CoChat
Sign Up
Cited by 697Topological Materials and PhenomenaAdvanced Condensed Matter Physics2D Materials and Applications

Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe

Open access
Xu, Su-Yang, Liu, Chang, Alidoust, N., Neupane, M., Qian, D., Belopolski, I., Denlinger, J.D., Wang, Y.J. +13 more·2012·Nature Communications
DOI 10.1038/ncomms2191
Open this paper in CoChat — free accountOpen PDF

Abstract

A topological insulator protected by time-reversal symmetry is realized via spin-orbit interaction-driven band inversion. The topological phase in the Bi(1-x)Sb(x) system is due to an odd number of band inversions. A related spin-orbit system, the Pb(1-x)Sn(x)Te, has long been known to contain an even number of inversions based on band theory. Here we experimentally investigate the possibility of a mirror symmetry-protected topological crystalline insulator phase in the Pb(1-x)Sn(x)Te class of materials that has been theoretically predicted to exist in its end compound SnTe. Our experimental results show that at a finite Pb composition above the topological inversion phase transition, the surface exhibits even number of spin-polarized Dirac cone states revealing mirror-protected topological order distinct from that observed in Bi(1-x)Sb(x). Our observation of the spin-polarized Dirac surface states in the inverted Pb(1-x)Sn(x)Te and their absence in the non-inverted compounds related via a topological phase transition provide the experimental groundwork for opening the research on novel topological order in quantum devices.

Integrity signals

Registry

Crossref · 10.1038/ncomms2191

Cites

46 of 46 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 49 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    Along cut 1, the mirror line direction, a pair of surface states is observed at the Fermi level.

    “In cut 1 (Fig. 3d), which is the mirror line ( G À X À G) direction, a pair of surface states are observed on the Fermi level.”
    Quote in the paperSubstantial claim
  • Findingown data

    The assignment of the two Fermi pockets to surface-umklapp or other bulk-related origins is ruled out by incident-photon-energy-dependent kz dispersion and spin polarization measurements.

    “The assignment of the observed two-Fermipockets as surface-umklapp processes or other bulk-related origins can be further ruled out by incident photon energy dependence (k z dispersion) measurements and our spin polarization studies of these metallic states (see Supplementary Figs S1-S5 in the Supplementary Information).”
    Quote in the paperSubstantial claim
  • Findingown data

    Near each X point, a pair of surface states is observed along the mirror line, one inside and one outside the first surface Brillouin zone.

    “In close vicinity to each X point, a pair of surface states are observed along the mirror line direction.One lies inside the first surface BZ whereas the other is located outside.”
    Quote in the paperSubstantial claim
  • Findingown data

    Spin-resolved measurements at 60 meV below the Fermi level along the mirror line reveal four spins pointing in the ± in-plane tangential direction for the surface states.

    “As shown in the net spin polarization measurement of SR-Cut 1 in Fig. 4c, in total four spins pointing in the (±) in-plane tangential direction are revealed for the surface states along the mirror line direction.”
    Quote in the paperSubstantial claim
  • Findingown data

    Fitting of momentum distribution curves for cut 2 shows that the experimental chemical potential lies roughly at or just below the Dirac point, EF = ED ± 0.02 eV.

    “Fitting of the momentum distribution curves of cut 2 (see Supplementary Fig. S6 for data analysis) shows that the experimental chemical potential (E F ) lies roughly at (or just below) the Dirac point energy (E D ), E F ¼ E D ± 0.02 eV.”
    Quote in the paperNot a substantial claim
  • May combine two claims. 34
  • Classified as probably not a substantial claim. 19

  • May combine two claims.

    Findingown data

    The zoomed mapping near the X point reveals two unconnected small pockets, with a momentum-space distance from each pocket center to X of about 0.09 Å^-1.

