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Cited by 464Topological Materials and PhenomenaPhysics of Superconductivity and MagnetismAdvanced Condensed Matter Physics

Observation of topological order in a superconducting doped topological insulator

Open access
Wray, L. Andrew, Xu, Su-Yang, Xia, Yuqi, Hor, Yew San, Qian, Dong, Fedorov, Alexei V., Lin, Hsin, Bansil, Arun +2 more·2010·Nature Physics
DOI 10.1038/nphys1762
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Abstract

When doped with copper, the topological insulator Bi2Se3 becomes superconducting. But for new physics and applications the search is not for just any superconductor; the material must retain its topological character. And indeed that is the case with doped Bi2Se3.

Integrity signals

Registry

Crossref · 10.1038/nphys1762

Cites

33 of 33 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 24 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    An unusual doping mechanism in Cu-doped Bi2Se3 keeps the spin-polarized topological surface states well preserved at the Fermi level where Cooper pairing occurs.

    “an unusual doping mechanism causes the spin-polarized topological surface states to remain well preserved at the Fermi level of the superconductor where Cooper pairing takes place.”
    Quote in the paperSubstantial claim
  • Findingown data

    In superconducting Cu-doped Bi2Se3, superconductivity takes place in a bulk relativistic quasiparticle regime.

    “Our data show that superconductivity occurs in a bulk relativistic quasiparticle regime”
    Quote in the paperSubstantial claim
  • Findingown data

    At copper doping x = 0.05, the surface-state band slope above the Dirac point is reduced by 30%.

    “The slope of the surface-state band represents particle velocity, and is globally reduced in amplitude by 30% above the Dirac point when copper doping of x = 0.05 is added to the stoichiometric compound (see Fig. 2c).”
    Quote in the paperSubstantial claim
  • Findingown data

    Copper atoms in Bi2Se3 can donate holes or electrons depending on which lattice site they prefer.

    “Our results, summarized in Fig. 1, suggest that copper atoms can add holes or electrons depending on their net preference for occupying different kinds of site in the Bi 2 Se 3 lattice.”
    Quote in the paperSubstantial claim
  • Findingown data

    Copper-doped Bi2Se3 becomes superconducting with a transition temperature as high as 3.8 K.

    “Here we present measurements of the bulk and surface electron dynamics in Bi 2 Se 3 doped with copper with a transition temperature T c up to 3.8 K”
    • Also stated in: § Methods · plain
      “Samples exhibit a superconducting transition at 3.8 K at optimal copper doping (x = 0.12).”
    Quote in the paperSubstantial claim
  • May combine two claims. 19
  • The quote only partly states this claim. 1
  • Classified as probably not a substantial claim. 3

  • May combine two claims.

    Findingown data

    Adding copper gradually enlarges the Fermi surface through electron doping and strongly reduces surface electron velocities by reshaping the surface conduction band.

    “The qualitative result of copper addition is a gradual enlargement of the Fermi surface from electron doping and, further surprisingly, a strong reduction in surface electron velocities through reshaping of the surface conduction band.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The phase-ordering temperature is about 60,000 K, roughly four orders above the 3.8 K critical temperature.

    “The phase-ordering temperature scale, also estimated from our data, is approximately T θ = 60,000 K, four orders of magnitude larger than the superconducting critical temperature of 3.8 K”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The Fermi velocity is 3.5±2 eV Å along Γ-M and 4.1±2 eV Å along Γ-K, estimated within 50 meV of the Fermi level.

    “Carefully tracing the band (Fig. 3e,f) reveals a Fermi velocity of 3.5±2 eV Å along -M and 4.1±2 eV Å along -K, estimated within 50 meV of the Fermi level.”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data

    A dispersion anomaly near 90 meV binding energy affects low-energy electron kinetics, making the bands more linear locally at the Fermi level.

    “A dispersion anomaly that we have noted in the inset to Fig. 3f also affects low-energy electron kinetics, making the bands more linear locally at the Fermi level.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Calculations predict that band inversion in CuxBi2Se3 occurs at the Γ point in the centre of the bulk conduction band, producing a spin-orbit-induced Dirac-like bulk band, in qualitative agreement with experiments.

    “In Cu x Bi 2 Se 3 , calculations predict that band inversion occurs at the -point (k x = k y = k z = 0) in the centre of the bulk conduction band, leading to a spin-orbit-induced Dirac-like bulk band, in qualitative agreement with our experiments.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    For an ideal Dirac band, the rest mass is half the gap, 150 meV, yielding M* = 0.15 eV, μ = 0.15 eV + 0.25 eV, and M*/μ ∼ 1/3.

    “In an ideal Dirac band structure, the rest mass will be equal to half the band gap, or 150 meV (giving M * = 0.15 eV, µ = 0.15 eV + 0.25 eV, and M * /µ ∼ 1/3).”
    Quote in the paperSubstantial claim
    • Rests on an assumption: For the relativistic Hamiltonian, the chemical potential is the rest mass plus the valence-band minimum binding energy.

