Fig. 1: Weyl points (WPs) with different topological charges.

a Schematic energy dispersions of the charge-1 WP (yellow dot), the charge-2 WP (green dot), and the maximally charged WP (red dot), respectively. b Spin structures of the charge-1 WP, the charge-2 WP, and the maximally charged WP, respectively. Insets are the top views of the spin structures (see Supplementary Note 1 for more details). c Surface dispersions near the projections of the charge-1 WP, the charge-2 WP, and the maximally charged WP, respectively. The solid blue cones, the helicoid sheets, and the green lines represent the projected bulk dispersions, the surface dispersions, and the Fermi arcs, respectively. The surface dispersions are topologically equivalent to the Riemann surface of \({{{{{\rm{Im}}}}}}\left[{{\log }}\root {|C|} \of {{k}^{{|C|}}}\right]\), with k = k_x + ik_y and |C| being the magnitude of topological charge (see Supplementary Note 2 for more details). d Typical Fermi arcs (green curves) wrapping around the surface Brillouin zone torus. For the charge-1 WP (yellow dot), the single Fermi arc forms an open curve; For the charge-2 WP (green dot), the double Fermi arcs can form a single noncontractible loop, characterised by W = {1,0} or {0,1}; For the maximally charged WP (red dot), the quadruple Fermi arcs can form double noncontractible loops, characterised by W = {1,1}. These three cases are topologically distinct from each other. In this work, we mainly focus on the maximally charged WP (highlighted as a shaded area).