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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SnTe crystals undergo a rhombohedral distortion that breaks crystal mirror symmetries and excludes a gapless topological crystalline insulator phase.
“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]
Pb-rich samples have the ideal averaged sodium chloride structure without global rhombohedral distortion, preserving the crystal symmetry required for the predicted topological crystalline insulator phase.
“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]
Hsieh et al. predicted that topological surface states in SnTe are protected by crystalline space group symmetries, unlike the time-reversal protection in Z2 topological insulators.
“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]
The observed spin polarization configuration of the surface states is in qualitative agreement with the first-principles spin texture of SnTe topological crystalline insulator surface states.
“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]
ARPES measurements suggest that the x=0.4 sample lies in the inverted composition regime and that its observed surface states are related to the band inversion transition as predicted theoretically.
“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]
The overall electronic structure of the observed surface states is in qualitative agreement with the theoretically predicted topological crystalline insulator surface states in SnTe.
“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]
A TCI phase with metallic surface states is theoretically predicted when the band gap is inverted toward SnTe.
“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]
The topological crystalline insulator phase was predicted to be observed on the band-inverted side and absent on the non-inverted side.
“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]
The experimentally derived Mirror Chern number n_M = -2 agrees with the theoretical prediction for SnTe.
“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]
SnTe is in the inverted regime and is theoretically expected to be a topological crystalline insulator.
“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]
Spin-resolved measurements were performed along the mirror line because the electronic and spin structure along that direction is most critically relevant to the predicted topological crystalline insulator phase.
“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]
PbTe is in the noninverted regime and is theoretically expected to be a conventional band insulator.
“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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“The rock-salt IV-VI semiconductors have been identified by Fu and collaborators [1, 2] as a novel class of insulators – the topological crystalline insulators (TCIs) – which display surface states that are protected by crystalline symmetry.”
Background
- 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 › Atomic and Molecular Physics, and Optics › 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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