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Cited by 581Topological Materials and PhenomenaAdvanced Condensed Matter PhysicsSurface and Thin Film Phenomena

A topological insulator surface under strong Coulomb, magnetic and disorder perturbations

Open access
Wray, L. Andrew, Xu, Su-Yang, Xia, Yuqi, Hsieh, David, Fedorov, Alexei V., Hor, Yew San, Cava, Robert J., Bansil, Arun +2 more·2011·Nature Physics
DOI 10.1038/nphys1838
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Abstract

Topological insulators embody a state of bulk matter characterized by spin-momentum-locked surface states that span the bulk bandgap. This highly unusual surface spin environment provides a rich ground for uncovering new phenomena. Understanding the response of a topological surface to strong Coulomb perturbations represents a frontier in discovering the interacting and emergent many-body physics of topological surfaces. Here we present the first controlled study of topological insulator surfaces under Coulomb and magnetic perturbations. We have used time-resolved deposition of iron, with a large Coulomb charge and significant magnetic moment, to systematically modify the topological spin structure of the Bi_2Se_3 surface. We observe that such perturbation leads to the creation of odd multiples of Dirac fermions and that magnetic interactions break time-reversal symmetry in the presence of band hybridizations. We present a theoretical model to account for the observed electron dynamics of the topological surface. Taken collectively, these results are a critical guide in controlling electron mobility and quantum behaviour of topological surfaces, not only for device applications but also in setting the stage for creating exotic particles such as axions or imaging monopoles on the surface.

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Crossref · 10.1038/nphys1838

Cites

7 of 7 references verified0 citation errors · 0 not checkable

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Nothing to recompute.

Claims the paper makes

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

  • Findingown data

    A theoretical simulation of a non-magnetic surface Coulomb perturbation on Bi2Se3 qualitatively reproduces the progressive appearance of new Dirac points with increasing iron deposition.

    “Theoretical simulation of non-magnetic surface Coulomb perturbation on Bi 2 Se 3 is shown in Fig. 3a, and qualitatively reproduces the progressive appearance of new Dirac points with increasing iron deposition.”
    Quote in the paperSubstantial claim
  • Findingown data

    After heavy iron deposition, the surface electronic structure of Bi2Se3 is greatly altered, indicating a significant change in the surface electronic environment.

    “As seen in Fig. 1d the surface electronic structure after heavy iron deposition is greatly altered, showing that a significant change in the surface electronic environment has been achieved.”
    Quote in the paperSubstantial claim
  • Findingown data

    In sample no 2, when the chemical potential is above the bulk conduction-band minimum, new surface states disperse across the full bulk bandgap.

    “When the chemical potential is positioned above the bulk conduction-band minimum, as in sample no 2 (Fig. 2c), the dispersion of new surface states across the full bulk bandgap is visible within the photoemission image.”
    Quote in the paperSubstantial claim
  • Findingown data

    The Rashba description is accurate for Bi2Se3 only in a small region around the Brillouin zone centre, because at larger momenta the electronic states pair off and are nearly spin degenerate.

    “Our data and simulations show that this description is only accurate for Bi 2 Se 3 in a small part of the Brillouin zone surrounding the Brillouin zone centre, because at momenta further from the point the electronic states pair off and are nearly spin degenerate (see Fig. 3b).”
    Quote in the paperSubstantial claim
  • Findingown data

    Electron velocities near the D1 and D2 Dirac points increase monotonically as iron is added.

    “Electron velocities (band slope) near the D1 and D2 Dirac points increase monotonically as iron is added”
    Quote in the paperSubstantial claim
  • May combine two claims. 25
  • Classified as probably not a substantial claim. 9

  • May combine two claims.

    Findingown data

    In both samples, positively charged Fe surface ions progressively lower the surface-state energy and cause new surface states with energy-momentum contours similar to the bottom of the bulk conduction band.

    “In each case, it is observed that the presence of positively charged Fe surface ions progressively lowers the energy of the surface state and causes the appearance of new surface states with energy-momentum contours similar to the bottom of the bulk conduction band.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    A gap appears at the D0 Dirac point after heavy iron deposition, and the lower D0 Dirac cone acquires a buckled shape with a local energy minimum at zero momentum.

