Minimal Odd-Node Weyl-Dirac Complex and Strain-Induced Topological Phase Transition

The Nielsen-Ninomiya theorem enforces vanishing total topological charge, typically realized by pairwise nodes of the same type. Whether a minimal, odd-numbered heterogeneous configuration of chiral Weyl-Dirac fermions can exist in crystalline systems remains elusive. Here, by an exhaustive symmetry analysis of all 230 space groups (SGs), we reveal that only 3 (6) SGs without (with) spin-orbit coupling can host an isolated three-terminal Weyl-Dirac complex (TWDC). Guided by this symmetry requirement, we predict a previously unreported 3D boron allotrope (ATBCN-B28) hosting exactly three unpaired topological nodes near the Fermi level: one C = -2 Dirac point (DP) and two C = +1 Weyl points (WPs). This zero-net-chirality complex manifests unique bulk-boundary correspondences, featuring extended and ultra-long “S”-shaped double Fermi arcs. Furthermore, a symmetry-breaking shear strain drives a topological phase transition, splitting the DP to yield the absolute minimal configuration of exactly four conventional WPs allowable in non-magnetic systems. Our work circumvents the conventional even-node pairing paradigm, establishing a theoretical and material foundation for exploring minimal mixed-chirality topological fermions and their dynamic phase transitions.