  • May combine two claims.

    Findingown data

    Bulk Fermi momenta are 0.110±3 Å-1 along Γ-M and 0.106±3 Å-1 along Γ-K.

    “Bulk Fermi momenta of 0.110±3 Å -1 and 0.106 ± 3 Å -1 are observed along the -M and -K directions respectively.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Attempting to create Cu_Bi replacement defects by adding less bismuth gives very weak hole doping in Cu0.1Bi1.9Se3, raising the bulk conduction band entirely above the Fermi level.

    “We also observed that attempting to force the creation of Cu Bi replacement defects by adding less bismuth results in very weak hole doping for Cu 0.1 Bi 1.9 Se 3 (Fig. 1c), raising the bulk conduction band entirely above the Fermi level.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Because of asymmetries between conduction- and valence-band dispersion, a larger effective rest mass is used to fit the conduction-band curvature, consistent with M*/μ = 3/4.

    “Owing to asymmetries between conduction-and valence-band dispersion in the real experimental system, a larger effective rest mass is used to fit the curvature of the bottom of the conduction band in Fig. 3f, consistent with a ratio of M * /µ = 3/4.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: For the relativistic Hamiltonian, the chemical potential is the rest mass plus the valence-band minimum binding energy.

  • May combine two claims.

    Findingown data

    Bulk pairing takes place while a non-degenerate, spin-polarized 2D topological surface state is present.

    “establishing that bulk superconducting pairing occurs in the presence of a non-degenerate, spin-polarized two-dimensional topological surface state”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Near the Fermi level, the spin-textured surface and doubly degenerate bulk bands are separated by 0.04 Å-1 in momentum and by about 130 meV in energy.

    “probing near the Fermi level, our data show that the spin-textured surface and doubly degenerate bulk bands are well separated by 0.04 Å -1 in momentum and by an energy spacing of about ∆ E = 130 meV”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Copper intercalated between selenium planes acts as a single electron donor, while copper substituting bismuth contributes two holes.

    “Copper atoms intercalated between van der Waals-like bonded selenium planes (Cu int ) in the crystal are known to be single electron donors, whereas substitutional defects in which copper replaces bismuth in the lattice (Cu Bi ) contribute two holes to the system, which is similar to the behaviour reported in the impurity-atom study on the Bi 2 Se 3 matrix 25 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [25] Vasko, A. Amphoteric nature of copper in Bi2Se3 crystals. Appl. Phys. 5, 217–221 (1974). source

      Not checked in the free run.

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

    Premisecitation

    Pairing that arises on a 2D topological surface state via proximity to a bulk superconductor is thought to be unconventional and may support non-Abelian particles like Majorana fermions in vortices.

    “Theoretically, superconducting pairing induced on a two-dimensional topological surface state through proximity to a bulk superconductor is believed to be inherently unconventional, with the potential to host non-Abelian (non-commutative) particles such as Majorana fermions in their vortices 12,13,20 .”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [12] Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008). source

      Not checked in the free run.

    • cites [13] Wilczek, F. Majorana returns. Nature Phys. 5, 614–618 (2009). source

      Not checked in the free run.

    • cites [20] Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3. Preprint at http://arxiv.org/abs/0912.3294 (2009).

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The surface of CuxBi2Se3 can support 2D vortices, a requirement for detecting non-Abelian statistics of vortex Majorana fermions on the topological surface.

    “Therefore, our experimental results, in contrast to first-principle calculations, suggest that the crystal surface of Cu x Bi 2 Se 3 can, in fact, host two-dimensional vortices, which is critical for observing the non-Abelian statistics of the vortex Majorana fermions on the topological surface.”
    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

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

    “ARPES measurements were carried out at the Advanced Light Source beamlines 10 and 12 using 35.5-48 eV photons and at the Stanford Synchrotron Radiation Lightsource (7-22 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

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

    Premisecitation

    In topological spin-orbit materials, a 3D massive Dirac-like dispersion is expected to arise from band inversion, and it has been seen in Bi1-xSbx alloys.

    “A three-dimensional massive Dirac-like dispersion in topological spin-orbit materials is expected as a direct result of the band-inversion mechanism that causes the topological insulator state, and has also been experimentally observed in other topological insulator Bi 1-x Sb x alloys 4 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • 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.

  • May combine two claims.

    Premisecitation

    Even parity results in a fully gapped band structure, while odd parity generates new surface states.

    “Of the two remaining possibilities, even parity will result in a fully gapped band structure, and odd parity will generate new surface states resembling those shown in Fig. 4d (ref.20).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [20] Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3. Preprint at http://arxiv.org/abs/0912.3294 (2009).