    “The mapping zoomed- in near the X point (Fig. 3c) reveals two unconnected small pockets (dots).The momentum space distance from the centre of each pocket to the X point is about 0.09 Å À 1 .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    First-principles calculations confirm that PbTe is a conventional band insulator with a single hole-like bulk valence band near each X point, consistent with ARPES on Pb-rich Pb0.8Sn0.2Te.

    “Our calculations confirm that PbTe is a conventional band insulator, whose electronic structure can be described as a single hole-like bulk valence band in the vicinity of each X point, which is consistent with our ARPES results on Pb-rich Pb 0.8 Sn 0.2 Te.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The x=0.2 Pb0.8Sn0.2Te sample is gapped, with no band crossing the Fermi level in Fermi surface maps.

    “The system at x ¼ 0.2 is observed to be gapped: No band is observed to cross the Fermi level in the Fermi surface maps (Fig. 2a).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In Pb0.6Sn0.4Te, surface states are present only along the mirror line directions, and no other states are found along other momentum directions at the Fermi level.

    “The surface states are observed to be present, and only present, along the mirror line ( G À X À G) directions.No other states are found along any other momentum directions on the Fermi level.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    At 18 eV, bulk valence band intensity overlaps strongly with surface states and masks the inner branches; at 10 and 24 eV, the surface states are relatively better isolated.

    “At a photon energy of 18 eV, the intermixing (intensity overlap) is strong, and the inner two branches of the surface states are masked by the bulk intensity.At photon energies of 10 and 24 eV, the surface states are found to be relatively better isolated.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The surface state velocity is 2.8±0.1 eV Å along cut 2 and 1.1±0.3 eV Å for the two outer branches along cut 1.

    “The surface states' velocity is obtained to be 2.8±0.1 eV Å (4.2±0.2Â 10 5 m s À 1 ) along cut 2, and 1.1 ± 0.3 eV Å (1.7 ± 0.4 Â 10 5 m s À 1 ) for the two outer branches along cut 1, respectively.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingnone given

    The natural Fermi level of the x=0.4 samples is very close to the Dirac point, which is spin degenerate.

    “Considering that the natural Fermi level of our x ¼ 0.4 samples are very close to the Dirac point (which is spin degenerate), the spin polarization of the surface states are measured at 60 meV below the Fermi level to gain proper contrast, namely SR-Cut 1 in Fig. 4a.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    For GeBi2Te4, a single surface Dirac cone is observed enclosing the time-reversal invariant momentum Gamma in both ARPES and calculation, demonstrating its Z2 topological insulator state and time-reversal symmetry protection.

    “As shown in Figs 5a-c, for GeBi 2 Te 4 , a single surface Dirac cone is observed enclosing the time-reversal invariant (Kramers') momentum G in both ARPES and calculation results, demonstrating its Z 2 TI state and the time-reversal symmetry protection of its single Dirac cone surface states.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [31][32][33]

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data

    The spectral intensity contribution of Sn peaks in the x=0.4 sample is higher than in the x=0.2 sample, consistent with the larger Sn concentration in x=0.4.

    “In addition, the spectral intensity contribution of the Sn peaks in the x ¼ 0.4 sample (red) is found to be higher than that of in the x ¼ 0.2 sample (blue), which is also consistent with the larger Sn concentration in the x ¼ 0.4 samples.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Low-energy states near the Fermi level in Pb0.6Sn0.4Te are highly dominated by surface states, while high-binding-energy states are highly dominated by the bulk valence band.

    “We study the spin polarization of the low-energy states of the Pb 0.6 Sn 0.4 Te samples, which are highly dominated by the surface states near the Fermi level.We further compare and contrast their spin behaviour with that of the states at high binding energies away from the Fermi level, which are highly dominated by the bulk valence band in the same sample.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The x=0.2 sample has a non-inverted bulk band gap, while the x=0.4 sample has an inverted bulk band gap.

    “The insets of a and d show the non-inverted and inverted bulk band gap of the x ¼ 0.2 and x ¼ 0.4 samples, respectively.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data

    The energy splitting of the Pb orbital is larger than that of the Sn orbital, consistent with stronger spin-orbit coupling of the heavier Pb nuclei.

