Two types of surface states in topological crystalline insulators

Liu, Junwei; Duan, Wenhui; Fu, Liang

doi:10.1103/physrevb.88.241303

Two types of surface states in topological crystalline insulators

Journal Article · Tue Dec 10 23:00:00 EST 2013 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/physrevb.88.241303· OSTI ID:1505722

Liu, Junwei ^[1]; Duan, Wenhui ^[2]; Fu, Liang ^[3]

Tsinghua Univ., Beijing (China); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
Tsinghua Univ., Beijing (China)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Topological crystalline insulators (TCIs) are new states of matter whose topological distinction relies on the crystal symmetry of periodic solids. The first material realization of TCIs has recently been predicted and observed in IV-VI semiconductor SnTe and related alloys. By combining k∙p theory and band structure calculation, we present a unified approach to study topological surface states on various crystal surfaces of these TCI materials based on the electronic structure of the bulk. Depending on the surface orientation, we find two types of surface states with qualitatively different properties. Specifically, the (111) surface states consist of four Dirac cones centered at $$\overline{Γ}$$ and $$\overline{m}$$, while Dirac cones on (001) and (110) surfaces are located at non-time-reversal-invariant momenta. The latter types of surface states exhibit a Lifshitz transition as a function of Fermi energy, which is joined by a Van Hove singularity in the density of states arising from saddle points in the band structure.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division

Grant/Contract Number:: SC0010526

OSTI ID:: 1505722

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 24 Vol. 88; ISSN 1098-0121; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (45)

Molecular beam epitaxy of IV–VI semiconductor hetero- and nano-structures Springholz, Gunther; Bauer, Günther physica status solidi (b), Vol. 244, Issue 8 https://doi.org/10.1002/pssb.200675616	journal	August 2007
Relativistic empirical tight-binding theory of the energy bands of GeTe, SnTe, PbTe, PbSe, PbS, and their alloys Lent, Craig S.; Bowen, Marshall A.; Dow, John D. Superlattices and Microstructures, Vol. 2, Issue 5 https://doi.org/10.1016/0749-6036(86)90017-0	journal	January 1986
The birth of topological insulators Moore, Joel E. Nature, Vol. 464, Issue 7286 https://doi.org/10.1038/nature08916	journal	March 2010
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
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
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
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
The great topological expansion Drew, H. Dennis Nature Physics, Vol. 8, Issue 11 https://doi.org/10.1038/nphys2473	journal	November 2012
The space group classification of topological band-insulators Slager, Robert-Jan; Mesaros, Andrej; Juričić, Vladimir Nature Physics, Vol. 9, Issue 2 https://doi.org/10.1038/nphys2513	journal	December 2012
Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect Tatemizo, Nobuyuki; Imada, Saki; Okahara, Kizuna Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-58835-5	journal	February 2020
Subbands in the gap in inverted-band semiconductor quantum wells Korenman, V.; Drew, H. D. Physical Review B, Vol. 35, Issue 12 https://doi.org/10.1103/PhysRevB.35.6446	journal	April 1987
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1−xSbx 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
Antiferromagnetic topological insulators Mong, Roger S. K.; Essin, Andrew M.; Moore, Joel E. Physical Review B, Vol. 81, Issue 24 https://doi.org/10.1103/PhysRevB.81.245209	journal	June 2010
PbTe/PbSnTe heterostructures as analogs of topological insulators Buczko, Ryszard; Cywiński, Łukasz Physical Review B, Vol. 85, Issue 20 https://doi.org/10.1103/PhysRevB.85.205319	journal	May 2012
Surface states of topological insulators Zhang, Fan; Kane, C. L.; Mele, E. J. Physical Review B, Vol. 86, Issue 8 https://doi.org/10.1103/PhysRevB.86.081303	journal	August 2012
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
Spin-polarized (001) surface states of the topological crystalline insulator Pb 0.73 Sn 0.27 Se Wojek, B. M.; Buczko, R.; Safaei, S. Physical Review B, Vol. 87, Issue 11 https://doi.org/10.1103/PhysRevB.87.115106	journal	March 2013
Nontrivial spin texture of the coaxial Dirac cones on the surface of topological crystalline insulator SnTe Wang, Yung Jui; Tsai, Wei-Feng; Lin, Hsin Physical Review B, Vol. 87, Issue 23 https://doi.org/10.1103/PhysRevB.87.235317	journal	June 2013
Topological crystalline insulator (Pb,Sn)Te: Surface states and their spin polarization Safaei, S.; Kacman, P.; Buczko, R. Physical Review B, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevB.88.045305	journal	July 2013
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 classification of crystalline insulators with space group symmetry Jadaun, Priyamvada; Xiao, Di; Niu, Qian Physical Review B, Vol. 88, Issue 8 https://doi.org/10.1103/PhysRevB.88.085110	journal	August 2013
Theory of quasiparticle interference in mirror-symmetric two-dimensional systems and its application to surface states of topological crystalline insulators Fang, Chen; Gilbert, Matthew J.; Xu, Su-Yang Physical Review B, Vol. 88, Issue 12 https://doi.org/10.1103/PhysRevB.88.125141	journal	September 2013
Topological Crystalline Insulators Fu, Liang Physical Review Letters, Vol. 106, Issue 10 https://doi.org/10.1103/PhysRevLett.106.106802	journal	March 2011
Gapless Interface States between Topological Insulators with Opposite Dirac Velocities Takahashi, Ryuji; Murakami, Shuichi Physical Review Letters, Vol. 107, Issue 16 https://doi.org/10.1103/PhysRevLett.107.166805	journal	October 2011
Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition Fu, Liang; Kane, C. L. Physical Review Letters, Vol. 109, Issue 24 https://doi.org/10.1103/PhysRevLett.109.246605	journal	December 2012
Topological Crystalline Insulators in Transition Metal Oxides Kargarian, Mehdi; Fiete, Gregory A. Physical Review Letters, Vol. 110, Issue 15 https://doi.org/10.1103/PhysRevLett.110.156403	journal	April 2013
Existence of Majorana-Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions Teo, Jeffrey C. Y.; Hughes, Taylor L. Physical Review Letters, Vol. 111, Issue 4 https://doi.org/10.1103/PhysRevLett.111.047006	journal	July 2013
Physical Realization of the Parity Anomaly in Condensed Matter Physics Fradkin, Eduardo; Dagotto, Elbio; Boyanovsky, Daniel Physical Review Letters, Vol. 57, Issue 23 https://doi.org/10.1103/PhysRevLett.57.2967	journal	December 1986
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
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
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
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
Observation of Unconventional Quantum Spin Textures in Topological Insulators Hsieh, D.; Xia, Y.; Wray, L. Science, Vol. 323, Issue 5916, p. 919-922 https://doi.org/10.1126/science.1167733	journal	February 2009
Topological Crystalline Insulators Fu, Liang arXiv https://doi.org/10.48550/arxiv.1010.1802	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
The space group classification of topological band insulators Slager, Robert-Jan; Mesaros, Andrej; Juricic, Vladimir arXiv https://doi.org/10.48550/arxiv.1209.2610	text	January 2012
Topological Crystalline Insulators in Transition Metal Oxides Kargarian, Mehdi; Fiete, Gregory A. arXiv https://doi.org/10.48550/arxiv.1212.4162	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
The topological-crystalline-insulator (Pb,Sn)Te - surface states and their spin-polarization Safaei, S.; Kacman, P.; Buczko, R. arXiv https://doi.org/10.48550/arxiv.1303.7119	text	January 2013
Observation of unconventional quantum spin textures in topological insulators Hsieh, D.; Xia, Y.; Wray, L. American Association for the Advancement of Science (AAAS) https://doi.org/10.5167/uzh-26397	text	January 2009
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

