February 1991
- Exel, Ruy; Loring, Terry A.
- Journal of Functional Analysis, Vol. 95, Issue 2
Geometrically averaged density of states as a measure of localization
journal, July 2007
- Song, Yun; Atkinson, W. A.; Wortis, R.
- Physical Review B, Vol. 76, Issue 4
Topological insulators with inversion symmetry
journal, July 2007
- Fu, Liang; Kane, C. L.
- Physical Review B, Vol. 76, Issue 4
Prediction of Two-Dimensional Topological Crystalline Insulator in PbSe Monolayer
journal, September 2014
- Wrasse, Ernesto O.; Schmidt, Tome M.
- Nano Letters, Vol. 14, Issue 10
Topological Order and the Quantum Spin Hall Effect
journal, September 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 14, Article No. 146802
Tight-binding model and interactions scaling laws for silicon and germanium
journal, June 1995
- Grosso, G.; Piermarocchi, C.
- Physical Review B, Vol. 51, Issue 23
Topology of crystalline insulators and superconductors
journal, October 2014
- Shiozaki, Ken; Sato, Masatoshi
- Physical Review B, Vol. 90, Issue 16
Simplified LCAO Method for the Periodic Potential Problem
journal, June 1954
- Slater, J. C.; Koster, G. F.
- Physical Review, Vol. 94, Issue 6
A complete catalogue of high-quality topological materials
journal, February 2019
- Vergniory, M. G.; Elcoro, L.; Felser, Claudia
- Nature, Vol. 566, Issue 7745
Fifty years of aperiodic crystals
journal, September 2012
- Janssen, T.
- Acta Crystallographica Section A Foundations of Crystallography, Vol. 68, Issue 6
The noncommutative geometry of the quantum Hall effect
journal, October 1994
- Bellissard, J.; van Elst, A.; Schulz‐ Baldes, H.
- Journal of Mathematical Physics, Vol. 35, Issue 10
Colloquium: Topological insulators
journal, November 2010
- Hasan, M. Z.; Kane, C. L.
- Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067
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
Quantized Hall conductance as a topological invariant
journal, March 1985
- Niu, Qian; Thouless, D. J.; Wu, Yong-Shi
- Physical Review B, Vol. 31, Issue 6
Quantum Spin Hall Effect in Graphene
journal, November 2005
- Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 95, Issue 22
Approximants of quasiperiodic structures generated by the inflation mapping
journal, November 1989
- Duneau, M.
- Journal of Physics A: Mathematical and General, Vol. 22, Issue 21
Bulk topological invariants in noninteracting point group symmetric insulators
journal, September 2012
- Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
- Physical Review B, Vol. 86, Issue 11
Electrically tunable quantum spin Hall state in topological crystalline insulator thin films
journal, February 2015
- Liu, Junwei; Fu, Liang
- Physical Review B, Vol. 91, Issue 8
Dual Topological Character of Chalcogenides: Theory for
journal, January 2014
- Rauch, Tomáš; Flieger, Markus; Henk, Jürgen
- Physical Review Letters, Vol. 112, Issue 1
Crystal Field Effect Induced Topological Crystalline Insulators In Monolayer IV–VI Semiconductors
journal, March 2015
- Liu, Junwei; Qian, Xiaofeng; Fu, Liang
- Nano Letters, Vol. 15, Issue 4
Many-Body Chern Number without Integration
journal, April 2019
- Kudo, Koji; Watanabe, Haruki; Kariyado, Toshikaze
- Physical Review Letters, Vol. 122, Issue 14
Comprehensive search for topological materials using symmetry indicators
journal, February 2019
- Tang, Feng; Po, Hoi Chun; Vishwanath, Ashvin
- Nature, Vol. 566, Issue 7745
Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides
journal, January 2014
- Weng, Hongming; Zhao, Jianzhou; Wang, Zhijun
- Physical Review Letters, Vol. 112, Issue 1
Topological phase transition in a topological crystalline insulator induced by finite-size effects
journal, July 2014
- Ozawa, Hideyuki; Yamakage, Ai; Sato, Masatoshi
- Physical Review B, Vol. 90, Issue 4
Supersymmetry in heterojunctions: Band-inverting contact on the basis of Pb1xSnxTe and Hg1xCdxTe
journal, January 1987
- Pankratov, O. A.; Pakhomov, S. V.; Volkov, B. A.
- Solid State Communications, Vol. 61, Issue 2
Topological Anderson Insulator
journal, April 2009
- Li, Jian; Chu, Rui-Lin; Jain, J. K.
- Physical Review Letters, Vol. 102, Issue 13
Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator
journal, December 2013
- Liu, Junwei; Hsieh, Timothy H.; Wei, Peng
- Nature Materials, Vol. 13, Issue 2
Layered Topological Crystalline Insulators
journal, August 2015
- Kim, Youngkuk; Kane, C. L.; Mele, E. J.
- Physical Review Letters, Vol. 115, Issue 8
Symmetry study of the Mn‐Si‐Al octagonal quasicrystal by convergent beam electron diffraction
journal, June 1988
- Wang, N.; Fung, K. K.; Kuo, K. H.