    “The energy splitting of the Pb orbital is observed to be larger than that of the Sn orbital, which is consistent with the stronger spin-orbit coupling of the heavier Pb nuclei.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Spin polarization measurements show that the surface states are spin-polarized and their spin polarization direction is locked to their momentum.

    “Spin polarization measurements show that these surface states are spin-polarized and their spin polarization direction is locked with their momentum (spin-momentum locking).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationcitation

    The surface states in Pb0.6Sn0.4Te have a relatively broad spectrum, possibly due to strong scattering in the disordered alloy, similar to the broad spectrum of topological surface states in Bi1-xSbx.

    “The surface states in our Pb 0.6 Sn 0.4 Te samples are found to have a relatively broad spectrum, which can be possibly understood by the strong scattering in the disordered alloy system similar to the broad spectrum of the topological surface states in the Bi 1 À x Sb x alloy 23 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [23] Hsieh D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation

    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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    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 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [16] Iizumi M. et al. Phase transition in SnTe with low carrier concentration. J. Phys. Soc. Jpn. 38, 443–449 (1975). source

      Not checked in the free run.

    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisenone given

    The topological phase in the Bi1-xSbx system arises from an odd number of band inversions.

    “The topological phase in the Bi 1 À x Sb x system is due to an odd number of band inversions.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    An odd number of bulk band inversions separates a Z2 topological insulator with spin-polarized surface states from a conventional band insulator, as demonstrated in Bi1-xSbx and Bi2Se3.

    “The odd number of band inversion transitions in the bulk demarcate a Z 2 topological insulator (TI) phase with spin-polarized surface states from that of a conventional band insulator phase, as previously demonstrated in TI Bi 1 À x Sb x and the Bi 2 Se 3 series [1][2][3][4][5] .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [1][2][3][4][5]

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    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 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [16] Iizumi M. et al. Phase transition in SnTe with low carrier concentration. J. Phys. Soc. Jpn. 38, 443–449 (1975). source

      Not checked in the free run.

    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    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 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [11][12][13]

      Not checked in the free run.

    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    In total, four surface states are observed within the first surface Brillouin zone, in agreement with the four band inversions in Pb1-xSnxTe.

    “Therefore, in total four surface states are observed within the first surface BZ, in agreement with the fact that there are four band inversions in Pb 1 À x Sn x Te.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    SnTe crystals are typically heavily p-type because Sn vacancies are thermodynamically stable, placing the chemical potential below the bulk valence band maximum.

    “More importantly, SnTe crystals are typically heavily p-type 17 due to the fact that Sn vacancies are thermodynamically stable 17 , which makes the chemical potential of SnTe to lie below the bulk valence band maximum (VBM), consequently not cutting across the surface states.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17] Burke J. R. Jr, Allgaier R. S., Houston B. B. Jr, Babiskin J., Siebenmann P. G. Shubnikov-de Haas effect in SnTe. Phys. Rev. Lett. 14, 360–361 (1965). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation

    Theoretical calculations predicted surface or interface states within the inverted band gap upon the band inversion transition.

    “Theoretical calculations have also predicted the occurrence of surface or interface states within the inverted band gap upon the band inversion transition [11][12][13]”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [11][12][13]

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation

    Pb1-xSnxTe has long been known from band theory to contain an even number of band inversions as the Sn/Pb ratio tunes its electronic structure.

    “lead tin telluride Pb 1 À x Sn x Te, which is a narrow band gap semiconductor widely used for infrared optoelectronic and thermoelectric devices 6,7 , has long been known to contain an even number of band inversions as electronic structure is tuned via the Sn/Pb ratio [8][9][10][11][12][13] .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [8][9][10][11][12][13]

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Because SnTe's chemical potential lies below the valence band maximum, surface states within the gap are unoccupied and cannot be studied by photoemission.

