Research ArticleMATERIAL PROPERTIES

Superconducting topological surface states in the noncentrosymmetric bulk superconductor PbTaSe2

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Science Advances  23 Nov 2016:
Vol. 2, no. 11, e1600894
DOI: 10.1126/sciadv.1600894
  • Fig. 1 Crystal structure and calculated band structure.

    (A) Crystal structure of PbTaSe2 and the Brillouin zone of bulk (blue) and the Pb-terminated surface (red). (B) The HAADF image projected along the c axis, overlapped with a crystal structure signifying Ta (Pb/Se) atomic columns. (C) The HAADF image along the [110] projection, revealing the characteristic Pb monolayer and 1H-TaSe2 cages of PbTaSe2. Calculated band structure of PbTaSe2 (D) without SOC and (E) with SOC. The size of blue and red dots indicates the Pb p and Ta d orbital contributions, respectively. Large SOC splitting can be observed in Pb p and Ta d bands. The gray-shaded area indicates the continuous gap. (F) The decomposed surface band structure on the Pb-terminated surface of PbTaSe2 shows the projection of the Ta d and Pb p orbitals of the surface atoms. The gray circles indicate where the outer TSS merges into the bulk conduction bands.

  • Fig. 2 Topographic images and tunneling spectra.

    (A) Topography of PbTaSe2 showing atomically flat terraces and step edges (V = 100 mV and I = 2 pA). (B) The height profile deduced from the red line in (A). (C) The atomic-resolution topographic image on the Se-terminated surface (V = 10 mV and I = 300 pA). The inset shows the fast Fourier transform (FFT) of this topographic image. Yellow and red circles indicate the position of Bragg peaks and the peak of the 2 × 2 superstructure, respectively. (D) Topography on the Pb-terminated surface (V = 10 mV and I = 100 pA) shows strong LDOS modulation from QPI of TSSs. (E) The atomic-resolution topographic image on the Pb-terminated surface (V = −10 mV and I = 300 pA). (F) FFT of the topographic image in (D). Bragg peaks are marked by a yellow circle, and the dispersive signals from QPI are observed (green ellipse). The normalized tunneling spectrum and calculated partial density of states (PDOS) on (G) Se-terminated and (H) Pb-terminated surfaces, respectively (T = 0.26 K, V = 800 mV, I = 1 nA, and lock-in modulation = 0.5 mV). The superconducting gap near EF is not resolved clearly because of the large modulation in lock-in measurements. a.u., arbitrary units.

  • Fig. 3 Visualization of QPI on a Pb-terminated surface.

    (A to F) A sequence of normalized differential conductance dI/dV(r, E) maps taken at normal state (T = 6 K). The field of view (FOV) of each image is adjusted to access the region of interest in q space. A larger FOV is required at higher energy near the Dirac point to resolve the smaller q vector. Scale bar, 10 nm (in each image). (G to L) The corresponding FFT of normalized dI/dV(r, E) maps taken in (A) to (F). (M to R) The simulated QPI images at the corresponding energy considering two topological surface bands, with band structures shown in Fig. 1F (details in note S4).

  • Fig. 4 Energy dispersion of topological surface bands by QPI.

    The calculated constant energy contours (CECs) of two TSSs with spin texture at (A) E = 950 meV and (B) EF. The black arrows represent the in-plane spin direction, and the blue/red contours show the sign and the magnitude of out-of-plane spin. The color scale indicates the ratio of out-of-plane spin to total spin polarization. The blue and red arrows in each image indicate the relation between topological surface bands with scattering vectors q1 and q2, respectively. The seemingly Rashba surface states are due to the unusual dispersion of the Dirac cone in Fig. 1F, in which the outer and inner CECs (upper and lower parts of the Dirac cone) exist at the same energy. The outer TSS and the bulk state strongly overlap below E ~ 300 meV around Embedded Image [gray regions in (B)], leaving a small portion near EF. The energy dispersion of (C) q1 from E = 500 meV to E = 1000 meV and (D) q1, q2, and q3 from E = −200 meV to E = 300 meV. Hollow circles are extracted from the measured QPI images along the Embedded Image direction, which are in agreement with the QPI dispersion obtained from our calculated topological surface band structure (solid lines). We do not extract the exact |q| in the energy range between 300 and 500 meV, in which blurry q1 occurs because of flat band dispersion and larger <Sz> in the TSS. q3 is associated with the intraband scattering on hole-like bulk bands at Embedded Image.

  • Fig. 5 Superconducting state and vortex imaging.