    “A gap appears at the D0 Dirac point after heavy iron deposition, and the lower D0 Dirac cone acquires a buckled shape with a local energy minimum at zero momentum.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Evidence of Landau levels is neither seen in the data nor expected from theory.

    “Evidence of Landau levels is neither seen in our data nor in this context expected from theory.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Sample no 1 before deposition is slightly p-type with resistivity ρ = 23 mΩ cm, and sample no 2 is electron-doped from Se vacancy defects.

    “The bulk electronic state of sample no 1 before deposition is slightly p type with significant resistivity (ρ = 23 m cm), and sample no 2 is electron doped from Se vacancy defects in as-grown Bi 2 Se 3 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The new low-energy features have no z-axis momentum dependence, confirming they are largely two-dimensional.

    “Unlike the bulk electronic states of Bi 2 Se 3 (ref.22), these features have no z-axis momentum dependence, confirming that they are largely two dimensional in nature (Fig. 1e).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [22] Wray, L. A., Xu, S-Y., Xia, Y., Hor, Y. S., Qian, D., Fedorov, A. V., Lin, H., Bansil, A., Cava, R. J. & Hasan, M. Z. Observation of topological order in a superconducting doped topological insulator. Nature Phys. 6, 855–859 (2010). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data

    In sample no 2, after five minutes of Fe deposition a new strongly split surface band with a D1 Dirac point at Γ appears, but no D2 bands appear after longer deposition.

    “A new, strongly split surface band is observed in sample no 2 after five minutes of Fe deposition with a (D1) Dirac point at the point, but no further (for example, D2) bands appeared after longer deposition.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Experimentally observed surface states begin to pair off at momentum separation greater than about 0.1 Å−1 from the Brillouin zone centre, with upper D0 approaching degeneracy with lower D1 and upper D1 connecting to lower D2.

    “Through comparison with our numerical result, we can see that the experimentally observed surface states begin to pair off at momentum separation greater than ∼0.1 Å -1 from the Brillouin zone centre, with the upper D0 Dirac cone approaching degeneracy with the lower D1 band, and the upper D1 band connecting to the lower D2 band.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The mass induced in the upper D0 Dirac cone after full deposition is approximately 0.1 electron masses, and the surface bandgap is about 100 meV.

    “The mass induced in the upper D0 Dirac cone after full deposition is approximately 0.1 M e (electron masses), and the surface bandgap is about 100 meV.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    After 12 minutes of deposition, the D0 Dirac point binding energy sank by about 0.6 eV, and further deposition did not change electron binding energies.

    “After 12 min of deposition, the binding energy of the D0 Dirac point was found to have sunk by approximately 0.6 eV in energy, and the electron binding energies ceased to change under further deposition.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Five surface bands, an odd number, intersect the Fermi level after heavy iron deposition, rather than one, and extend below the Fermi level as multiple Dirac cones.

    “Five (odd number of) surface bands intersect the Fermi level rather than just one, and extend below the Fermi level in the form of multiple Dirac cones.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The photoemission image becomes qualitatively sharper with increasing iron coverage in a certain regime, corresponding approximately to increasing clarity of the D0 gap.

    “Contrary to the usual trend of deposition experiments, in which photoemission images become increasingly blurry as molecules are haphazardly added to the surface, we identify a regime in which the image becomes qualitatively sharper with the increasing coverage of iron (seen in Fig. 4d and the first three panels of Fig. 2a), corresponding approximately to the increasing clarity of the D0 gap.”
    Quote in the paperSubstantial claim

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

    Findingown data

    Doping evolution of the lower D0 Dirac cone is much less clear in the data because of the disordered surface and close proximity of features.

    “Doping evolution of the lower D0 Dirac cone is much less clear in the data, owing to the disordered surface and close proximity of features.”
    Quote in the paperNot a substantial claim

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

    Premisecitation

    Magnetic interactions in Bi2Se3 can be controlled through magnetic ions such as Fe or Mn.

    “magnetic interactions can be controlled through magnetic ions such as Fe or Mn (refs 9, 10).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [9] Hor, Y. S. et al. Development of ferromagnetism in the magnetically doped topological insulator Bi2−xMnxTe3 . Phys. Rev. B 81, 195203 (2010). source

      Not checked in the free run.

