Fig. 1. Electronic structure and anomalous Hall effect (AHE) of magnetic Weyl semimetal Co₃Sn₂S₂.

a Optical Hall conductivity σ_xy(ω) calculated for a single anti-crossing point in the two-dimensional electronic structure with mass gap m = 0.03 eV and chemical potential μ = 0.05 eV. The red and blue curves are the real and imaginary parts of σ_xy(ω), respectively. The inset shows the schematics of the band structure assumed in this calculation. b The crystal structure of Co₃Sn₂S₂ and kagome network within Co₃Sn layer. c Band structure obtained from the first-principles calculation. The red and blue lines represent the spin-up and spin-down bands, respectively, without spin–orbit coupling. The dotted line represents the band structure with the spin–orbit coupling. d Schematic illustrations of the simplified band structures: nodal ring structure (left) open the gaps with the anti-crossing nodal line connected to the Weyl points (right) due to the spin–orbit coupling. e Magnetic-field dependence of the Hall conductivity for each temperature when the magnetic field is applied parallel to the c axis for the bulk single crystal. f Temperature dependence of Hall conductivity at 0 T (red open circles) and at 0.1 T (red filled circles), and resistivity at 0 T (blue line) for the bulk single crystal.