Observation of topological order in a superconducting doped topological insulator

Journal name:
Nature Physics
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Experimental observation of topological order in three-dimensional bulk solids has recently led to a flurry of research activity1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21. Unlike the two-dimensional electron gas or quantum Hall systems, three-dimensional topological insulators can harbour superconductivity and magnetism, making it possible to study the interplay between topologically ordered phases and broken-symmetry states. One outcome of this interplay is the possible realization of Majorana fermions—quasiparticles that are their own antiparticles—on topological surfaces, which is of great interest in fundamental physics9, 10, 11, 12, 13, 22, 23, 24. Here we present measurements of the bulk and surface electron dynamics in Bi2Se3 doped with copper with a transition temperature Tc up to 3.8K, observing its topological character for the first time. Our data show that superconductivity occurs in a bulk relativistic quasiparticle regime where 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. These results suggest that the electron dynamics in superconducting Bi2Se3 are suitable for trapping non-Abelian Majorana fermions. Details of our observations constitute important clues for developing a general theory of topological superconductivity in doped topological insulators.

At a glance


  1. Superconductivity in CuxBi2Se3 crystals.
    Figure 1: Superconductivity in CuxBi2Se3 crystals.

    a, A low-energy electron diffraction image taken at 200eV electron energy provides evidence for a well-ordered surface with no sign of superstructure modulation. b, Resistivity and magnetic susceptibility measurements for samples used in this study. Samples exhibit a superconducting transition at 3.8K at optimal copper doping (x=0.12). c, The number of charge carriers is calculated from the Luttinger count (Fermi surface area/Brillouin zone (BZ) area, ×2 for the doubly degenerate bulk band). Local density approximation (LDA) predictions show the carrier density obtained by aligning the local-density-approximation band structure with the experimentally determined binding energy of the Dirac point.

  2. Surface electron kinematics of CuxBi2Se3.
    Figure 2: Surface electron kinematics of CuxBi2Se3.

    a, The hexagonal surface Brillouin zone of CuxBi2Se3 shown above a diagram of the three-dimensional bulk Brillouin zone. b, Symmetrized surface-state Fermi surfaces, with (right) a generalized gradient approximation prediction based on the experimental Fermi level. c, Photoemission measurements at high photon energy (E>20eV) for non-superconducting CuxBi2Se3, demonstrating a reduced surface-state dispersion after copper is added. d, When the Bi–Se plane spacing at the surface of a 12-layer slab is increased by 0.2Å (1.64–1.84Å), dispersion in the upper Dirac cone increases by 16%. Binding energy scales have been rigidly shifted in c and d to align the Dirac points.

  3. Band topology at the superconducting composition.
    Figure 3: Band topology at the superconducting composition.

    a,b, Momentum dependence of the bulk and surface conduction bands in superconducting Cu0.12Bi2Se3 measured with low-energy (9.75eV) photons for enhanced bulk sensitivity. c, Dispersion along the z axis, examined by varying incident photon energy. d, Bulk and surface bands remain separate at intermediate kz values. e,f, Energy of the bulk electrons compared with Dirac (vC=6eVÅ) and classical (parabolic) fits with a mass of 0.155Me. Surface-state (SS) dispersion is also plotted. Inset: Self-energy with respect to the Dirac fit. g, The surface electronic structure presents a non-trivial topological setting for superconductivity because (green) surface and (blue) bulk bands do not overlap.

  4. Superconducting symmetry breaking on the topological surface.
    Figure 4: Superconducting symmetry breaking on the topological surface.

    a, Bulk and surface electrons are non-degenerate at the Fermi level. VB, valence band; CB, conduction band. b, A phase diagram compares (expt) the measured superconducting topology with preliminary expectations based on cases in which (A) each Cu atom donates one doped electron, (B) the experimental chemical potential is applied to generalized-gradient-approximation band structure and (C) the experimental chemical potential is applied to the band structure of undoped Bi2Se3. cf, Electronic states expected below TC for even-parity superconductivity (c,e) and an example of odd-parity ‘topological superconductivity’ (d,f). e and f show states within 5meV of the Fermi level. Both cases allow the superconducting state to host non-Abelian particles such as Majorana fermions.


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  1. Joseph Henry Laboratories, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

    • L. Andrew Wray,
    • Su-Yang Xu,
    • Yuqi Xia,
    • Dong Qian &
    • M. Zahid Hasan
  2. Princeton Center for Complex Materials, Princeton University, Princeton, New Jersey 08544, USA

    • L. Andrew Wray
  3. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94305, USA

    • L. Andrew Wray,
    • Alexei V. Fedorov &
    • M. Zahid Hasan
  4. Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

    • Yew San Hor &
    • Robert J. Cava
  5. Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

    • Hsin Lin &
    • Arun Bansil
  6. Princeton Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA

    • M. Zahid Hasan


L.A.W. and S-Y.X. contributed equally to the experiment with assistance from Y.X., D.Q. and M.Z.H.; A.V.F. provided beamline assistance; Y.S.H. and R.J.C. provided samples; H.L. and A.B. carried out the theoretical calculations; M.Z.H. was responsible for the overall direction, planning and integration among different research units.

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