Research ArticleMATERIALS SCIENCE

Visualizing weakly bound surface Fermi arcs and their correspondence to bulk Weyl fermions

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Science Advances  19 Aug 2016:
Vol. 2, no. 8, e1600709
DOI: 10.1126/sciadv.1600709
  • Fig. 1 Quasiparticle interference of trivial bands and Fermi arcs in TaAs.

    (A) Topography (VB = −400 meV; It = 350 pA) of the (001) surface of TaAs with a few As vacancies. Inset: Atomic resolution with a lattice constant a = 3.47 Å. (B) dI/dV map of (A) (VB = 0 meV) shows elongated QPI around vacancies on top of an atomically modulated local density of states (inset). (C) Fourier analysis of (B) reveals an intricate QPI pattern centered on both q = 0 and Bragg peaks. (D) SSP based on density functional theory (DFT) calculation shows marked resemblance to the central zone in (C): ellipse-shaped (blue) and bowtie-shaped (yellow) , spin-orbit-split double squares (green), intra–Fermi arc scattering around Go (that is, q = 0) and inter–Fermi arc along Go-GM. Some SSP features appear in (C) around both Go and the Bragg peaks G±X, G±Y. (E) DFT-calculated Fermi surface of As-terminated TaAs contains bowtie- and ellipse-shaped bands and topological Fermi arcs emanating from Weyl nodes W1 and W2 at energies −13 and 1.5 meV, respectively (red). Intra- and interband scattering processes are represented by colored arrows. Intra– (Q1, Q3, and Q4) and inter– (Q2) Fermi arc processes are labeled. (F) A magnified view of the Go vicinity (left) reveals a round arc beyond the ellipse pattern (left). It agrees well with the SSP of scattering around the Fermi arc (Q1) and that of the ellipse (right). (G) Measured dI/dV spectrum (solid) and calculated density of states of As- and Ta-terminated (001) surfaces (blue and red, respectively), indicating the As termination of the measured sample.

  • Fig. 2 Fermi arcs on Ta and trivial bands on As.

    (A) Step edge topography oriented 49° with respect to the crystal axis. (B) Corresponding 49° cut (dashed line) across the SSP. (C) dI/dV map along the dashed line in (A) shows modulations in the density of states. Inset: Its commensuration with the topographic profile. It exhibits high density of states on As atoms and lower density of states on Ta, as well as dispersive interference patterns. (D) Fourier analysis of (C) shows the energy dispersion of the ellipse (blue arrow), the squares (green arrows), and the Fermi arcs (Q2 in Fig. 1E). (E) SSP cut along the dashed line in (B) identifies Q2 with inter–Fermi arc scattering, extending above and below the Weyl nodes’ energies (EW2 ≈ 2 meV and EW1 ≈ −13 meV, respectively). (F and G) Density of states on As sites (blue) and on Ta sites (red) reveals two different dispersing modes. (H) Fourier analysis of (F) detects the energy dispersion of the ellipse QPI. Inset: Calculated electronic local density of states (LDOS) of the ellipse band shows high localization on As sites. (I) Fourier analysis of (G) unveils QPI pattern associated with the Fermi arcs, which extrapolates to W2. Inset: Fermi arc wave function is localized on Ta sites. (J) Left: SSP of Fermi arcs only; right: dispersion extracted from left panel. Note its resemblance to (H). One of the modes extrapolates to the projection of W2 due to shrinkage of the Fermi arc (D, inset).

  • Fig. 3 Correlation between modulations and replications set by the electronic wave function.

    (A to C) Left panels: dI/dV in a vacancy-free region at three representative energies shows strong modulation, whose strength and orientation change with energy. The bars represent the Bragg peak intensities, Embedded Image, along the two crystallographic directions. Insets: DFT calculation of the local charge density that captures a similar modulation. Right panels: Fourier analysis of extended dI/dV maps in the presence of vacancies at the corresponding energies. The intensity and anisotropy of the replications of QPI features are correlated with the modulation detected in the vacancy-free region.

  • Fig. 4 Replicated QPI patterns as a spectroscopic tool.

    (A) Energy dependence of the Bragg peaks’ intensities in the vacancy-free region. Inset: Fourier transform of the dI/dV map from which the intensities are extracted. (B) Energy dependence of the QPI intensities of the bowtie and ellipse patterns (orange and blue, respectively; see this method of extraction in the Supplementary Materials) around q = 0 and around the Bragg peaks (see inset for legend). The ellipse is correlated with the Bragg peaks along Γ-Y, whereas the bowtie is correlated with Bragg peaks along Γ-X. (C) Subtraction of QPI peaks at G±Y times α = 1.14 (the ratio between extracted intensities of ellipse QPI at G0, and GY at EF) from the central zone eliminates the ellipse from around q = 0, while leaving the QPI pattern of the Γ-X Fermi arc unaffected. Signatures of scatterings among the Γ-Y Fermi arc are revealed. (D) SSP of Fermi arcs alone. Inset: Contributing scattering processes (Q4a to Q4c) within the Fermi arc along Γ-Y.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/8/e1600709/DC1

    Extended q-space map

    dI/dV maps: Raw data and symmetrization

    Fermi arc scattering signature

    Agreement between vacancy- and step edge–induced QPI

    Fermi arc dispersion

    Correlation between scatterer-free dI/dV modulations and replications of QPI patterns

    Correspondence between QPI patterns and Bloch wave function

    Band structure calculations

    Extracting the intensity of QPI features

    Splitting the line-cut dI/dV into submaps

    fig. S1. Extended q-space map.

    fig. S2. dI/dV maps: Raw data and symmetrization.

    fig. S3. QPI pattern involving Fermi arc scattering from a different vacancy distribution.

    fig. S4. Agreement between vacancy- and step edge–induced QPI.

    fig. S5. Calculated Fermi arc dispersion.

    fig. S6. Structure of the Bloch wave function and its correspondence to QPI.

    fig. S7. Wave function distribution.

    fig. S8. Extraction of QPI feature intensities.

    Reference (36)

  • Supplementary Materials

    This PDF file includes:

    • Extended q-space map
    • dI/dV maps: Raw data and symmetrization
    • Fermi arc scattering signature
    • Agreement between vacancy- and step edge–induced QPI
    • Fermi arc dispersion
    • Correlation between scatterer-free dI/dV modulations and replications of QPI patterns
    • Correspondence between QPI patterns and Bloch wave function
    • Band structure calculations
    • Extracting the intensity of QPI features
    • Splitting the line-cut dI/dV into submaps
    • fig. S1. Extended q-space map.
    • fig. S2. dI/dV maps: Raw data and symmetrization.
    • fig. S3. QPI pattern involving Fermi arc scattering from a different vacancy distribution.
    • fig. S4. Agreement between vacancy- and step edge–induced QPI.
    • fig. S5. Calculated Fermi arc dispersion.
    • fig. S6. Structure of the Bloch wave function and its correspondence to QPI.
    • fig. S7. Wave function distribution.
    • fig. S8. Extraction of QPI feature intensities.
    • Reference (36)

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