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Topological crystalline insulators in the SnTe material class
Open accessAbstract
Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe by identifying its non-zero topological index. We predict that as a manifestation of this non-trivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust against disorder and topologically protected by reflection symmetry of the crystal with respect to {110} mirror plane. Breaking this mirror symmetry via elastic strain engineering or applying an in-plane magnetic field can open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectrics, infra-red detection and tunable electronics. Closely related semiconductors PbTe and PbSe also become topological crystalline insulators after band inversion by pressure, strain and alloying.
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In the citing paper
“However, it is experimentally known that SnTe crystals actually are subjected to a rhombohedral distortion 16 , which, strictly speaking, breaks the crystal mirror symmetries and hence excludes a gapless TCI phase 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“On the other hand, the Pb-rich samples are reported to possess the ideal (averaged) sodium chloride structure without global rhombohedral distortion 16 , which thus preserve the proper crystal symmetry required for the predicted TCI phase 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“In a recent calculation 15 , Hsieh et al. predicted that the topological surface states in SnTe 15 are protected by crystalline space group symmetries, in contrast to the time-reversal symmetry protection in the well-known Z 2 TIs.”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“Our observed spin polarization configuration of the surface states is also in qualitative agreement with the first-principles calculation spin texture of the SnTe TCI surface states (see Supplementary Figs S7-S9 for texture calculation);”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“These ARPES measurements suggest that the x ¼ 0.4 sample lies on the inverted composition regime and that the observed surface states are related to the band inversion transition in Pb 1 À x Sn x Te as predicted theoretically [11][12][13]15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“The overall electronic structure observed for our surface states are in qualitative agreement with the theoretically predicted surface states of the TCI phase in SnTe 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“A TCI phase with metallic surface states is theoretically predicted when the band gap is inverted (towards SnTe) 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“The TCI phase was predicted to be observed in the band inverted side and absent in the non-inverted side 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“and experimental derived topological invariant (Mirror Chern number 27,28 ) n M ¼ À 2 also agrees with theoretical prediction for SnTe 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“SnTe, which lies on the inverted regime, is theoretically expected to be a topological crystalline insulater 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“As shown in Fig. 4a, our spin-resolved measurements are performed along the mirror line ( G À X À G) direction, as the electronic and spin structure along this direction is most critically relevant to the predicted TCI phase 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
In the citing paper
“PbTe, which lies on the noninverted regime, is theoretically expected to be a conventional band insulator 15 .”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [15]
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Zhou, J., & Jena, P. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.081102 · Cited by 11
Analytical Solutions for the Surface States of Bi1−xSbx (0 ≤ x \( \lesssim \) 0.1)
Fuseya, Y., & Fukuyama, H. (2018) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.87.044710 · Cited by 11
Ran, K., Zhong, R., Chen, T., Gan, Y., Wang, J., Winn, B., Christianson, A. D., Li, S., Ma, Z., Bao, S., et al. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.220502 · Cited by 11
Gong, Y., Zhu, K., Li, Z., Zang, Y., Feng, X., Zhang, D., Song, C., Wang, L., Li, W., Chen, X., et al. (2018) · Nano Research · doi:10.1007/s12274-018-2120-y · Cited by 11
Electrical properties of tin oxide materials
Suman, P. H. (2019) · Elsevier eBooks · doi:10.1016/b978-0-12-815924-8.00003-7 · Cited by 11
Jin, W., & Osgood, R. M. (2019) · Advances in Physics X · doi:10.1080/23746149.2019.1688187 · Cited by 11
“Figure 9(a–d) shows the first measured topmost valance band of a 1-3ML and bulk MoS2 along high symmetry direction of the SBZ.”
BackgroundInteracting topological mirror excitonic insulator in one dimension
Hu, L., Zhang, R.-X., Zhang, F., & Wu, C. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.235115 · Cited by 12
Observation of unoccupied states of SnTe(111) using pump-probe ARPES measurement
ITO, H. T., Otaki, Y., Tomohiro, Y., Ishida, Y., Akiyama, R., Kimura, A., Shin, S., & Kuroda, S. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.043120 · Cited by 12
Linear response in topological materials
Noky, J., & Sun, Y. (2019) · MPG.PuRe (Max Planck Society) · Cited by 11
Local structural distortions in SnTe investigated by EXAFS
Fornasini, P., Grisenti, R., Dapiaggi, M., & Agostini, G. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ac0082 · Cited by 11
Yadav, A., Kumar, S., Muruganathan, M., & Kumar, R. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ac06ee · Cited by 11
Robust dual topological insulator phase in NaZnBi
Lee, H., Kang, Y., Jung, M., Han, M. J., & Chang, K. J. (2022) · NPG Asia Materials · doi:10.1038/s41427-022-00383-7 · Cited by 12
Berry phase in quantum oscillations of topological materials
Zhao, W., & Wang, X. L. (2022) · Advances in Physics X · doi:10.1080/23746149.2022.2064230 · Cited by 12
“predicted that, in SnTe, the mirror symmetry can protect the topological edge states [16], which was soon experimentally verified [17,18].”
