New classes of topological crystalline insulators having surface rotation anomaly

Fang, Chen; Fu, Liang

doi:10.1126/sciadv.aat2374

Title: New classes of topological crystalline insulators having surface rotation anomaly

Journal Article · 20 December 2019 · Science Advances

DOI: https://doi.org/10.1126/sciadv.aat2374 · OSTI ID:1625991

^[1];

^[2]

Chinese Academy of Sciences (CAS), Beijing (China). Inst. of Physics. Beijing National Lab. for Condensed Matter Physics (BNLCP-CAS); Songshan Lake Materials Lab., Dongguan (China);; Chinese Academy of Sciences (CAS), Beijing (China). Kavli Institute for Theoretical Sciences
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics

We discover new types of quantum anomalies in two-dimensional systems with time-reversal symmetry (T) and discrete rotation symmetry with order of n = 2, 4, and 6 (C_n). The new anomalous states have n flavors of massless Dirac fermions protected by T and C_n, whereas any two-dimensional lattices having the two symmetries must have a multiple of 4, 8, and 12 Dirac cones for n = 2, 4, and 6, respectively. We show that these anomalous states are physically realized on the surface of new classes of topological crystalline insulators, normal to the rotation axis. Moreover, these topological crystalline insulators support n gapless one-dimensional helical mode on the otherwise fully gapped side surface, connecting the anomalous two-dimensional states on the top and bottom surfaces. The presence of these helical modes enables a new quantum device made from a topological crystalline insulator nanorod, a “helical nanorod,” which has a quantized longitudinal conductance of ne²/h.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Key Research and Development Program of China; NSFC

Grant/Contract Number:: SC0010526; 2016YFA0302400; 11674370

OSTI ID:: 1625991

Journal Information:: Science Advances, Vol. 5, Issue 12; ISSN 2375-2548

Publisher:: AAASCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 88 works

Citation information provided by
Web of Science

References (74)