    “The surface states, which may exist within the band gap, are thus unoccupied and cannot be experimentally studied by photoemission experiments 18 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [18] Littlewood P. B. et al. Band structure of SnTe studied by photoemission spectroscopy. Phys. Rev. Lett. 105, 086404 (2010). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    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 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Rhombohedral distortion in SnTe occurs only in Sn-rich compositions (x>0.5) and only at low temperature.

    “(the rhombohedral distortion is found to only occur in the Sn-rich compositions (x40.5) and only at low temperature 16 ).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [16] Iizumi M. et al. Phase transition in SnTe with low carrier concentration. J. Phys. Soc. Jpn. 38, 443–449 (1975). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductreasoning

    Spin polarization measurements have an error bar of approximately ±0.01 per data point.

    “Typical electron counts on the detector reach 5 Â 10 5 , which places an error bar of approximately ± 0.01 for each point on our measured polarization curves.”
    • Also stated in: § Sample growth. · plain
      “The error bar is ± 0.01 for data points in all spin polarization measurements.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data

    Cleavage surface orientation in ARPES measurements was cross-checked by Laue back-reflection X-ray measurements.

    “To cross-check the cleavage surface orientation in ARPES measurements, the Laue back-reflection X-ray measurements were performed at the ALS using a Realtime Laue delay-line detector from the Multiwire Laboratories (Ithaca, NY), and diffraction spot indexing was performed using the MWL NorthStar orientation package.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductnone given

    Spin-resolved ARPES measurements had energy resolution better than 60 meV and momentum resolution better than 3% of the surface Brillouin zone.

    “Energy resolution was bettern than 60 meV and momentum resolution was better than 3% of the surface BZ for the spin-resolved measurements.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductown data

    Spin-orbit coupling was included in the self-consistent first-principles calculations.

    “The spin-orbital coupling is included in the selfconsistent cycles.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    For Pb0.6Sn0.4Te, none of the surface states encloses any time-reversal invariant momentum, suggesting they are not protected by time-reversal symmetry.

    “On the other hand, for the Pb 0.6 Sn 0.4 Te samples (Figs 5d-f), none of the surface states is observed to enclose any of the time-reversal invariant momentum, suggesting their irrelevance to the time-reversal symmetry-related protection.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Current ARPES works have not demonstrated resolution better than 5 meV, so fitting cannot exclude gap values below 5 meV.

    “The current ARPES works 29,30 have not demonstrated resolution better than 5 meV, and thus fitting of the energy-momentum distribution curves lacks the resolving power to exclude gap values o5 meV (see Supplementary Fig. S10 and Supplementary Discussion).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [29] Dziawa P. et al. Topological crystalline insulator states in Pb1−xSnxSe. Nat. Mater (e-pub ahead of print 30 September 2012; doi:10.1038/nmat3449). source

      Not checked in the free run.

    • cites [30] Xu S.-Y. et al. Observation of topological crystalline insulator phase in the lead tin chalcogenide Pb1−xSnxTe material class. Preprint at http://arXiv.org/abs/1206.2088 (2012). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductcitation

    Spin-resolved ARPES systematically measures all three components of the electron spin as a function of energy and momentum.

    “SR ARPES measurements were performed on the SIS beamline at the Swiss Light Source using the COPHEE spectrometer with two 40 kV classical Mott detectors and a photon energy of 24 eV, which systematically measures all three components of the spin of the electron (P x , P y and P z ) as a function of its energy and momentum 25,26 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [25] Hoesch M. et al. Spin-polarized Fermi surface mapping. J. Electron Spectrosc. Relat. Phenom. 124, 263–279 (2002). source

      Not checked in the free run.

    • cites [26] Dil J. H. et al. Spin and angle resolved photoemission on non-magnetic low-dimensional systems. J. Phys. Condens. Matter 21, 403001 (2009). source

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationcitation

    Although the existence of surface states correlated with the band inversion transition is established, whether they are gapped or gapless requires surface transport experiments on improved-quality samples, which is currently not possible.