    • cites [10] Hsieh, D. et al. Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3 . Phys. Rev. Lett. 103, 146401 (2009). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    Because magnetic-field perturbations from the submonolayer iron coating are weak, the magnetic-phase term in perturbative Hamiltonians can be discounted, and the dominant magnetic effects are expected to be described by a local Heisenberg-exchange term representing direct wavefunction overlap between surface electrons and spin-polarized Fe 3d orbitals.

    “Because magnetic-field perturbations from the submonolayer iron coating are quite weak, the magnetic-phase term in perturbative Hamiltonians can be discounted, and the dominant magnetic effects are expected to be described by a local Heisenberg-exchange term representing direct wavefunction overlap (hopping) between surface electrons and spin-polarized Fe 3d orbitals 11 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [11] Biswas, R. R. & Balatsky, A. V. Impurity-induced states on the surface of 3D topological insulators. Phys. Rev. B 81, 233405 (2010). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Surface electrons in Bi2Se3 form a Dirac cone spanning the bulk insulating gap and consist of spin-momentum-locked helical states.

    “Spinresolved photoemission studies reveal that surface electrons in Bi 2 Se 3 form a Dirac cone spanning the bulk insulating gap, composed of spin-momentum-locked helical states (Fig. 1a).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premiseown data

    Placing the Fermi level at the Dirac point in the presence of bulk magnetic impurities can produce a small gap at the Fermi level, but its full character cannot be decisively resolved because of lineshape broadening.

    “Placing the Fermi level at the Dirac point in the presence of magnetic impurities in the bulk can lead to a small gap at the Fermi level (Fig. 1b); however, the full character of this gap cannot be decisively resolved owing to the lineshape broadening effects.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    Topological insulators are a state of bulk matter with spin-momentum-locked surface states that span the bulk bandgap.

    “Topological insulators embody a state of bulk matter characterized by spin-momentum-locked surface states that span the bulk bandgap 1-7 .”
    Quote in the paperSubstantial claim0 of 7 sources checked
    • cites [1] Moore, J. E. Topological insulators: The next generation. Nature Phys. 5, 378–380 (2009). source

      Not checked in the free run.

    • cites [2] Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). source

      Not checked in the free run.

    • cites [3] Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007). source

      Not checked in the free run.

    • cites [4] 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.

    • cites [5] Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919–922 (2009). source

      Not checked in the free run.

    • cites [6] Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009). source

      Not checked in the free run.

    • cites [7] Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    In a normal three-dimensional material, electrons interacting with surface-deposited magnetic impurities can scatter away from the surface over a 2π solid angle, so two-dimensional magnetic interactions typically decay over several ångstroms.

    “In a normal three-dimensional material, electrons that interact with surface-deposited magnetic impurities are free to scatter away from the surface over a 2π solid angle, and the two-dimensional magnetic interactions therefore typically decay over several ångstroms (see, for example, ref. 27).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [27] Wahl, P. et al. Exchange interaction between single magnetic adatoms. Phys. Rev. Lett. 98, 056601 (2007). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    If the D0 bandgap were due to an isotropic out-of-plane magnetic field, a similar gap would be expected at the D1 and D2 Dirac points, which is not observed.

    “If the D0 bandgap were due to an isotropic out-of-plane magnetic field, a similar gap would be expected at the D1 and D2 Dirac points, which is clearly not observed.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisecitation

    The spin-splitting of topological surface bands is often described as a special case of the Rashba effect, where surface states become spin-split by an energy proportional to momentum k.

    “The spin-splitting of topological surface bands is often discussed as a special case of the Rashba effect (see, for example, refs 3,20), in which surface electronic states become spin-split by an energy proportional to their momentum k.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [3] Fu, L., Kane, C. L. & Mele, E. J. Topological insulators in three dimensions. Phys. Rev. Lett. 98, 106803 (2007). source

      Not checked in the free run.

    • cites [20] Hasan, M. Z. et al. Warping the cone on a topological insulator. Physics 2, 108 (2009). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Iron deposited on a Se-terminated Bi2Se3 surface is expected to form a mild chemical bond, occupy an ionization state between 2+ and 3+, and have roughly 4 μB magnetic moment.

    “Iron deposited on a Se 2-surface is expected to form a mild chemical bond, occupying a large ionization state between 2 + and 3 + with roughly 4 µ B magnetic moment 25 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [25] Kawaminami, M. & Okazaki, A. Neutron diffraction study of Fe7Se8. II. J. Phys. Soc. Jpn 29, 649–655 (1970). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    The origin of the topological insulator state in Bi2Se3 is a symmetry inversion at Γ, and electronic states near the Brillouin-zone boundary resemble those of topologically trivial materials.

