Symmetry-constrained coexistence of charge-three and charge-one Weyl points in nonmagnetic crystals

High-charge Weyl semimetals (WSMs), particularly those hosting charge-three Weyl point (C-3 WPs), have attracted considerable interest owing to their unconventional topological properties and enhanced boundary phenomena. However, ideal C-3 WSMs remain rare, and the symmetry-constrained coexistence of charge-three and charge-one Weyl point (C-1 WPs) in nonmagnetic crystals remains largely unexplored. Here, we investigate a representative eight-node Weyl configuration, consisting of two C-3 WPs and six C-1 WPs with opposite chirality, corresponding to two identical $\{3,-1,-1,-1\}$ irreducible Weyl molecules. By combining topological charge conservation with space-group symmetry analysis, we systematically classify all 230 space groups and identify 12 and 23 candidate groups without and with spin–orbit coupling (SOC), respectively. First-principles calculations without SOC reveal that the boron allotropes TBR-B${}_{48}$ and chiral OBD-B${}_{48}$ realize this configuration, hosting hourglass-type and non-hourglass-type C-3 WPs, respectively. Surface-state calculations reveal six Fermi-arc branches at the shared projection of the charge-three pair and three at each individual projection. Reversing the structural chirality of OBD-B${}_{48}$ reverses the signs of all Weyl charges, establishing a direct correspondence between crystal and momentum-space chirality. Furthermore, breaking the protecting $C_6$ symmetry in TBR-B${}_{48}$ splits each C-3 WP into three C-1 WPs and reconstructs the surface Fermi arcs. Our work establishes symmetry-based guidelines for designing and searching for nonmagnetic WSMs hosting charge-three and charge-one Weyl-point coexistence.