BackgroundObservation of Weyl and Dirac fermions at smooth topological Volkov-Pankratov heterojunctions
Bermejo-Ortiz, J., Krizman, G., Jakieła, R., Khosravizadeh, Z., Hajlaoui, M., Bauer, G., Springholz, G., de Vaulchier, L.-A., & Guldner, Y. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.075129 · Cited by 13
Non-monotonic pressure dependence of band gap in SnTe
Li, W., He, Q., Chen, J., Pan, Z., & Wang, T. (2014) · Chemical Physics Letters · doi:10.1016/j.cplett.2014.10.050 · Cited by 12
Simma, M., Bauer, G. E., & Springholz, G. (2014) · Physical Review B · doi:10.1103/physrevb.90.195310 · Cited by 11
Formation of Nanoscale Composites of Compound Semiconductors Driven by Charge Transfer
Gao, W., dos Reis, R., Schelhas, L. T., Pool, V. L., Toney, M. F., Yu, K. M., & Walukiewicz, W. (2016) · Nano Letters · doi:10.1021/acs.nanolett.6b02395 · Cited by 11
Kalish, S., Chamon, C., El-Batanouny, M., Santos, L. H., Sankar, R., & Chou, F. C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.116101 · Cited by 11
Unconventional topological phase transition in non-symmorphic material KHgX (X = As, Sb, Bi)
Kuo, C.-S., Chang, T., Xu, S., & Jeng, H. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0201-4 · Cited by 11
Spin Transport Revealed by Spin Quantum Geometry
Xiang, L., Jin, H., & Wang, J. (2025) · Physical Review Letters · doi:10.1103/14mp-263q · Cited by 12
He, F.-G., Klein, E., Bartling, S., Saeidpour, S., Corzilius, B., Lesyuk, R., & Klinke, C. (2022) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.2c06262 · Cited by 10
Machine learning search for stable binary Sn alloys with Na, Ca, Cu, Pd, and Ag
Thorn, A., Gochitashvili, D., Kharabadze, S., & Kolmogorov, A. N. (2023) · Physical Chemistry Chemical Physics · doi:10.1039/d3cp02817h · Cited by 10
“They range from pure α -Sn [54] and Sn-Te/Pb [55–58] 3D materials to atom-thick stanene with a buckled honeycomb morphology [25, 59–61].”
BackgroundCodebase release 0.0 for DFT2kp
Cassiano, J. V. V., Araújo, A. L., Faria, P. E., & Ferreira, G. J. (2024) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.25 · Cited by 11
“In contrast, SnTe shows inverted bands, with ¯ L +6 below ¯ L − 6 , yielding a topological insulator phase [118, 119].”
Tautomerization Makes Topological Phase Transition in 2D Organometallic Lattices
Li, J., Liu, Z., Li, X., & Yang, J. (2024) · Advanced Functional Materials · doi:10.1002/adfm.202400610 · Cited by 10
Metadata
- Authors
- Hsieh, T. H., Lin, H., Liu, J., Duan, W., Bansil, A., & Fu, L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Northeastern University (US)
- State Key Laboratory of Low-Dimensional Quantum Physics (CN)
- Corresponding author
- Fu, Liang
- Venue
- Nature Communications
- Published
- 2012-07-31
- Volume
- 3
- Issue
- 1
- Pages
- 982-982
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W1991577814
- Cited by
- 1,449
- References
- 39
- Citations by year
- 2026: 52 · 2025: 99 · 2024: 84 · 2023: 94 · 2022: 126 · 2021: 122 · 2020: 128 · 2019: 135 · 2018: 120 · 2017: 119 · 2016: 109 · 2015: 100 · 2014: 93 · 2013: 55 · 2012: 13
- FWCI
- 43.21
- Type
- journal article
- Language
- en
- Update notices
- correction (2013-05-21)
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nature Communications (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DSpace@MIT (Massachusetts Institute of Technology) (submittedVersion, cc-by-nc)
- arXiv (Cornell University)
- Funders
- National Science Foundation (1005541, 0645960)
- U.S. Department of Energy (DEFG0207ER46352, DE‐FG02‐, FG02-07ER46352)
- National Energy Research Scientific Computing Center
- National Natural Science Foundation of China (2011CB606405, 2011CB921901)
- Division of Materials Research
- Basic Energy Sciences (DE-FG-02-07ER46352, DE-FG02)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Physical Sciences › Materials Science › Materials Chemistry › 2D Materials and Applications
- Keywords
- topological crystalline insulators, SnTe, topological indices, surface states, Dirac cones, reflection symmetry, mirror plane, strain engineering, in-plane magnetic field, band gap tuning, PbTe, lead selenide, band inversion, thermoelectric materials, infrared detection
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