Anomalous Ward Identities in Spinor Field Theories Bardeen, William A. Physical Review, Vol. 184, Issue 5 https://doi.org/10.1103/PhysRev.184.1848	journal	August 1969
Axial-Vector Vertex in Spinor Electrodynamics Adler, Stephen L. Physical Review, Vol. 177, Issue 5 https://doi.org/10.1103/PhysRev.177.2426	journal	January 1969
A PCAC puzzle: π0→γγ in the σ-model Bell, J. S.; Jackiw, R. Il Nuovo Cimento A, Vol. 60, Issue 1 https://doi.org/10.1007/BF02823296	journal	March 1969
A no-go theorem for regularizing chiral fermions Nielsen, H. B.; Ninomiya, M. Physics Letters B, Vol. 105, Issue 2-3 https://doi.org/10.1016/0370-2693(81)91026-1	journal	October 1981
Axial-Anomaly-Induced Fermion Fractionization and Effective Gauge-Theory Actions in Odd-Dimensional Space-Times Niemi, A. J.; Semenoff, G. W. Physical Review Letters, Vol. 51, Issue 23 https://doi.org/10.1103/PhysRevLett.51.2077	journal	December 1983
Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly" Haldane, F. D. M. Physical Review Letters, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevLett.61.2015	journal	October 1988
Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors Ryu, Shinsei; Moore, Joel E.; Ludwig, Andreas W. W. Physical Review B, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevB.85.045104	journal	January 2012
New classes of three-dimensional topological crystalline insulators: Nonsymmorphic and magnetic Fang, Chen; Fu, Liang Physical Review B, Vol. 91, Issue 16 https://doi.org/10.1103/PhysRevB.91.161105	journal	April 2015
Z 2 topology in nonsymmorphic crystalline insulators: Möbius twist in surface states Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori Physical Review B, Vol. 91, Issue 15 https://doi.org/10.1103/PhysRevB.91.155120	journal	April 2015
A Four-Dimensional Generalization of the Quantum Hall Effect Zhang, S. -C. Science, Vol. 294, Issue 5543 https://doi.org/10.1126/science.294.5543.823	journal	October 2001
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 98, Issue 10, Article No. 106803 https://doi.org/10.1103/PhysRevLett.98.106803	journal	March 2007
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials Ando, Yoichi; Fu, Liang Annual Review of Condensed Matter Physics, Vol. 6, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031214-014501	journal	March 2015
Classification of topological quantum matter with symmetries Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P. Reviews of Modern Physics, Vol. 88, Issue 3 https://doi.org/10.1103/RevModPhys.88.035005	journal	August 2016
Topological crystalline materials: General formulation, module structure, and wallpaper groups Shiozaki, Ken; Sato, Masatoshi; Gomi, Kiyonori Physical Review B, Vol. 95, Issue 23 https://doi.org/10.1103/PhysRevB.95.235425	journal	June 2017
( d − 2 ) -Dimensional Edge States of Rotation Symmetry Protected Topological States Song, Zhida; Fang, Zhong; Fang, Chen Physical Review Letters, Vol. 119, Issue 24 https://doi.org/10.1103/PhysRevLett.119.246402	journal	December 2017
Bulk topological invariants in noninteracting point group symmetric insulators Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115112	journal	September 2012
Topological crystalline insulators in the SnTe material class Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei Nature Communications, Vol. 3, Article No. 982 https://doi.org/10.1038/ncomms1969	journal	January 2012
Experimental realization of a topological crystalline insulator in SnTe Tanaka, Y.; Ren, Zhi; Sato, T. Nature Physics, Vol. 8, Issue 11 https://doi.org/10.1038/nphys2442	journal	September 2012
Topological crystalline insulator states in Pb1−xSnxSe Dziawa, P.; Kowalski, B. J.; Dybko, K. Nature Materials, Vol. 11, Issue 12 https://doi.org/10.1038/nmat3449	journal	September 2012
Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe Xu, Su-Yang; Liu, Chang; Alidoust, N. Nature Communications, Vol. 3, Issue 1 https://doi.org/10.1038/ncomms2191	journal	January 2012
Observation of Dirac Node Formation and Mass Acquisition in a Topological Crystalline Insulator Okada, Y.; Serbyn, M.; Lin, H. Science, Vol. 341, Issue 6153 https://doi.org/10.1126/science.1239451	journal	August 2013
Hourglass fermions Wang, Zhijun; Alexandradinata, A.; Cava, R. J. Nature, Vol. 532, Issue 7598 https://doi.org/10.1038/nature17410	journal	April 2016
Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb Ma, Junzhang; Yi, Changjiang; Lv, Baiqing Science Advances, Vol. 3, Issue 5 https://doi.org/10.1126/sciadv.1602415	journal	May 2017
Topological Crystalline Insulators Fu, Liang Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.106802	journal	March 2011
Classification of topological insulators and superconductors in the presence of reflection symmetry Chiu, Ching-Kai; Yao, Hong; Ryu, Shinsei Physical Review B, Vol. 88, Issue 7 https://doi.org/10.1103/PhysRevB.88.075142	journal	August 2013
