The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index; none of the 26 sources its claims cite is checked for support yet.
Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator
Open accessAbstract
Two types of bulk insulator are realized in the same family of compounds through chemical doping.
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TL;DR
The paper reports a tunable topological quantum phase transition in BiTl(S₁₋δSeδ)₂, visualized by ARPES as the bulk gap closes and Dirac-like surface states emerge. It further observes a chirality inversion of the 3D spin texture as the chemical potential crosses the Dirac node, with implications for fractional charge ±e/2.
Key findings
- As Se concentration increases, the low-lying bulk bands separated by a 0.15 eV gap at δ = 0.0 approach each other, with the gap decreasing to less than 0.05 eV at δ = 0.4; Dirac-like surface bands emerge starting at δ = 0.6, placing the topological transition between δ = 0.4 and δ = 0.6 below 15 K.
- In BiTl(S₀Se₁)₂, the Fermi surface is almost perfectly hexagonal at the native Fermi level (E_B = 0.01 eV) and reverts to isotropic circular shapes near the Dirac node (E_B = 0.25 eV and E_B = 0.50 eV).
- Spin-resolved measurements show a 2D in-plane left-handed chirality spin vortex above the Dirac node and right-handed chirality below it, indicating a 180° turn-around of spin-momentum locking across the node.
- Spin-dependent scattering profiles show suppression of elastic backscattering consistent with topological order; for the hexagonal case, a six-fold symmetric quasi-particle scattering profile suggests possible fluctuating spin-density-wave instability.
Methods
- Systematic photoemission measurements (ARPES) on a series of BiTl(S₁₋δSeδ)₂ compositions, using incident photon energy modulation to probe k_z dispersion.
- Spin-resolved photoemission spectroscopy (spin-ARPES) to measure in-plane and out-of-plane spin polarization textures over a large binding-energy range.
- Scattering profiles estimated from measured spin-ARPES Fermi surfaces and topological spin textures to assess spin-independent and spin-dependent quasi-particle scattering.
Limitations
- The paper states that finer control of bulk compositional variation does not allow locating a precise value for the transition, which could also be a consequence of an intrinsically broader topological transition.
- The paper reports no significant out-of-plane spin-polarization component within experimental resolution, so the spin texture is described as mostly two-dimensional.
- Evident from the text: the chirality inversion and chemical tuning are not physically realizable in Bi₂Te₃ because the node is buried under other bands.
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Claims the paper makes
19 Own result · 10 Not checked yet · 8 Own interpretation · 6 No basis given · 5 Sources not found
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In the paper
“Finer control of bulk compositional variation does not allow locating a precise value for the transition”
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In the paper
“Incident photon energy modulation studies support the assignment of these Dirac-like bands to be of surface origin ( 25 ).”
What the sources say
- Not matchedcites [25] 25. Materials and methods are available as supporting material on Science Online.
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“where the topological insulator formation process is visualized for the first time.”
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In the paper
“The system enters a topologically non-trivial phase upon the occurrence of an electronic phase transition between δ = 0 . 4 and δ = 0 . 6 at temperatures below 15K.”
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- Rests on an assumption: Absence of surface states in ARPES within the bulk gap is a reliable indicator of topological triviality (ν0=0) for BiTl(S1-δSeδ)2.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“which collectively feature a chirality transition of its topological spin-textures as the spin-momentum locked (topologically ordered) electrons on the surface go through the zero carrier density point.”
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In the paper
“In the topological state, vortex-like polarization states are observed to exhibit 3D vectorial textures”
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In the paper
“Starting from δ = 0 . 6, a linearly dispersive band connecting the bulk conduction and valence bands emerges which threads across the bulk band gap.”
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In the paper
“As δ varies from 0.0 to 1.0 (Fig. 1C), the dispersion of the valence band evolves from a 'Λ'-shape to an 'M'-shape with a 'dip' at the ¯ Γ point ( k = 0);”
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“The in-plane measurements, on the other hand, show large polarization amplitudes (Fig. 3A), suggesting that the spin texture is mostly two dimensional.”
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In the paper
“On the hexagonal Fermi contour which is located above the Dirac node (Fig. 3B), the spin vectors obtained from the polarization measurements show that the groundstate features a 2D inplane left-handed chirality spin vortex (a Skyrmion in momentum space, Fig. 3, B and C).”
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- Probably not a substantial claim. 8
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In the paper
“while the band continua in the composition range of δ = 0 . 0 to δ = 0 . 4 are degenerate, the Dirac-like bands at δ = 0 . 6 and beyond are spin polarized (see Figs. 2, 3, and 4).”
