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Cited by 461Topological Materials and PhenomenaAdvanced Condensed Matter PhysicsMagnetic properties of thin films

Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator

Open access
Xu, Su-Yang, Xia, Y., Wray, L. A., Jia, S., Meier, F., Dil, J. H., Osterwalder, J., Slomski, B. +4 more·2011·Science
DOI 10.1126/science.1201607
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Abstract

Two types of bulk insulator are realized in the same family of compounds through chemical doping.

AI snapshot

Written from the paper’s full text.

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.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1126/science.1201607

Cites

32 of 32 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 26 cited sources checked · 0 supported · 0 flagged

  • Findingnone given
    § Abstract · p. 4

    Finer control of bulk compositional variation does not allow locating a precise value for the transition.

    “Finer control of bulk compositional variation does not allow locating a precise value for the transition”
    Quote in the paperNot a substantial claim
  • Findingcitation
    § Abstract · p. 4

    The Dirac-like bands at δ≥0.6 are of surface origin.

    “Incident photon energy modulation studies support the assignment of these Dirac-like bands to be of surface origin ( 25 ).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [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.

  • Findingown data
    § Abstract · p. 2

    The topological insulator formation process in BiTl(S1-δSeδ)2 is visualized for the first time.

    “where the topological insulator formation process is visualized for the first time.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Abstract · p. 4

    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.

    “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.”
    Quote in the paperSubstantial claim
    • 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.
  • Findingown data
    § Abstract · p. 2

    The topological spin textures collectively feature a chirality transition as the spin-momentum locked electrons on the surface go through the zero carrier density point.

    “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.”
    Quote in the paperSubstantial claim
  • May combine two claims. 10
  • The quote only partly states this claim. 1
  • Classified as probably not a substantial claim. 8

  • May combine two claims.

    Findingown data
    § Abstract · p. 4

    While the band continua in the composition range δ=0.0 to δ=0.4 are degenerate, the Dirac-like bands at δ=0.6 and beyond are spin polarized.

    “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).”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Findingown data
    § Abstract · p. 2

    The authors observed a topological phase transition in the tunable spin-orbit system BiTl(S1-δSeδ)2 by directly measuring the topological invariants.

    “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”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation
    § Abstract · p. 4

    Both bands demarcating the gap show three-dimensional dispersion where binding energies vary with momentum perpendicular to the surface, kz, and roughly correspond to the expected position for the valence and conduction bands.

    “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.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [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.

  • May combine two claims.

    Findingown data
    § Abstract · p. 4

    The δ=0.0 compound features a direct band gap in its bulk, whereas the δ=1.0 indicates a slightly indirect gap.

    “the δ = 0 . 0 compound features a direct band gap in its bulk, whereas the δ = 1 . 0 indicates a slightly indirect gap.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Abstract · p. 4

    As selenium concentration is increased, the low-lying bands separated by a gap of energy 0.15 eV at δ=0.0 approach each other and the gap decreases to less than 0.05 eV at δ=0.4.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Abstract · p. 6

    Above the Dirac node, a quasi-particle moving in +k (+x) direction is locked with +y spin-polarization state, whereas below the node, the +k moving quasi-particle state is locked with -y spin.

    “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.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data
    § Abstract · p. 7

    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 Fermi surface.

    “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).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisenone given
    § Abstract · p. 3

    A ν0=1=θ/π topology requires the terminated surface to have a Fermi surface that supports a nonzero Berry's phase (an odd multiple of π), which is not realizable in an ordinary spin-orbit or trivial (ν0=0=θ) insulator.

    “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.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract · p. 2

    A trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice via an odd number of band inversions, driving the system through a topological quantum phase transition.

    “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 ).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source

      Not checked in the free run.

    • cites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source

      Not checked in the free run.

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

    Premisecitation
    § Abstract · p. 3

    Three-dimensional topological insulators are nonmagnetic insulators with novel surface states that are a consequence of the nontrivial topology of electronic wavefunctions in the bulk.

    “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 ).”
    Quote in the paperNot a substantial claim0 of 5 sources checked
    • cites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source

      Not checked in the free run.

    • cites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source

      Not checked in the free run.