Topological nonsymmorphic crystalline insulators Liu, Chao-Xing; Zhang, Rui-Xing; VanLeeuwen, Brian K. Physical Review B, Vol. 90, Issue 8 https://doi.org/10.1103/PhysRevB.90.085304	journal	August 2014
Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry Alexandradinata, A.; Fang, Chen; Gilbert, Matthew J. Physical Review Letters, Vol. 113, Issue 11 https://doi.org/10.1103/PhysRevLett.113.116403	journal	September 2014
Wallpaper fermions and the nonsymmorphic Dirac insulator Wieder, Benjamin J.; Bradlyn, Barry; Wang, Zhijun Science, Vol. 361, Issue 6399 https://doi.org/10.1126/science.aan2802	journal	July 2018
Möbius Kondo insulators Chang, Po-Yao; Erten, Onur; Coleman, Piers Nature Physics, Vol. 13, Issue 8 https://doi.org/10.1038/nphys4092	journal	April 2017
Topology of crystalline insulators and superconductors Shiozaki, Ken; Sato, Masatoshi Physical Review B, Vol. 90, Issue 16 https://doi.org/10.1103/PhysRevB.90.165114	journal	October 2014
Theory of interacting topological crystalline insulators Isobe, Hiroki; Fu, Liang Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.081304	journal	August 2015
Quantized electric multipole insulators Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L. Science, Vol. 357, Issue 6346 https://doi.org/10.1126/science.aah6442	journal	July 2017
Higher-order topological insulators Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G. Science Advances, Vol. 4, Issue 6 https://doi.org/10.1126/sciadv.aat0346	journal	June 2018
Reflection-Symmetric Second-Order Topological Insulators and Superconductors Langbehn, Josias; Peng, Yang; Trifunovic, Luka Physical Review Letters, Vol. 119, Issue 24 https://doi.org/10.1103/PhysRevLett.119.246401	journal	December 2017
Entanglement and inversion symmetry in topological insulators Turner, Ari M.; Zhang, Yi; Vishwanath, Ashvin Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.241102	journal	December 2010
Inversion-symmetric topological insulators Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei Physical Review B, Vol. 83, Issue 24 https://doi.org/10.1103/PhysRevB.83.245132	journal	June 2011
Hourglass fermion surface states in stacked topological insulators with nonsymmorphic symmetry Ezawa, Motohiko Physical Review B, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevB.94.155148	journal	October 2016
Building crystalline topological phases from lower-dimensional states Huang, Sheng-Jie; Song, Hao; Huang, Yi-Ping Physical Review B, Vol. 96, Issue 20 https://doi.org/10.1103/PhysRevB.96.205106	journal	November 2017
Two types of surface states in topological crystalline insulators Liu, Junwei; Duan, Wenhui; Fu, Liang Physical Review B, Vol. 88, Issue 24 https://doi.org/10.1103/PhysRevB.88.241303	journal	December 2013
Topological crystalline insulators and Dirac octets in antiperovskites Hsieh, Timothy H.; Liu, Junwei; Fu, Liang Physical Review B, Vol. 90, Issue 8 https://doi.org/10.1103/PhysRevB.90.081112	journal	August 2014
Maximally localized generalized Wannier functions for composite energy bands Marzari, Nicola; Vanderbilt, David Physical Review B, Vol. 56, Issue 20 https://doi.org/10.1103/PhysRevB.56.12847	journal	November 1997
Wannier representation of Z 2 topological insulators Soluyanov, Alexey A.; Vanderbilt, David Physical Review B, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevB.83.035108	journal	January 2011
Symmetry-based indicators of band topology in the 230 space groups Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00133-2	journal	June 2017
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer Nature, Vol. 547, Issue 7663 https://doi.org/10.1038/nature23268	journal	July 2017
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevB.80.155131	journal	October 2009
Symmetry-Protected Topological Orders in Interacting Bosonic Systems Chen, X.; Gu, Z. -C.; Liu, Z. -X. Science, Vol. 338, Issue 6114 https://doi.org/10.1126/science.1227224	journal	December 2012
Higher-order topological insulators Schindler, Frank; Cook, Ashley M.; Vergniory, Maia G. American Association for the Advancement of Science https://doi.org/10.5167/uzh-158543	text	January 2018
Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe Xu, Su-Yang; Liu, Chang; Alidoust, N. Nature Publishing Group https://doi.org/10.5167/uzh-71068	text	January 2012
Higher-order topological insulators Neupert, Titus Banff International Research Station for Mathematical Innovation and Discovery https://doi.org/10.14288/1.0370981	audiovisual	January 2018
Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order Gu, Zheng-Cheng; Wen, Xiao-Gang arXiv https://doi.org/10.48550/arxiv.0903.1069	text	January 2009
Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors Ryu, Shinsei; Moore, Joel E.; Ludwig, Andreas W. W. arXiv https://doi.org/10.48550/arxiv.1010.0936	text	January 2010