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In the paper
“we report the observation of a topological phase transition in a tunable spin-orbit system BiTl(S 1 -δ Se δ ) 2”
- Also stated in: § Abstract · p. 3 · boosted
“We demonstrate the existence of a topological phase transition in TlBi(S 1 -δ Se δ ) 2”
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In the paper
“Both bands demarcating the gap show three dimensional dispersion where binding energies vary with momentum perpendicular to the surface, k z , [as probed via varying incident photon energy ( 25 )] and roughly correspond to the expected position for the valence and conduction bands.”
What the sources say
- Not matchedcites [25] 25. Materials and methods are available as supporting material on Science Online.
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In the paper
“the δ = 0 . 0 compound features a direct band gap in its bulk, whereas the δ = 1 . 0 indicates a slightly indirect gap.”
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“As the selenium concentration is increased, the low-lying bands separated by a gap of energy 0.15eV at δ = 0 . 0 are observed to approach each other and the gap decreases to less than 0.05eV at δ = 0 . 4.”
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In the paper
“Above the Dirac node, a quasi-particle moving in + k (+ˆ x ) direction is locked with +ˆ y spin-polarization state, whereas below the node, the + k moving quasi-particle state is locked with -ˆ y spin.”
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In the paper
“Interestingly, for the hexagonal case, a six-fold symmetric quasi-particle scattering profile is seen, indicating the possibility for a fluctuating spin-density-wave type magnetic instability which connects the parallel pieces of the observed spin-polarized FS (Fig. 3, C and D).”
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In the paper
“In particular, a ν 0 = 1 = θ/π topology requires the terminated surface to have a Fermi surface (FS) that supports a nonzero Berry's phase (an odd as opposed to an even multiple of π = θ =axion angle), which is not realizable in an ordinary spin-orbit or trivial ( ν 0 = 0 = θ ) insulator.”
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In the paper
“It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice via odd number of band inversions, driving the system through a topological quantum phase transition.”
- Also stated in: § Abstract · p. 3 · hedged
“It is believed that a trivial insulator can be twisted into a ν 0 = 1 = θ/π topological state by signaling the appearance of unusual spin vortex-like [or Skyrmionlike ( 1 )] arrangements via increasing spin-orbit interaction or by modulating the lattice parameters, thereby driving the system through a topological quantum phase transition ( 1, 2 ).”
What the sources say
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In the paper
“Topological insulators (TIs) in three dimensions are nonmagnetic insulators with novel surface states (SSs) that are a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the materials ( 1-5 ).”
What the sources say
- Not checked yetcites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source
- Not checked yetcites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source
- Not checked yetcites [3] 3. J. E. Moore, Topological insulators: the next generation. Nature Physics 5 , 378 (2009).http://www.nature.com/nphys/journal/v5/n6/full/nphys1294.html source
- Not checked yetcites [4] 4. X.-L. Qi, T. L. Hughes, S.-C. Zhang, Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78 , 195424 (2008). source
- Not checked yetcites [5] 5. M. Z. Hasan, H. Lin, A. Bansil, Warping the cone on a topological insulator. Physics 2 , 108 (2009) and http://www.nature.com/nphys/journal/v5/n6/full/nphys1294.html source
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Strong TIs are distinguished from ordinary insulators by a finite topological quantum number or an invariant ( ν 0 ) or equivalently an axion angle parameter ( θ ).”
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In the paper
“Spins tangentially arranged on such a circular FS lead to a Berry's phase of π , which is also a measure of the topological invariant and the axion angle ( ν 0 = 1 = θ/π ) of the system ( 1, 4, 6 ).”
What the sources say
- Not checked yetcites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source
- Not checked yetcites [4] 4. X.-L. Qi, T. L. Hughes, S.-C. Zhang, Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78 , 195424 (2008). source
- Not checked yetcites [6] 6. D. Hsieh et al ., A tunable topological insulator in the spin helical Dirac transport regime. Nature 460 , 1101 (2009); and D. Hsieh et al ., A topological Dirac insulator in a quantum spin Hall phase. Nature 452 , 970 (2008). Work completed and submitted in 2007, also see, http://online.itp.ucsb.edu/online/motterials07/hasan/ (2007) source
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In the paper
“The value of ν 0 or θ depends on the parity eigenvalues of the wavefunctions in time reversal symmetric materials ( 1, 2 )”
What the sources say
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In the paper
“this could also be a consequence of an intrinsically broader topological transition.”