    “Therefore, although the existence of surface states correlated with band inversion transition is established here in our work, their gapped or gaplessness nature requires surface transport experiments on samples with improved quality, which is currently not possible 29 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [29] Dziawa P. et al. Topological crystalline insulator states in Pb1−xSnxSe. Nat. Mater (e-pub ahead of print 30 September 2012; doi:10.1038/nmat3449). source

      Not checked in the free run.

    • Rests on an assumption: In the Pb1-xSnxTe alloy, the space group symmetry is only of averaged type, so the spatial mirror symmetry required for topological protection is preserved only in a globally averaged sense.

  • Classified as probably not a substantial claim.

    Premisecitation

    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 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based).

    Interpretationnone given

    The novel magnetic and superconducting states enabled by this topology are not strongly tied to whether the TCI phase is gapless or gapped.

    “The novel magnetic and superconducting states to be realized with this novel topology are not strongly related to the question of gapless or gapped nature of the TCI phase.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Even a gap smaller than 1 meV can produce observable changes in spin-transport experiments and destroy the delicate topological crystalline insulator phase.

    “Even a gap size of even o1 meV can lead to observable change in spin-transport experiments, thus destroying the delicate TCI phase.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The observations suggest that Pb1-xSnxTe is a tunable spin-orbit insulator analogous to BiTl(S1-dSed)2, with a topological phase transition across the band inversion transition.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [5] Xu S.-Y. et al. Topological phase transition and texture inversion in a tunable topological insulator. Science 332, 560–564 (2011). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    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 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    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 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [15] Hsieh H. et al. Topological crystalline insulators in the SnTe material class. Nat. Comm. 3, 982 (2012). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    Magnetic surface states that remain topologically protected can be realized in Pb1-xSnxTe, because its protection from crystalline mirror symmetries does not rely on time-reversal symmetry, unlike Z2 topological insulators.

    “Sn 0.4 Te surface states and therefore the topological protection by the crystalline mirror symmetries, it is then possible to realize magnetic yet topologically protected surface states in the Pb 1 À x Sn x Te system due to its irrelevance to the time-reversal symmetry-related protection, which is fundamentally not possible in the Z 2 TI systems.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductown data

    Spin-integrated ARPES measurements had energy resolution better than 15 meV and momentum resolution better than 1% of the surface Brillouin zone.

    “Energy resolution was better than 15 meV and momentum resolution was better than 1% of the surface BZ.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    A key difference is that odd band inversions in BiTl(S1-dSed)2 lead to an odd number of surface states, while even band inversions in Pb1-xSnxTe lead to an even number of surface states per surface Brillouin zone.

    “However, the key difference is that odd number of band inversions in the BiTl(S 1 À d Se d ) 2 system leads to odd number of surface states, whereas even number of band inversions in Pb 1 À x Sn x Te system leads to even number of surface states per surface BZ.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

    Interpretationreasoning

    The spin-polarized surface states observed here offer a platform for realizing unusual surface magnetic and superconducting states in future experiments.

    “Therefore, our observation of the spin-polarized surface states presented here provides the much desired platform for realizing unusual surface magnetic and superconducting states in future experiments.”
    Quote in the paperNot a substantial claim
45 of 45

  • The paper relies on this without support.

    In the Pb1-xSnxTe alloy, the space group symmetry is only of averaged type, so the spatial mirror symmetry required for topological protection is preserved only in a globally averaged sense.

    “It is important to note that in an alloy, the space group symmetry is only of the averaged type.The spatial mirror symmetry required for the topological protection is only preserved in a globally averaged sense.”

  • The paper relies on this without support.

    No experimental evidence of surface states in Pb1-xSnxTe had been reported before this study.

    “but no experimental evidence of the surface states has been reported so far.”

  • The paper relies on this without support.