    (A) The tunneling spectrum on the Pb-terminated surface at T = 0.26 K (V = 25 mV, I = 600 pA, and lock-in modulation = 50 μV). The black line is the result of a single BCS s-wave gap fitting (details in note S7). The inset shows the zoom-in of the spectrum between 0.2 and −0.2 meV. (B) Temperature evolution of a tunneling spectrum on the Pb-terminated surface. Each spectrum is shifted by 10 nS for clarity. (C) The temperature dependence of a superconducting gap. The black line represents the theoretical temperature dependence from the BCS theory. (D) Differential conductance map at EF shows the triangular vortex lattice, with an applied magnetic field of 0.05 T at T = 0.26 K (V = 10 mV, I = 60 pA, and lock-in modulation = 250 μV). (E) The tunneling spectrum at the vortex core shows the structure of a vortex bound state (V = 30 mV, I = 400 pA, modulation = 60 μV, applied magnetic field = 0.05 T, and T = 0.26 K). (F) The spatial dependence of a tunneling spectrum from the center of a vortex core toward the next nearest vortex core (V = 30 mV, I = 600 pA, lock-in modulation = 60 μV, applied magnetic field = 0.05 T, and T = 0.26 K).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/11/e1600894/DC1

    note S1. Crystal structures and electron diffraction patterns of PbTaSe2.

    note S2. Spin-decomposed surface band structures of PbTaSe2.

    note S3. The 2 × 2 superstructure on a Se-terminated surface.

    note S4. Verification of helical spin polarization in TSSs by QPI imaging.

    note S5. Superconducting gap on a Se-terminated surface.

    note S6. Single-s-wave gap and two-s-wave gap fitting.

    note S7. Comparison of normalized differential conductance at normal and superconducting states on a Pb-terminated surface.

    note S8. Upper critical field, lattice parameter of Abrikosov lattice, and normalized zero bias conductance of a vortex.

    note S9. Spatial distribution of the superconducting gap on a Pb-terminated surface.

    note S10. Topographic images and parameters of differential conductance maps on a Pb-terminated surface.

    note S11. Setpoint effect of normalized differential conductance maps on a Pb-terminated surface.

    note S12. Raw Fourier transform of normalized differential conductance maps on a Pb-terminated surface.

    note S13. Differential conductance map at Fermi energy.

    fig. S1. Electron diffraction patterns along [001] and [110] projection.

    fig. S2. Projection of the spin polarizations of bands contributed from the surface atoms.

    fig. S3. The simulated surface structure on the Se-terminated surface.

    fig. S4. Spin-dependent QPI.

    fig. S5. Temperature dependence of the superconducting gap.

    fig. S6. BCS fitting of superconducting tunneling spectrum.

    fig. S7. Normalized differential conductance taken on Pb-terminated surface.

    fig. S8. Magnetic field dependence of superconducting vortex lattice and vortex bound states.

    fig. S9. Homogenous superconducting gap on a Pb-terminated surface.

    fig. S10. Topographic images of differential conductance maps on the Pb-terminated surface.

    fig. S11. Bias independence of LDOS mapping and QPI imaging.

    fig. S12. Raw data FFT of normalized differential conductance maps.

    fig. S13. Visualization of QPI at Fermi energy.

    movie S1. Normal-state QPI maps taken on a Pb-terminated surface.

  • Supplementary Materials

    This PDF file includes:

    • note S1. Crystal structures and electron diffraction patterns of PbTaSe2.
    • note S2. Spin-decomposed surface band structures of PbTaSe2.
    • note S3. The 2 × 2 superstructure on a Se-terminated surface.
    • note S4. Verification of helical spin polarization in TSSs by QPI imaging.
    • note S5. Superconducting gap on a Se-terminated surface.
    • note S6. Single–s-wave gap and two–s-wave gap fitting.
    • note S7. Comparison of normalized differential conductance at normal and superconducting states on a Pb-terminated surface.
    • note S8. Upper critical field, lattice parameter of Abrikosov lattice, and normalized zero bias conductance of a vortex.
    • note S9. Spatial distribution of the superconducting gap on a Pb-terminated surface.
    • note S10. Topographic images and parameters of differential conductance maps on a Pb-terminated surface.
    • note S11. Setpoint effect of normalized differential conductance maps on a Pb-terminated surface.
    • note S12. Raw Fourier transform of normalized differential conductance maps on a Pb-terminated surface.
    • note S13. Differential conductance map at Fermi energy.
    • fig. S1. Electron diffraction patterns along 001 and 110 projection.
    • fig. S2. Projection of the spin polarizations of bands contributed from the surface atoms.
    • fig. S3. The simulated surface structure on the Se-terminated surface.
    • fig. S4. Spin-dependent QPI.
    • fig. S5. Temperature dependence of the superconducting gap.
    • fig. S6. BCS fitting of superconducting tunneling spectrum.
    • fig. S7. Normalized differential conductance taken on Pb-terminated surface.
    • fig. S8. Magnetic field dependence of superconducting vortex lattice and vortex bound states.
    • fig. S9. Homogenous superconducting gap on a Pb-terminated surface.
    • fig. S10. Topographic images of differential conductance maps on the Pb-terminated surface.
    • fig. S11. Bias independence of LDOS mapping and QPI imaging.
    • fig. S12. Raw data FFT of normalized differential conductance maps.
    • fig. S13. Visualization of QPI at Fermi energy.

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mpg format). Normal-state QPI maps taken on a Pb-terminated surface.

    Files in this Data Supplement:

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