Research ArticlePHYSICS

Quasiparticle interference evidence of the topological Fermi arc states in chiral fermionic semimetal CoSi

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Science Advances  20 Dec 2019:
Vol. 5, no. 12, eaaw9485
DOI: 10.1126/sciadv.aaw9485
  • Fig. 1 Crystal structure and electronic structure of CoSi single crystals.

    (A) Lattice structure of CoSi (a = b = c = 4.45 Å). The blue and yellow balls represent Co and Si atoms, respectively. (B) Reciprocal BZ of CoSi. Г, X, M, and R points are high-symmetry positions of the bulk BZ. The purple, yellow, and green planes indicate the projected surface crossing at Г for the (001), (011), and (111) orientation, respectively. (C) DFT-calculated bulk band structure with SOC along high-symmetry directions. (D) Schematic illustration of the fourfold degenerated spin-3/2 RSW fermion node at the Γ point and the sixfold degenerated double spin-1 Weyl nodes at the R point. (E to G) Schematic illustrations of the surface BZs and Fermi arcs for the (001), (011), and (111) surfaces. The colored dashed lines in (F) and (G) represent the projected surfaces as shown in (D). The red and blue solid dots indicate the surface projections of Γ and R points, respectively. They are located at Γ¯ and Μ¯ position for the (001) surface and Γ¯ and X¯ positions for the (011) surface as displayed in (E) and (F). The black arcs schematically show the surface Fermi arcs connecting the projections of bulk chiral nodes. Γ and R are projected to the same Γ¯ point on the (111) surface.

  • Fig. 2 STM/STS characterization of CoSi surfaces.

    (A) Large-scale STM topographic image (55 nm by 55 nm, U = 2 V, It = 50 pA) of the CoSi (001) surface. Inset: Line-scan profile measured along the white arrowed line, the step height is measured to be ~4.5 Å. (B) High-resolution STM image (4 nm by 4 nm, U = 500 mV, It = 100 pA) taken on the (001) surface. Inset: STM image (U = 60 mV, It = 1 nA) showing the zigzag atomic structure. (C) High-resolution STM image (4 nm by 4 nm, U = −100 mV, It = 500 pA) of the (011) surface. (D) High-resolution STM topography (4 nm by 4 nm, U = −500 mV, It = 100 pA) taken on the (111) surface. The corresponding unit cells are also indicated by the square, the rectangle, and the parallelogram. The blue and yellow dots mark the Co and Si atoms, respectively. Scale bars, 8 Å (B to D). (E) Small-range dI/dV spectra taken on the three surfaces of CoSi. The green, blue, and red curves represent the dI/dV spectrum for (001), (011), and (111), respectively. a.u., arbitrary units. (F) DFT-calculated (001) projected surface DOS (up black) and experimentally measured dI/dV curve on the (001) surface (green), calculated bulk DOS without surface states (down black), and measured dI/dV curve on the (111) surface (red).

  • Fig. 3 QPI patterns on various surfaces of CoSi.

    (A and B) FFT images transformed from the dI/dV maps taken on the (001) surface over an area of 25 nm by 21 nm at 0 and +20 mV. U = +60 mV, I = 200 pA; modulation: 12 mV. The yellow arrows indicate the eye-shaped feature, and the green arrow indicates the crescent moon–like pattern around the Bragg peak. The red dashed square marks the surface first BZ. (C and D) QPI simulations including SOC that are generated from both the surface states and the bulk states at EF (Fermi energy) and EF + 20 mV for (001). There exist two kinds of prominent interference patterns as marked by yellow and green arrows. The black dashed squares mark the first surface BZ, the same as in (A) and (B). (E and F) Calculated QPI simulation by removing the surface states part from (C) and (D) for the (001) surface at EF and EF + 20 mV, respectively. (G and H) Calculated constant energy contours at EF and EF + 20 mV of the (001) surface with Fermi arcs traversing the whole BZ. The black arrows in (G) indicate the corresponding scattering processes of two kinds of prominent QPI patterns in (C). (I) FFT image transformed from the dI/dV map taken on the (011) surface (U = −80 mV, It = 100 pA; modulation: 13 mV) over an area of 40 nm by 40 nm. The red rectangle marks the first BZ of the (011) surface, and the yellow arc highlights the arc-shaped feature. (J) QPI simulation including SOC and surface states at −80 mV for the (011) surface. The black dashed rectangle marks the first surface BZ. The yellow arrow indicates the corresponding QPI feature as in (I). (K) Calculated constant energy contour for the (011) surface at −80 mV. (L) FFT image transformed from the dI/dV map taken on the (111) surface at 0 mV (U = −60 mV, It = 200 pA; modulation: 12 mV) over an area of 10 nm by 10 nm. (M) QPI simulation including SOC and surface states at EF for (111). (N) Calculated constant energy contour for the (111) surface at EF.