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In the paper
“however, that the surface remains gapped at δ = 0 . 4 suggests that the material is still on the trivial side.”
hedged- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
- Rests on an assumption: Absence of surface states in ARPES within the bulk gap is a reliable indicator of topological triviality (ν0=0) for BiTl(S1-δSeδ)2.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Such terms correspond to analogs of cubic and higher order Dresselhaus effects arising from the symmetry of the crystal potential.”
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In the paper
“can be determined from spin texture details of the spin-orbit surface states that form when the bulk is terminated as demonstrated by Hsieh et al . ( 6, 7 ).”
What the sources say
- Not checked yetcites [6] 6. D. Hsieh et al ., A tunable topological insulator in the spin helical Dirac transport regime. Nature 460 , 1101 (2009); and D. Hsieh et al ., A topological Dirac insulator in a quantum spin Hall phase. Nature 452 , 970 (2008). Work completed and submitted in 2007, also see, http://online.itp.ucsb.edu/online/motterials07/hasan/ (2007) source
- Not checked yetcites [7] 7. D. Hsieh et al ., Observation of unconventional quantum spin textures in topological insulators. Science 323 , 919 (2009). source
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Based on a mean field Zener theory, it has recently been shown that a helical magnetic order (HMO) is expected if the surface state topology is in the 3D vectorial spin texture (Fig. 4D) regime, the system can then achieve unusually high critical temperature, even up to T HMO ∼ 100 K ( 30 ).”
What the sources say
- Not checked yetcites [30] 30. J. H. Jiang, S. Wu, Spin susceptibility and helical magnetic order at the edge of topological insulators due to Fermi surface nesting. http://arxiv.org/abs/1012.1299v2 (2010).
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“A more extreme example is the TI, ntype bulk doped Bi 2 Te 3 , which features a highly warped concave-in snowflake-shaped FS because of its large k F and a small band gap ( 25 ).”
What the sources say
- Not matchedcites [25] 25. Materials and methods are available as supporting material on Science Online.
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
The paper relies on this without support.
The TIs Bi2X3 (X=Se,Te) cannot be tuned out from a trivial insulator version without a structural phase transition.
“However, the TIs Bi 2 X 3 (X=Se,Te) cannot be tuned out from a trivial insulator version without a structural phase transition;”
The paper relies on this without support.
In Bi-Sb semiconductors, the lack of gating control prevents observation of the topological phase transition.
“and the lack of gating control necessary for its observation.”
The paper relies on this without support.
Absence of surface states in ARPES within the bulk gap is a reliable indicator of topological triviality (ν0=0) for BiTl(S1-δSeδ)2.
“The absence of SSs within the bulk gap suggests that the compound is topologically trivial ( ν 0 = 0 = θ ) for composition range of δ = 0 . 0 and δ = 0 . 4.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
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In the citing paper
“It has also been noted that the BDS state can be achieved at the critical point of a topological phase transition20,21 between a normal insulator and a TI, which requires fine-tuning of the chemical doping/alloying composition thus by effectively varying the spin-orbit coupling strength.”
From Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2 (2014) · cites this paper as [20]
Experimental — accuracy not yet measuredIn the citing paper
“These results show that the topological order observed in Pb 1 À x Sn x Te is distinct from that previously discovered in Bi 1 À x Sb x or Bi 2 Se 3 (refs 1-5).”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [5]
In the citing paper
“Our observations of spin-momentum locked surface states in the inverted composition and their absence in the non-inverted composition suggest that Pb 1 À x Sn x Te system is a tunable spinorbit insulator analogous to the BiTl(S 1 À d Se d ) 2 system 5 , which features a topological phase transition across the band inversion transition.”
