Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators

Qi, Yang; Fu, Liang

doi:10.1103/physrevlett.115.236801

Title: Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators

Journal Article · Wed Dec 02 00:00:00 EST 2015 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.115.236801· OSTI ID:1505737

Qi, Yang ^[1]; Fu, Liang ^[2]

Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics

The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface topological order, in which the anyon excitations carry anomalous symmetry fractionalization that cannot be realized in a genuine two-dimensional system. We show here that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern number $n=4$, its surface can be gapped out by an anomalous $${\mathbb{Z}}_{2}$$ topological order, where all anyons carry mirror-symmetry fractionalization $${M}^{2}={-}1$$. The identification of such anomalous crystalline symmetry fractionalization implies that in a two-dimensional $${\mathbb{Z}}_{2}$$ spin liquid, the vison excitation cannot carry $${M}^{2}={-}1$$ if the spinon carries $${M}^{2}={-}1$$ or a half-integer spin.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Tsinghua Univ., Beijing (China)

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

Grant/Contract Number:: SC0010526; 2011CBA00108; 11104154

OSTI ID:: 1505737

Alternate ID(s):: OSTI ID: 1227745

Journal Information:: Physical Review Letters, Vol. 115, Issue 23; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 28 works

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References (31)

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
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Interaction effect on topological classification of superconductors in two dimensions Yao, Hong; Ryu, Shinsei Physical Review B, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevB.88.064507	journal	August 2013
The birth of topological insulators Moore, Joel E. Nature, Vol. 464, Issue 7286 https://doi.org/10.1038/nature08916	journal	March 2010
Microscopic models for fractionalized phases in strongly correlated systems Senthil, T.; Motrunich, O. Physical Review B, Vol. 66, Issue 20 https://doi.org/10.1103/PhysRevB.66.205104	journal	November 2002
Detecting crystal symmetry fractionalization from the ground state: Application to $Z_{2}$ spin liquids on the kagome lattice Qi, Yang; Fu, Liang Physical Review B, Vol. 91, Issue 10 https://doi.org/10.1103/PhysRevB.91.100401	journal	March 2015
Surface states and topological invariants in three-dimensional topological insulators: Application to ${Bi}_{1 - x} {Sb}_{x}$ Teo, Jeffrey C. Y.; Fu, Liang; Kane, C. L. Physical Review B, Vol. 78, Issue 4, Article No. 045426 https://doi.org/10.1103/PhysRevB.78.045426	journal	July 2008
Classifying fractionalization: Symmetry classification of gapped $Z_{2}$ spin liquids in two dimensions Essin, Andrew M.; Hermele, Michael Physical Review B, Vol. 87, Issue 10 https://doi.org/10.1103/PhysRevB.87.104406	journal	March 2013
Competing orders, nonlinear sigma models, and topological terms in quantum magnets Senthil, T.; Fisher, Matthew P. A. Physical Review B, Vol. 74, Issue 6 https://doi.org/10.1103/PhysRevB.74.064405	journal	August 2006
Quantum orders and symmetric spin liquids Wen, Xiao-Gang Physical Review B, Vol. 65, Issue 16 https://doi.org/10.1103/PhysRevB.65.165113	journal	April 2002
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
A new class of (2 + 1)-dimensional topological superconductors with $\mathbb {Z}_8$ topological classification Qi, Xiao-Liang New Journal of Physics, Vol. 15, Issue 6 https://doi.org/10.1088/1367-2630/15/6/065002	journal	June 2013
Mean-field theory of spin-liquid states with finite energy gap and topological orders Wen, X. G. Physical Review B, Vol. 44, Issue 6 https://doi.org/10.1103/PhysRevB.44.2664	journal	August 1991
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
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Interacting topological phases and modular invariance Ryu, Shinsei; Zhang, Shou-Cheng Physical Review B, Vol. 85, Issue 24 https://doi.org/10.1103/PhysRevB.85.245132	journal	June 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 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 three spatial dimensions Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira Physical Review B, Vol. 78, Issue 19 https://doi.org/10.1103/PhysRevB.78.195125	journal	November 2008
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
Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators Zeljkovic, Ilija; Okada, Yoshinori; Serbyn, Maksym Nature Materials, Vol. 14, Issue 3 https://doi.org/10.1038/nmat4215	journal	February 2015
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model Fidkowski, Lukasz; Chen, Xie; Vishwanath, Ashvin Physical Review X, Vol. 3, Issue 4 https://doi.org/10.1103/PhysRevX.3.041016	journal	November 2013
Interacting fermionic topological insulators/superconductors in three dimensions Wang, Chong; Senthil, T. Physical Review B, Vol. 89, Issue 19 https://doi.org/10.1103/PhysRevB.89.195124	journal	May 2014
Kagome´- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons Sachdev, Subir Physical Review B, Vol. 45, Issue 21 https://doi.org/10.1103/PhysRevB.45.12377	journal	June 1992
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
Many-Body Spin Berry Phases Emerging from the $π$ -Flux State: Competition between Antiferromagnetism and the Valence-Bond-Solid State Tanaka, Akihiro; Hu, Xiao Physical Review Letters, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevLett.95.036402	journal	July 2005
Coherent transmutation of electrons into fractionalized anyons Barkeshli, M.; Berg, E.; Kivelson, S. Science, Vol. 346, Issue 6210 https://doi.org/10.1126/science.1253251	journal	November 2014
Topological phases of fermions in one dimension Fidkowski, Lukasz; Kitaev, Alexei Physical Review B, Vol. 83, Issue 7 https://doi.org/10.1103/PhysRevB.83.075103	journal	February 2011
Topological Orders and Chern-Simons Theory in Strongly Correlated Quantum Liquid Wen, Xiao-Gang International Journal of Modern Physics B, Vol. 05, Issue 10 https://doi.org/10.1142/S0217979291001541	journal	June 1991

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Classification and surface anomaly of glide symmetry protected topological phases in three dimensions Lu, Fuyan; Shi, Bowen; Lu, Yuan-Ming New Journal of Physics, Vol. 19, Issue 7 https://doi.org/10.1088/1367-2630/aa769b	journal	July 2017
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Surface field theories of point group symmetry protected topological phases Huang, Sheng-Jie; Hermele, Michael Physical Review B, Vol. 97, Issue 7 https://doi.org/10.1103/physrevb.97.075145	journal	February 2018
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Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators Mross, David F.; Essin, Andrew; Alicea, Jason arXiv https://doi.org/10.48550/arxiv.1507.01587	text	January 2015
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Time-reversal and spatial reflection symmetry localization anomalies in (2+1)D topological phases of matter Barkeshli, Maissam; Cheng, Meng arXiv https://doi.org/10.48550/arxiv.1706.09464	text	January 2017
Dynamical Signature of Symmetry Fractionalization in Frustrated Magnets Sun, Guang Yu; Wang, Yan-Cheng; Fang, Chen arXiv https://doi.org/10.48550/arxiv.1803.10969	text	January 2018
Crystalline topological phases as defect networks Else, Dominic V.; Thorngren, Ryan arXiv https://doi.org/10.48550/arxiv.1810.10539	text	January 2018
Reentrance of Topological Phase in Spin-1 Frustrated Heisenberg Chain Yang, Yuan; Ran, Shi-Ju; Chen, Xi arXiv https://doi.org/10.48550/arxiv.1904.12493	text	January 2019

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FIG. 1(p. 4)

FIG. 2(p. 5)

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