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    CuxBi2Se3 has a band structure and strong spin-orbit coupling that suggest its topological invariant n may be non-zero, so topological superconductivity is possible.

    “The specific band structure and strong spin-orbit coupling of Cu x Bi 2 Se 3 suggest that the topological invariant 'n' may be non-zero, allowing the possibility of topological superconductivity in Cu x Bi 2 Se 3 .”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Because superconductivity in CuxBi2Se3 occurs in linear bulk bands, the bulk state can mix spin and orbital character unusually, giving pairing an unusual form.

    “The fact that superconductivity occurs in the relativistically linear bulk bands in Cu x Bi 2 Se 3 as seen in our data allows unusual combinations of spin and orbital mixing in the bulk superconducting state, making pairing take an unusual form”
    Quote in the paperSubstantial claim
19 of 19

  • The authors state this as an assumption.

    The Dirac point of the surface state has a fixed energy relative to the bulk bands.

    “Assuming that the surface-state Dirac point energy is fixed relative to bulk bands”

  • The authors state this as an assumption.

    The velocity v_C of the three-dimensional Dirac band is isotropic.

    “For this discussion, we assume that v C is isotropic to illustrate the essential points”

  • The authors state this as an assumption.

    Scattering is minimal, and the superconducting gap follows the BCS relation to Tc.

    “assuming minimal scattering and a superconducting gap related to T C by the Bardeen-Cooper-Schrieffer formula.”

  • The paper relies on this without support.

    For the relativistic Hamiltonian, the chemical potential is the rest mass plus the valence-band minimum binding energy.

    “The chemical potential of this Hamiltonian is equal to the sum of the rest mass and the binding energy of the valence-band minimum”

  • The paper relies on this without support.

    Bi2Se3 is a centrosymmetric crystal.

    “Bi 2 Se 3 is a centrosymmetric crystal.”

  • The paper relies on this without support.

    A topological superconductor naturally supports a Majorana surface state.

    “Topological superconductors spontaneously realize a Majorana surface state.”
6 of 6

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?

  • Magnetic and superconducting orders on Pb1-xSnxTe surface states may differ from those seen in Z2 topological insulators due to the distinct topology of its surface electronic structure.

    “Such magnetic and superconducting orders on the surface states in Pb 1 À x Sn x Te can be different from those recently observed in the Z 2 TIs 37,38 because of its very distinct topology of surface electronic structure.”

    From Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe (2012) · cites this paper as [37]

  • 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).”

    From A topological insulator surface under strong Coulomb, magnetic and disorder perturbations (2011) · cites this paper as [22]

  • 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).”

    From A topological insulator surface under strong Coulomb, magnetic and disorder perturbations (2011) · cites this paper as [22]

Cites

Flagged first, then by citations

Research works printed but not linked: 5

  1. Hasan, M. Z. & Kane, C. L. Topological insulators. Preprint at http://arxiv.org/abs/1002.3895 (2010). · arXiv
  2. Kitaev, A. Proc. of the L.D. Landau Memorial Conf. ‘Advances in Theoretical Physics’, June 22–26 (2008).
  3. Fu, L. & Berg, E. Odd-parity topological superconductors: theory and application to CuxBi2Se3. Preprint at http://arxiv.org/abs/0912.3294 (2009). · arXiv
  4. Carlson, E. W. et al. in The Physics of Conventional and Unconventional Superconductors (eds Bennemann, K. H. & Ketterson, J. B.) (Springer-Verlag,2002).
  5. Blaha, P. et al. Computer Code WIEN2K (Vienna Universityof Technology, 2001).

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Authors
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.
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
2010-09-19
Volume
6
Issue
11
Pages
855-859
ISSN
  • 1745-2473 (ISSN-L)
  • 1745-2481
DOI
10.1038/nphys1762
OpenAlex
W1767686761
Semantic Scholar
28e8bd9546e82f3fc6ddec020df5f72266a60f44
Cited by
464
References
33
Citations by year
2026: 3 · 2025: 11 · 2024: 24 · 2023: 28 · 2022: 30 · 2021: 25 · 2020: 33 · 2019: 34 · 2018: 29 · 2017: 35 · 2016: 34 · 2015: 36 · 2014: 31 · 2013: 38 · 2012: 37
FWCI
19.04
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (0819860)
  • U.S. Department of Energy (DEFG0207ER46352, AC03-76SF00098, DE‐FG02‐, DEFG0205ER46200, FG02-07ER46352)
  • Alfred P. Sloan Foundation
  • Division of Materials Research (DMR-0819860)
  • 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 › Physics of Superconductivity and Magnetism
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
Keywords
topological superconductivity, doped topological insulators, Bi2Se3, copper doping, Majorana fermions, topological surface states, spin-polarized surface states, Cooper pairing, topological order, electron dynamics

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