    “This can be understood because the origin of the topological insulator state in Bi 2 Se 3 is a symmetry inversion that occurs at the point 7,18 , and the electronic states close to the Brillouin-zone boundary are similar to those of topologically trivial materials.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [7] Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009). source

      Not checked in the free run.

    • cites [18] Zhang, H. et al. Model Hamiltonian for topological insulators. Phys. Rev. B 82, 045122 (2010). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationcitation

    The exact time at which the bandgap appears is difficult to identify, probably because there is no long-range order of iron spins on the surface and differently ordered domains contribute differently gapped signals.

    “It is difficult to identify the exact time at which the bandgap appears, probably because there is no long-range order of iron spins on the surface 28,29 , and differently ordered domains will yield differently gapped contributions to the photoemission signal.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [28] Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966). source

      Not checked in the free run.

    • cites [29] Zhang, R-J. & Willis, R. F. Thickness-dependent Curie temperatures of ultrathin magnetic films: Effect of the range of spin–spin interactions. Phys. Rev. Lett. 86, 2665–2668 (2001). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationnone given

    The role of magnetic domains in reshaping low-energy band structure is expected to be more subtle than Coulomb perturbations and may be limited to changes near Dirac points and self-energy lineshape effects.

    “The role of magnetic domains in reshaping low-energy band structure is expected to be more subtle than Coulomb perturbations, and may be limited to changes near the Dirac points and in self-energy lineshape effects (see Fig. 3c,d).”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Premisenone given

    The Fermi level of as-grown Bi2Se3 crystals is usually located in the bulk conduction band because of selenium vacancy defects.

    “The Fermi level of grown crystals is usually found to be located in the bulk conduction band due to selenium vacancy defects;”
    Quote in the paperSubstantial claim

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

    Premisecitation

    In topological insulators, surface-state electrons are confined to two-dimensional Dirac cones, and interactions between deposited impurities are suggested to be mediated over many nanometres.

    “In topological insulators, surface-state electrons are naturally confined to the surface in two-dimensional Dirac cones, and it is suggested that interactions between deposited impurities can be mediated over many nanometres (see the illustration in Fig. 4c; refs 11,26).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [11] Biswas, R. R. & Balatsky, A. V. Impurity-induced states on the surface of 3D topological insulators. Phys. Rev. B 81, 233405 (2010). source

      Not checked in the free run.

    • cites [26] Liu, Q. et al. Magnetic impurities on the surface of a topological insulator. Phys. Rev. Lett. 102, 156603 (2009). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Ca doping or NO2 surface deposition can place the Fermi level at the Dirac point and reach the topological transport regime.

    “with Ca doping or NO 2 surface deposition the Fermi level can be placed at the Dirac point, reaching the topological transport regime 6”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [6] Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009). source

      Not checked in the free run.

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

    Study design and conductcitation

    Momentum along the z axis was determined using an inner potential of 9.5 eV, consistent with previous photoemission investigations of undoped Bi2Se3.

    “Momentum along the ẑ axis is determined using an inner potential of 9.5 eV, consistent with previous photoemission investigations of undoped Bi 2 Se 3 (refs 7,22).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [7] Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Phys. 5, 398–402 (2009). source

      Not checked in the free run.

    • cites [22] Wray, L. A., Xu, S-Y., Xia, Y., Hor, Y. S., Qian, D., Fedorov, A. V., Lin, H., Bansil, A., Cava, R. J. & Hasan, M. Z. Observation of topological order in a superconducting doped topological insulator. Nature Phys. 6, 855–859 (2010). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Out-of-plane magnetic order causes a gap in topological Dirac surface electrons, while in-plane magnetic domains cause bands to shift in momentum space.

    “The general effect of Zeeman-type magnetic symmetry breaking on topological Dirac surface electrons is shown in Fig. 3c, illustrating that out-of-plane magnetic order will cause a gap, and in-plane magnetic domains will cause bands to shift in momentum space 12 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [12] Garate, I. & Franz, M. Inverse spin-galvanic effect in a topological-insulator/ferromagnet interface. Phys. Rev. Lett. 104, 146802 (2010). source

      Not checked in the free run.