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Strain engineering Dirac surface states in heteroepitaxial topological crystalline insulator thin films Zeljkovic, Ilija; Walkup, Daniel; Assaf, Badih A. Nature Nanotechnology, Vol. 10, Issue 10 https://doi.org/10.1038/nnano.2015.177	journal	August 2015
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Massive and massless Dirac fermions in Pb1−xSnxTe topological crystalline insulator probed by magneto-optical absorption Assaf, B. A.; Phuphachong, T.; Volobuev, V. V. Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep20323	journal	February 2016
A methodical study of quantum phase engineering in topological crystalline insulator SnTe and related alloys Yarmohammadi, Mohsen; Mirabbaszadeh, Kavoos Physical Chemistry Chemical Physics, Vol. 21, Issue 38 https://doi.org/10.1039/c9cp03655e	journal	January 2019
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Strain engineering of valley polarized currents in topological crystalline insulators Kanjouri, F.; Piri Pishekloo, S.; Khani, H. Journal of Physics: Condensed Matter, Vol. 31, Issue 30 https://doi.org/10.1088/1361-648x/ab1113	journal	May 2019
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Ferromagnetic phase transition in topological crystalline insulator thin films: Interplay of anomalous Hall angle and magnetic anisotropy Adhikari, R.; Volobuev, V. V.; Faina, B. Physical Review B, Vol. 100, Issue 13 https://doi.org/10.1103/physrevb.100.134422	journal	October 2019
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Engineering relativistic effects in ferroelectric SnTe Plekhanov, Evgeny; Barone, Paolo; Di Sante, Domenico arXiv https://doi.org/10.48550/arxiv.1402.2574	text	January 2014
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