    It is not theoretically known whether only averaged mirror symmetry is sufficient for the predicted topological crystalline insulator phase.

    “To this date, it is not even theoretically known whether only averaged mirror symmetry is sufficient for the predicted TCI phase.”
3 of 3

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?

  • The Pb and Te atoms form interpenetrating face-centered cubic lattices.

    “The Pb and Te atoms form an arrangement of interpenetrating face-centered cubic lattices [19].”

    From Magnetic Control of Soft Chiral Phonons in PbTe (2022) · cites this paper as [19]

  • PbTe belongs to the space group Fm-3m with Oh point group.

    “PbTe belongs to the space group Fm 3m with O h point group.”

    From Magnetic Control of Soft Chiral Phonons in PbTe (2022) · cites this paper as [19]

  • Current ARPES works have not demonstrated resolution better than 5 meV, so fitting cannot exclude gap values below 5 meV.

    “The current ARPES works 29,30 have not demonstrated resolution better than 5 meV, and thus fitting of the energy-momentum distribution curves lacks the resolving power to exclude gap values o5 meV (see Supplementary Fig. S10 and Supplementary Discussion).”

    From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [30]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Figure 3b is described as a Fermi-surface map but uses a nonzero binding energy

    Minor

    The Results describe Figure 3b as a Fermi-surface map, while its caption specifies a contour measured 0.02 eV below the Fermi level. The caption identifies the separate Figure 3c map, at 0.0 eV binding energy, as the Fermi-surface map.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Okamoto K. et al. Observation of a highly spin polarized topological surface state in GeBi2Te4 . Preprint at http://arXiv.org/abs/1207.2088 (2012). · arXiv

Cited by

Sorted by citations

Related

Authors
Xu, S.-Y., Liu, C., Alidoust, N., Neupane, M., Qian, D., Belopolski, I., Denlinger, J. D., Wang, Y. J., Lin, H., Wray, L. A., Landolt, G., Slomski, B., Dil, J. H., Marcinkova, A., Morosan, E., Gibson, Q., Sankar, R., Chou, F. C., Cava, R. J., Bansil, A., & Hasan, M. Z.
Affiliations
  • Princeton University (US)
  • Shanghai Jiao Tong University (CN)
  • Lawrence Berkeley National Laboratory (US)
  • Northeastern University (US)
  • University of Zurich (CH)
  • Rice University (US)
  • National Taiwan University (TW)
Corresponding author
Hasan, M.Z.
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2012-11-13
Volume
3
Issue
1
Pages
1192-1192
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/ncomms2191
OpenAlex
W2171045861
Cited by
691
References
46
Citations by year
2026: 18 · 2025: 41 · 2024: 33 · 2023: 38 · 2022: 52 · 2021: 48 · 2020: 53 · 2019: 58 · 2018: 74 · 2017: 54 · 2016: 54 · 2015: 64 · 2014: 65 · 2013: 37 · 2012: 2
FWCI
27.66
Type
journal article
Language
en
Update notices
correction (2016-08-04)
Open access
Licence
Locations
  • Nature Communications (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DORA PSI (Paul Scherrer Institute) (submittedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (0819860, 1006492)
  • U.S. Department of Energy (DEFG0207ER46352, AC03-76SF00098, DE‐FG02‐, DEFG0205ER46200, FG02-07ER46352)
  • Alfred P. Sloan Foundation
  • National Energy Research Scientific Computing Center
  • Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (DMR-0819860)
  • National Science Council (NSC 100)
  • Division of Materials Research (DMR-0819860, 1006492)
  • Basic Energy Sciences (DE-FG-02-07ER46352, AC03-76SF00098, DE-FG-02-05ER46200, DE-FG02)
  • Lawrence Berkeley National Laboratory
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, lead tin telluride, topological phase transition, mirror symmetry, spin-orbit coupling, band inversion, SnTe, Bi1-xSbx, topological order

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.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-06.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-06.

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 ›

Are you an author, or do you see a problem with this page? Request a review