    • cites [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 in the free run.

    • cites [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 in the free run.

    • cites [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

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisenone given
    § Abstract · p. 3

    Strong topological insulators are distinguished from ordinary insulators by a finite topological quantum number or invariant (ν0) or equivalently an axion angle parameter (θ).

    “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 ).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § Abstract · p. 4

    Spins tangentially arranged on such a circular Fermi surface lead to a Berry's phase of π, which is also a measure of the topological invariant and axion angle (ν0=1=θ/π) of the system.

    “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 ).”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source

      Not checked in the free run.

    • cites [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 in the free run.

    • cites [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 in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract · p. 3

    The value of ν0 or θ depends on the parity eigenvalues of the wavefunctions in time reversal symmetric materials.

    “The value of ν 0 or θ depends on the parity eigenvalues of the wavefunctions in time reversal symmetric materials ( 1, 2 )”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [1] 1. M. Z. Hasan, C. L. Kane, Topological insulators. Rev. Mod. Phys. 82 , 3045 (2010). source

      Not checked in the free run.

    • cites [2] 2. L. Fu, C. L. Kane, E. J. Mele, Topological insulators in three dimensions. Phys. Rev. Lett. 98 , 106803 (2007). source

      Not checked in the free run.

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

    Interpretationown data
    § Abstract · p. 4

    The inability to locate a precise transition value could be a consequence of an intrinsically broader topological transition.

    “this could also be a consequence of an intrinsically broader topological transition.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data
    § Abstract · p. 4

    At δ=0.4, the surface remains gapped, suggesting the material is still on the trivial side.

    “however, that the surface remains gapped at δ = 0 . 4 suggests that the material is still on the trivial side.”
    Quote in the paperSubstantial claim
    • 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.

  • Classified as probably not a substantial claim.

    Premisenone given
    § Abstract · p. 4

    Non-linear spin-orbit terms correspond to analogs of cubic and higher order Dresselhaus effects arising from the symmetry of the crystal potential.

    “Such terms correspond to analogs of cubic and higher order Dresselhaus effects arising from the symmetry of the crystal potential.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation
    § Abstract · p. 3

    The value of ν0 or θ can be determined from spin texture details of the spin-orbit surface states that form when the bulk is terminated.

    “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 ).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [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 in the free run.

    • cites [7] 7. D. Hsieh et al ., Observation of unconventional quantum spin textures in topological insulators. Science 323 , 919 (2009). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § Abstract · p. 7

    Based on a mean field Zener theory, a helical magnetic order is expected if the surface state topology is in the 3D vectorial spin texture regime, and the system can then achieve unusually high critical temperature, even up to THMO ∼ 100 K.

    “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 ).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [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).

      Not checked in the free run.

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

    Premisecitation
    § Abstract · p. 4

    The TI n-type bulk doped Bi2Te3 features a highly warped concave-in snowflake-shaped Fermi surface because of its large kF and a small band gap.

    “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 ).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [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.

19 of 19

  • 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.”
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 BDS state can be achieved at the critical point of a topological phase transition between a normal insulator and a TI, requiring fine-tuning of chemical doping/alloying composition.

    “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]

    The Abstract (pp. 3–4) reports that changing the sulfur-to-selenium ratio tunes spin-orbit strength and produces a transition from a trivial insulator to a topological insulator. It does not establish a BDS state at the critical point; on p. 4, it says finer compositional control did not locate a precise transition value. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • The topological order observed in Pb1-xSnxTe is distinct from that previously discovered in Bi1-xSbx or Bi2Se3.

    “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]

  • 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.”

    From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [5]

Cites

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Research works printed but not linked: 1

  1. 10.1103/physrevlett.103.066402 · DOI · Paper page

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Related

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
Publisher
American Association for the Advancement of Science (AAAS)
Published
2011-04-29
Volume
332
Issue
6029
Pages
560-564
ISSN
  • 0036-8075 (ISSN-L)
  • 1095-9203
DOI
10.1126/science.1201607
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
Licence
www.sciencemag.org/site/feature/contribinfo/prep/license.xhtml (vor)
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 › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › 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

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