  • Fig. 4 Energy dispersion of surface states with chirality.

    (A) Experimental FFT image (U = −10 mV) transformed from the dI/dV map taken on the (001) surface. Scale bar, 1.4 nm−1. The black straight line cuts (1 to 4) indicate the four high-symmetry directions Γ¯-Χ¯, Γ¯-Χ¯, Γ¯-Μ¯, and Γ¯-Μ¯. (B) E-q dispersion extracted along the loop cut as marked by the black circle in (A). The magnitude of the scattering wave vector (q) along the loop is 3π/2a. The θLoop is rotated anticlockwise and relative to the cut 1. The yellow arrows mark the right chirality of the QPI features along cut 2, cut 3, and cut 4, and the white arrow marks the left chirality of the QPI features along cut 1. (C) Calculated E-q dispersion along the loop (q=3π/2a) based on a series of surface states–based QPI simulations. The yellow and white arrows mark the right and left chiral features, respectively. (D to G) E-q dispersions along Γ¯-Χ¯, Γ¯-Χ¯, Γ¯-Μ,¯ and Γ¯-Μ¯ as marked in (A) extracted from the energy-dependent QPI maps. The green guiding lines indicate two Dirac-like band crossings. These two Dirac nodes are located at ~+50 and −150 mV. The additional extensive dispersions of the surface Fermi arcs are marked by yellow lines.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/12/eaaw9485/DC1

    Determination of the various surface of single CoSi crystals

    LDOS peaks observed in the dI/dV curves on the (001) and (011) surfaces

    Measured QPI patterns on various terminations

    Fig. S1. Structural characterization for various terminations of a single CoSi crystal.

    Fig. S2. Spatially resolved dI/dV spectra taken on various terminations of a single CoSi crystal.

    Fig. S3. Energy-dependent QPI patterns for the CoSi (001) surface (data I).

    Fig. S4. Real-space dI/dV maps taken on the CoSi (011) surface.

    Fig. S5. Energy-dependent QPI patterns for the CoSi (011) surface.

    Fig. S6. Real-space dI/dV maps taken on the CoSi (111) surface.

    Fig. S7. Energy-dependent QPI patterns for the CoSi (111) surface.

    Fig. S8. Real-space dI/dV maps taken on the CoSi (001) surface (data II).

    Fig. S9. Energy-dependent QPI patterns for the CoSi (001) surface (data II).

    Fig. S10. Energy dispersions in different directions.

    Movie S1. Energy-dependent QPI patterns for the CoSi (011) surface.

    Movie S2. Energy-dependent QPI patterns for the CoSi (001) surface.

  • Supplementary Materials

    The PDFset includes:

    • Determination of the various surface of single CoSi crystals
    • LDOS peaks observed in the dI/dV curves on the (001) and (011) surfaces
    • Measured QPI patterns on various terminations
    • Fig. S1. Structural characterization for various terminations of a single CoSi crystal.
    • Fig. S2. Spatially resolved dI/dV spectra taken on various terminations of a single CoSi crystal.
    • Fig. S3. Energy-dependent QPI patterns for the CoSi (001) surface (data I).
    • Fig. S4. Real-space dI/dV maps taken on the CoSi (011) surface.
    • Fig. S5. Energy-dependent QPI patterns for the CoSi (011) surface.
    • Fig. S6. Real-space dI/dV maps taken on the CoSi (111) surface.
    • Fig. S7. Energy-dependent QPI patterns for the CoSi (111) surface.
    • Fig. S8. Real-space dI/dV maps taken on the CoSi (001) surface (data II).
    • Fig. S9. Energy-dependent QPI patterns for the CoSi (001) surface (data II).
    • Fig. S10. Energy dispersions in different directions.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). Energy-dependent QPI patterns for the CoSi (011) surface.
    • Movie S2 (.avi format). Energy-dependent QPI patterns for the CoSi (001) surface.

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