Topological Crystalline Insulators Fu, Liang arXiv https://doi.org/10.48550/arxiv.1010.1802	text	January 2010
Inversion Symmetric Topological Insulators Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei arXiv https://doi.org/10.48550/arxiv.1010.4508	text	January 2010
Topological crystalline insulator states in Pb(1-x)Sn(x)Se Dziawa, P.; Kowalski, B. J.; Dybko, K. arXiv https://doi.org/10.48550/arxiv.1206.1705	text	January 2012
Experimental realization of a topological crystalline insulator in SnTe Tanaka, Y.; Ren, Zhi; Sato, T. arXiv https://doi.org/10.48550/arxiv.1206.5399	text	January 2012
Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei arXiv https://doi.org/10.48550/arxiv.1207.5767	text	January 2012
Classification of topological insulators and superconductors in the presence of reflection symmetry Chiu, Ching-Kai; Yao, Hong; Ryu, Shinsei arXiv https://doi.org/10.48550/arxiv.1303.1843	text	January 2013
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials Ando, Yoichi; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1501.00531	text	January 2015
Theory of interacting topological crystalline insulators Isobe, Hiroki; Fu, Liang arXiv https://doi.org/10.48550/arxiv.1502.06962	text	January 2015
Classification of topological quantum matter with symmetries Chiu, Ching-Kai; Teo, Jeffrey C. Y.; Schnyder, Andreas P. arXiv https://doi.org/10.48550/arxiv.1505.03535	text	January 2015
Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry Ezawa, Motohiko arXiv https://doi.org/10.48550/arxiv.1607.00213	text	January 2016
Quantized Electric Multipole Insulators Benalcazar, Wladimir A.; Bernevig, B. Andrei; Hughes, Taylor L. arXiv https://doi.org/10.48550/arxiv.1611.07987	text	January 2016
Symmetry-based Indicators of Band Topology in the 230 Space Groups Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki arXiv https://doi.org/10.48550/arxiv.1703.00911	text	January 2017
Reflection symmetric second-order topological insulators and superconductors Langbehn, Josias; Peng, Yang; Trifunovic, Luka arXiv https://doi.org/10.48550/arxiv.1708.03640	text	January 2017
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0607699	text	January 2006
Correction: Corrigendum: Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe Xu, Su-Yang; Liu, Chang; Alidoust, N. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms12505	journal	August 2016
Topological crystalline insulators in the SnTe material class Hsieh, Timothy H.; Lin, Hsin; Liu, Junwei Nature Communications, Vol. 3, Article No. 982 https://doi.org/10.1038/ncomms1969	journal	January 2012
Erratum: Symmetry-based indicators of band topology in the 230 space groups Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-00724-z	journal	October 2017
Coupled-layer description of topological crystalline insulators Fulga, I. C.; Avraham, N.; Beidenkopf, H. Physical Review B, Vol. 94, Issue 12 https://doi.org/10.1103/physrevb.94.125405	journal	September 2016
Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb Ma, Junzhang; Yi, Changjiang; Lv, Baiqing Science Advances, Vol. 3, Issue 5 https://doi.org/10.1126/sciadv.1602415	journal	May 2017
Observation of Dirac node formation and mass acquisition in a topological crystalline insulator Okada, Yoshinori; Serbyn, Maksym; Lin, Hsin arXiv https://doi.org/10.48550/arxiv.1305.2823	text	January 2013
Hourglass Fermions Wang, Zhijun; Alexandradinata, A.; Cava, R. J. arXiv https://doi.org/10.48550/arxiv.1602.05585	text	January 2016
Topological quantum chemistry Bradlyn, Barry; Elcoro, L.; Cano, Jennifer arXiv https://doi.org/10.48550/arxiv.1703.02050	text	January 2017
A Four Dimensional Generalization of the Quantum Hall Effect Zhang, Shou-Cheng; Hu, Jiangping arXiv https://doi.org/10.48550/arxiv.cond-mat/0110572	text	January 2001

Cited By (5)

Strong and fragile topological Dirac semimetals with higher-order Fermi arcs Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-14443-5	journal	January 2020
Appearance of hinge states in second-order topological insulators via the cutting procedure Tanaka, Yutaro; Takahashi, Ryo; Murakami, Shuichi Physical Review B, Vol. 101, Issue 11 https://doi.org/10.1103/physrevb.101.115120	journal	March 2020
Strong and fragile topological Dirac semimetals with higher-order Fermi arcs Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer Freie Universität Berlin https://doi.org/10.17169/refubium-26770	text	January 2020
Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs Wieder, Benjamin J.; Wang, Zhijun; Cano, Jennifer arXiv https://doi.org/10.48550/arxiv.1908.00016	text	January 2019
Appearance of hinge states in second-order topological insulators via the cutting procedure Tanaka, Yutaro; Takahashi, Ryo; Murakami, Shuichi arXiv https://doi.org/10.48550/arxiv.1910.05938	text	January 2019