Research ArticleCONDENSED MATTER PHYSICS

Weyl fermions, Fermi arcs, and minority-spin carriers in ferromagnetic CoS2

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Science Advances  18 Dec 2020:
Vol. 6, no. 51, eabd5000
DOI: 10.1126/sciadv.abd5000
  • Fig. 1 Electronic structure and characterization of CoS2 samples.

    (A) Band structure obtained from LSDA. (B) Comparison of DOS from both spin channels for LSDA and GGA. The red solid area shows the majority spin, and the blue solid area shows the minority spins. (C) Band structure obtained from GGA. (D) Illustration of the Weyl points in the bulk Brillouin zone, which are located on the high symmetry planes kx = 0 and ky = 0 parallel to the magnetization direction M. Red dots indicate Weyl points with positive Chern number C; blue dots indicate Weyl points with negative Chern number. (E) Core-level spectroscopy measured with photon energy hv = 602 eV; arrows indicate elemental core levels and valence band (VB). Inset shows energy-dispersive x-ray spectroscopy (EDX) curves, showing an ideal stoichiometry. (F) Temperature dependence of magnetization curve under zero field-cooling (ZFC) and field-cooled (FC) conditions; the applied field is 0.1 T. The Curie point at 130 K is indicated. The inset shows the magnetic field dependence below and above the Curie temperature. The measurements were taken along the [100] direction.

  • Fig. 2 Bulk band structure of the kz = π plane measured on the (111) surface.

    (A) Experimental Fermi surface was measured on the (111) cleavage plane with photon energy hv = 602 eV and linear-vertical polarization, integrated over 50 meV below the Fermi energy. The red arrow indicates an electron pocket located at the R point. The black arrow indicates the position of the line cut shown in (C). (B) Calculated Fermi surface spectral function A(k,EF) for the same plane as shown in (A) obtained with the LSDA. (C) Line cut along the R-X-R direction as shown in (A); red arrows indicate the electron pockets at the R point. (D) Energy distribution curves for the two R points shown in (E). The black arrow indicates the magnitude of the exchange splitting of ΔE = 0.60(3) eV. (E) Calculated band structure obtained with LSDA; red arrows indicate minority-spin electron pocket.

  • Fig. 3 Bulk band structure of the kz = 0 plane.

    (A) Experimental Fermi surface measured on the (111) cleavage plane with photon energy hv = 512 eV and linear-vertical polarization, integrated over 50 meV below the Fermi energy. The black arrow indicates the position of the line cut shown in (E). (B) Calculated Fermi surface spectral function for the same plane as shown in (A) obtained with LSDA. (C) Experimental Fermi surface spectral function A(k,EF) measured on the (100) cleavage plane with photon energy hv = 475 eV and linear-vertical polarization, integrated over 50 meV below the Fermi energy. The black arrow indicates the position of the line cut shown in (E). (D) Calculated Fermi surface for the same plane as shown in (C) obtained with LSDA. (E) Line cuts along the M-Γ direction from the (111) surface, as shown in (A), and the Γ-M direction from the (100) surface, as shown in (C). (F) Second-derivative spectrum of (E). (G) Result of the momentum distribution curve (MDC) fitting of the bands along the M-Γ-M direction, where blue circles originate from data of the (111) plane, and red circles originate from data of the (100) plane. (H) Calculated band dispersion along the M-Γ direction. (I) Band dispersion along the M*-Γ direction where M* (0,0.5,0.4581)2πa is a point slightly displaced from the M point (see Fig. 1D), such that the k-path is passing through the Weyl point in the vicinity of M.

  • Fig. 4 Surface state structure on the (100) surface.

    (A) Experimental Fermi surface measured on the (100) cleavage plane with photon energy hv = 100 eV and linear-horizontal polarization. The dashed black line indicates the boundary of the surface Brillouin zone, and the black dashed arrow indicates the momentum direction of the line cuts shown in (C) to (F). (B) Illustration of the Fermi arcs and Weyl point projections in the vicinity of the surface Brillouin zone boundary (black dashed line) at the X¯ point. Red and blue dots indicate Weyl point projections, and black arrows indicate Fermi arc positions. (C) Experimental band dispersion of the Fermi arc surface states along the line cut shown in (A). The photon energy used here was hv = 100 eV and the polarization was linear-horizontal. (D) Calculated surface state dispersion along the same momentum direction as the experimental line cuts. (E to G) Same as in (B) but for photon energies of 90, 110, and 120 eV.

Supplementary Materials

  • Supplementary Materials

    Weyl fermions, Fermi arcs, and minority-spin carriers in ferromagnetic CoS2

    Niels B. M. Schröter, Iñigo Robredo, Sebastian Klemenz, Robert J. Kirby, Jonas A. Krieger, Ding Pei, Tianlun Yu, Samuel Stolz, Thorsten Schmitt, Pavel Dudin, Timur K. Kim, Cephise Cacho, Andreas Schnyder, Aitor Bergara, Vladimir N. Strocov, Fernando de Juan, Maia G. Vergniory, Leslie M. Schoop

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    This PDF file includes:

    • Sample characterization
    • Photon energy dependent ARPES measurements
    • Complementary experimental data of the bulk dispersion around the R-point
    • Complementary experimental data of the Weyl-cone dispersion
    • Effect of the magnetization direction on the Fermi-arc surface states
    • Further theoretical investigation of the topological nodal-lines in CoS2
    • Orbital character of the bulk band structure
    • High-symmetry directions for the (111) cleavage planes
    • Calculated spin-polarization of the surface Fermi-arcs
    • Figs. S1 to S10
    • References

    Files in this Data Supplement:

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