- Applied Physics Letters, Vol. 52, Issue 25
The space group classification of topological band-insulators
journal, December 2012
- Slager, Robert-Jan; Mesaros, Andrej; Juričić, Vladimir
- Nature Physics, Vol. 9, Issue 2
Topological crystalline insulators and Dirac octets in antiperovskites
journal, August 2014
- Hsieh, Timothy H.; Liu, Junwei; Fu, Liang
- Physical Review B, Vol. 90, Issue 8
Superlattice valley engineering for designer topological insulators
journal, September 2014
- Li, Xiao; Zhang, Fan; Niu, Qian
- Scientific Reports, Vol. 4, Issue 1
Two-Dimensional Topological Crystalline Insulator and Topological Phase Transition in TlSe and TlS Monolayers
journal, August 2015
- Niu, Chengwang; Buhl, Patrick M.; Bihlmayer, Gustav
- Nano Letters, Vol. 15, Issue 9
Disordered topological insulators: a non-commutative geometry perspective
journal, February 2011
- Prodan, Emil
- Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 11
Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry
journal, September 2014
- Alexandradinata, A.; Fang, Chen; Gilbert, Matthew J.
- Physical Review Letters, Vol. 113, Issue 11
Absence of backscattering in the quantum Hall effect in multiprobe conductors
journal, November 1988
- Büttiker, M.
- Physical Review B, Vol. 38, Issue 14
Localization and mobility gap in the topological Anderson insulator
journal, January 2012
- Zhang, Yan-Yang; Chu, Rui-Lin; Zhang, Fu-Chun
- Physical Review B, Vol. 85, Issue 3
Modifications and extensions to Harrison’s tight-binding theory
journal, November 2004
- Shi, Lei; Papaconstantopoulos, Dimitrios A.
- Physical Review B, Vol. 70, Issue 20
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
Almost commuting matrices, localized Wannier functions, and the quantum Hall effect
journal, January 2010
- Hastings, Matthew B.; Loring, Terry A.
- Journal of Mathematical Physics, Vol. 51, Issue 1
Two-dimensional quasicrystal with eightfold rotational symmetry
journal, August 1987
- Wang, N.; Chen, H.; Kuo, K. H.
- Physical Review Letters, Vol. 59, Issue 9
Highly convergent schemes for the calculation of bulk and surface Green functions
journal, April 1985
- Sancho, M. P. Lopez; Sancho, J. M. Lopez; Sancho, J. M. L.
- Journal of Physics F: Metal Physics, Vol. 15, Issue 4
Mapping topological order in coordinate space
journal, December 2011
- Bianco, Raffaello; Resta, Raffaele
- Physical Review B, Vol. 84, Issue 24
Disordered topological insulators: a non-commutative geometry perspective
journal, May 2011
- Prodan, Emil
- Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 23
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
Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect
text, January 2009
- Hastings, M. B.; Loring, T. A.
- arXiv
Localization and Mobility Gap in Topological Anderson Insulator
text, January 2011
- Zhang, Yan-Yang; Chu, Rui-Lin; Zhang, Fu-Chun
- arXiv
Topological crystalline insulator states in Pb(1-x)Sn(x)Se
text, January 2012
- Dziawa, P.; Kowalski, B. J.; Dybko, K.
- arXiv
Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
text, January 2012
- Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
- arXiv
The space group classification of topological band insulators
text, January 2012
- Slager, Robert-Jan; Mesaros, Andrej; Juricic, Vladimir
- arXiv
Topological Crystalline Insulators in Transition Metal Oxides
text, January 2012
- Kargarian, Mehdi; Fiete, Gregory A.
- arXiv
Classification of topological insulators and superconductors in the presence of reflection symmetry
text, January 2013
- Chiu, Ching-Kai; Yao, Hong; Ryu, Shinsei
- arXiv
Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides
text, January 2013
- Weng, Hongming; Zhao, Jianzhou; Wang, Zhijun
- arXiv
Two types of Dirac-cone surface states on (111) surface of topological crystalline insulator SnTe
text, January 2013
- Tanaka, Y.; Shoman, T.; Nakayama, K.
- arXiv
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
text, January 2015
- Ando, Yoichi; Fu, Liang
- arXiv
Electrically Tunable Quantum Spin Hall State in Topological Crystalline Insulator Thin films
text, January 2015
- Liu, Junwei; Fu, Liang
- arXiv
Layered Topological Crystalline Insulators
text, January 2015
- Kim, Youngkuk; Kane, C. L.; Mele, E. J.
- arXiv
Crystal Field Effect Induced Topological Crystalline Insulators In Monolayer IV-VI Semiconductors
text, January 2015
- Liu, Junwei; Qian, Xiaofeng; Fu, Liang
- arXiv
Symmetry-based Indicators of Band Topology in the 230 Space Groups
text, January 2017
- Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki
- arXiv
Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
text, January 2018
- Huang, Huaqing; Liu, Feng
- arXiv
The geometrically-averaged density of states as a measure of localization
text, January 2006
- Song, Yun; Atkinson, W. A.; Wortis, R.
- arXiv
Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
text, January 2006
- Bernevig, B. Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng
- arXiv
The Non-Commutative Geometry of the Quantum Hall Effect
text, January 1994
- Bellissard, J.; van Elst, A.; Schulz-Baldes, H.
- arXiv