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

    Study design and conductown data

    ARPES measurements had energy resolution better than 15 meV and angular resolution better than 1% of the Brillouin zone.

    “ARPES measurements were made at the Advanced Light Source beamlines 10 and 12 using 35.5-48 eV photons with better than 15 meV energy resolution and overall angular resolution better than 1% of the Brillouin zone.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The apparent ordering transition is driven by magnetic interactions mediated by the topological surface state, indicating how strong topological insulator order changes the physical environment of the material surface.

    “This apparent ordering transition driven by magnetic interactions that are mediated by the topological surface state is an indication of how strong topological insulator order changes the physical environment of the material surface.”
    Quote in the paperSubstantial claim

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

    Study design and conductown data

    The iron deposition flow rate was calibrated using a quartz microbalance with sub-ångstrom sensitivity.

    “A quartz microbalance supplied by Leybold-Inficon with sub-ångstrom sensitivity was used to calibrate the iron-deposition flow rate.”
    Quote in the paperNot a substantial claim
32 of 32

  • The paper relies on this without support.

    No systematic surface deposition of magnetic impurities to elicit a large systematic magnetic response and controlled changes in the surface band structure had been explored.

    “So far, no systematic surface deposition of magnetic impurities to elicit a large systematic magnetic response and bring about controlled changes in the surface band structure has been explored.”

  • The paper relies on this without support.

    Bi2Se3 cleaves on the (111) selenium surface plane, providing a homogeneous environment for deposited atoms.

    “Bismuth selenide cleaves on the (111) selenium surface plane, providing a homogeneous environment for deposited atoms.”

  • The paper relies on this without support.

    Global ferromagnetism breaks time-reversal symmetry, making it possible to induce a gap at the Dirac point, which is otherwise disallowed by crystal symmetry.

    “Global ferromagnetism breaks time-reversal symmetry, making it possible to induce a gap at the Dirac point, which is otherwise disallowed by the crystal symmetry.”
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?

  • They report key band parameters that constrain the form of the superconducting state.

    “Moreover, they report key band parameters that constrain the form of the superconducting state.”

    From Three-Dimensional Topological Insulators (2011) · cites this paper as [40]

  • Measurements of electronic band structure in Cu_xBi2Se3 (x=0 to 12%) by Wray et al. suggest that superconductivity occurs with electrons in a bulk relativistic kinematic regime and an unconventional doping mechanism causes the nontrivial topological surface character of the undoped compound to be preserved at the Fermi level of the superconducting compound, where Cooper pairing occurs.

    “Measurements of electronic band structure in Cu x Bi 2 Se 3 (x=0 to 12%) by Wray et.al., (40) suggest that superconductivity occurs with electrons in a bulk relativistic kinematic regime and we identify that an unconventional doping mechanism causes the nontrivial topological surface character of the undoped compound to be preserved at the Fermi level of the superconducting compound, where Cooper”

    From Three-Dimensional Topological Insulators (2011) · cites this paper as [40]

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.

  • Caption counts five Dirac cones where the text counts three

    Minor

    The Figure 2 caption says iron doping creates five Dirac cones, but the text identifies three Dirac points-D0, D1 and D2-and says that five bands, not five cones, intersect the Fermi level.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 24

