Three node Weyl complex in nonmagnetic crystals

Abstract The Nielsen–Ninomiya theorem requires the total chiral charge of Weyl points in a crystal to vanish, which usually yields an even number of nodes when all carry unit charge. Here, based on an exhaustive symmetry analysis of all 230 crystallographic space groups, that nonmagnetic chiral crystals with threefold, fourfold, or sixfold rotational symmetries can host a charge-neutral three-node Weyl complex in the spinless limit. This state contains one charge-two Weyl point at a high-symmetry point and two oppositely charged unit Weyl points on high-symmetry lines. Guided by symmetry constraints, first-principles calculations identify three chiral boron allotropes with weak spin-orbit coupling whose spinless band structures realize this complex near the Fermi level. Crystal symmetry fixes whether the nodes form a collinear or triangular arrangement, leading to characteristic surface Fermi-arc connectivity that may provide spectroscopic signatures. We identify 39 chiral space groups that support this minimal mixed-charge Weyl state.