From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [5]
Citations
Cites
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Self-citationTopological Insulators in Three Dimensions
Fu, L., Kane, C. L., & Mele, E. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.106803 · Cited by 4,651
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., et al. (2009) · Nature Physics · doi:10.1038/nphys1274 · Cited by 3,765
Self-citationA topological Dirac insulator in a quantum spin Hall phase
Hsieh, D., Qian, D., Wray, L., Xia, Y., Hor, Y. S., Cava, R. J., & Hasan, M. Z. (2008) · Nature · doi:10.1038/nature06843 · Cited by 3,523
Self-citationControlling the Electronic Structure of Bilayer Graphene
Ohta, T., Bostwick, A., Seyller, T. K., Horn, K., & Rotenberg, E. (2006) · Science · doi:10.1126/science.1130681 · Cited by 3,346
Topological field theory of time-reversal invariant insulators
Qi, X.-L., Hughes, T. L., & Zhang, S.-C. (2008) · Physical Review B · doi:10.1103/physrevb.78.195424 · Cited by 3,329
A tunable topological insulator in the spin helical Dirac transport regime
Hsieh, D., Xia, Y., Qian, D., Wray, L., Dil, J. H., Meier, F., Osterwalder, J., Patthey, L., Checkelsky, J. G., Ong, N. P., et al. (2009) · Nature · doi:10.1038/nature08234 · Cited by 1,979
Self-citationObservation of Unconventional Quantum Spin Textures in Topological Insulators
Hsieh, D., Xia, Y., Wray, L., Qian, D., Pal, A., Dil, J. H., Osterwalder, J., Meier, F., Bihlmayer, G., Kane, C. L., et al. (2009) · Science · doi:10.1126/science.1167733 · Cited by 1,239
Self-citationMassive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator
Chen, Y. L., Chu, J.-H., Analytis, J. G., Liu, Z. K., Igarashi, K., Kuo, H.-H., Qi, X. L., Mo, S. K., Moore, R. G., Lu, D. H., et al. (2010) · Science · doi:10.1126/science.1189924 · Cited by 1,185
Topological surface states protected from backscattering by chiral spin texture
Roushan, P., Seo, J., Parker, C. V., Hor, Y. S., Hsieh, D., Qian, D., Richardella, A., Hasan, M. Z., Cava, R. J., & Yazdani, A. (2009) · Nature · doi:10.1038/nature08308 · Cited by 1,052
Self-citation
Research works printed but not linked: 1
- 10.1103/physrevlett.103.066402 · DOI · Paper page
Cited by
Sorted by citations
Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528
Discovery of a Weyl fermion semimetal and topological Fermi arcs
Xu, S.-Y., Belopolski, I., Alidoust, N., Neupane, M., Bian, G., Zhang, C., Sankar, R., Chang, G., Yuan, Z., Lee, C.-C., et al. (2015) · Science · doi:10.1126/science.aaa9297 · Cited by 3,396
“Recently, it was understood that a Weyl fermion can emerge as a quasiparticle in certain crystals, Weyl fermion semimetals (1-22).”
BackgroundSelf-citationDirac semimetal and topological phase transitions in A 3 Bi ( A = Na , K, Rb)
Wang, Z., Sun, Y., Chen, X.-Q., Franchini, C., Xu, G., Weng, H., Dai, X., & Fang, Z. (2012) · Physical Review B · doi:10.1103/physrevb.85.195320 · Cited by 1,900
Topological Insulator Materials
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Metadata
- Authors
- Xu, S.-Y., Xia, Y., Wray, L. A., Jia, S., Meier, F., Dil, J. H., Osterwalder, J., Slomski, B., Bansil, A., Lin, H., Cava, R. J., & Hasan, M. Z.
- Affiliations
- Princeton University (US)
- Lawrence Berkeley National Laboratory (US)
- University of Zurich (CH)
- Northeastern University (US)
- Corresponding author
- Hasan, M. Z.
- ORCID
- Venue
- Science
- Published
- 2011-04-29
- Volume
- 332
- Issue
- 6029
- Pages
- 560-564
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2027600417
- Semantic Scholar
- 327af26f4ff6f53782926675aa78f4783ce9a256
- Cited by
- 461
- References
- 31
- Citations by year
- 2026: 8 · 2025: 17 · 2024: 16 · 2023: 19 · 2022: 29 · 2021: 27 · 2020: 32 · 2019: 28 · 2018: 33 · 2017: 28 · 2016: 44 · 2015: 44 · 2014: 39 · 2013: 53 · 2012: 32
- FWCI
- 23.44
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- PubMed (publishedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion, other-oa)
- DORA PSI (Paul Scherrer Institute) (submittedVersion)
- arXiv (Cornell University)
- Zurich Open Repository and Archive (University of Zurich)
- Funders
- Office of Basic Energy Sciences (DE-FG-02-05ER46200, AC03-76SF00098, DE-FG02-07ER46352)
- National Science Foundation (DMR-1006492)
- 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 › Physics and Astronomy › Condensed Matter Physics › Magnetic properties of thin films
- Keywords
- topological insulators, topological phase transition, spin-orbit coupling, fractional charge, topological invariants, three-dimensional topological insulators, spin-momentum locking
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-06, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-06 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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