  1. Moore, J. E. Topological insulators: The next generation. Nature Phys. 5, 378–380 (2009). · DOI · Paper page
  2. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). · DOI · Paper page
  3. Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919–922 (2009). · DOI · Paper page
  4. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009). · DOI · Paper page
  5. Xia, Y. et al. Electrons on the surface of Bi2Se3 form a topologically-ordered two dimensional gas with a non-trivial Berry’s phase. Preprint at http://arxiv.org/abs/0812.2078 (2008). · arXiv
  6. Hor, Y. S. et al. Development of ferromagnetism in the magnetically doped topological insulator Bi2−xMnxTe3 . Phys. Rev. B 81, 195203 (2010). · DOI
  7. Hsieh, D. et al. Observation of time-reversal-protected single-Dirac-cone topological-insulator states in Bi2Te3 and Sb2Te3 . Phys. Rev. Lett. 103, 146401 (2009). · DOI
  8. Biswas, R. R. & Balatsky, A. V. Impurity-induced states on the surface of 3D topological insulators. Phys. Rev. B 81, 233405 (2010). · DOI · Paper page
  9. Garate, I. & Franz, M. Inverse spin-galvanic effect in a topological-insulator/ferromagnet interface. Phys. Rev. Lett. 104, 146802 (2010). · DOI · Paper page
  10. Law, K. T., Lee, P. A. & Ng, T. K. Majorana fermion induced resonant Andreev reflection. Phys. Rev. Lett. 103, 237001 (2009). · DOI
  11. Qi, X-L. et al. Inducing a magnetic monopole with topological surface states. Science 323, 1184–1187 (2009). · DOI · Paper page
  12. Tse, W-K. & MacDonald, A. H. Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators. Phys. Rev. Lett. 105, 057401 (2010). · DOI
  13. Zhang, H. et al. Model Hamiltonian for topological insulators. Phys. Rev. B 82, 045122 (2010). · DOI · Paper page
  14. Lee, D-H. Surface states of topological insulators: The Dirac fermion in curved two-dimensional spaces. Phys. Rev. Lett. 103, 196804 (2009). · DOI
  15. Hasan, M. Z. et al. Warping the cone on a topological insulator. Physics 2, 108 (2009). · DOI · Paper page
  16. Fu, L. & Berg, E. Odd-parity topological superconductors: Theory and application to CuxBi2Se3 . Phys. Rev. Lett. 105, 097001 (2010). · DOI
  17. Xia, Y. et al. Topological control: Systematic control of topological insulator Dirac fermion density on the surface of Bi2Te3. Preprint at http://arxiv.org/abs/0907.3089 (2009). · arXiv
  18. Ye, F. et al. Spin helix of magnetic impurities in two-dimensional helical metal. Europhys. Lett. 90, 47001 (2010). · DOI
  19. Kawaminami, M. & Okazaki, A. Neutron diffraction study of Fe7Se8. II. J. Phys. Soc. Jpn 29, 649–655 (1970). · DOI · Paper page
  20. Liu, Q. et al. Magnetic impurities on the surface of a topological insulator. Phys. Rev. Lett. 102, 156603 (2009). · DOI · Paper page
  21. Wahl, P. et al. Exchange interaction between single magnetic adatoms. Phys. Rev. Lett. 98, 056601 (2007). · DOI · Paper page
  22. Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966). · DOI · Paper page
  23. Zhang, R-J. & Willis, R. F. Thickness-dependent Curie temperatures of ultrathin magnetic films: Effect of the range of spin–spin interactions. Phys. Rev. Lett. 86, 2665–2668 (2001). · DOI · Paper page
  24. Blaha, P. et al. Computer Code WIEN2K (Vienna Univ. Technology, 2001).

Cited by

Sorted by citations

Authors
Wray, L. A., Xu, S.-Y., Xia, Y., Hsieh, D., Fedorov, A. V., Hor, Y. S., Cava, R. J., Bansil, A., Lin, H., & Hasan, M. Z.
Affiliations
  • Lawrence Berkeley National Laboratory (US)
  • Princeton University (US)
  • Northeastern University (US)
Corresponding author
Hasan, M. Zahid
ORCID
Venue
Nature Physics
Publisher
Springer Science and Business Media LLC
Published
2010-12-12
Volume
7
Issue
1
Pages
32-37
ISSN
  • 1745-2473 (ISSN-L)
  • 1745-2481
DOI
10.1038/nphys1838
OpenAlex
W1983721030
Semantic Scholar
f76d445f45350d00bad90cace328edeb0fe6eac8
Cited by
581
References
7
Citations by year
2026: 12 · 2025: 11 · 2024: 16 · 2023: 18 · 2022: 24 · 2021: 30 · 2020: 46 · 2019: 28 · 2018: 34 · 2017: 48 · 2016: 54 · 2015: 50 · 2014: 51 · 2013: 64 · 2012: 62
FWCI
27.15
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
  • 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
  • Division of Materials Research (DMR-0819860, 1006492)
  • Basic Energy Sciences (DE-FG-02-07ER46352, AC03-76SF00098, DE-FG-02-05ER46200, 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 › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Surface and Thin Film Phenomena
Keywords
topological insulators, Bi2Se3, surface states, iron doping, magnetic disturbances, Dirac fermions, time-reversal symmetry breaking, band hybridization, spin-momentum locking, electron dynamics, axions, monopoles

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 ›

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