Single-pair charge-2 Weyl-Dirac composite semimetals

Abstract: The Nielsen--Ninomiya theorem requires that the total topological chiral charges in a crystal vanish, a constraint typically satisfied by identical nodes like Weyl--Weyl pairs. Whether a minimal heterogeneous configuration -- comprising a single Weyl point (WP) and a single Dirac point (DP) -- can exist in an electronic system has remained unresolved. Here, by systematically classifying all 1651 magnetic space groups (MSGs), we reveal that only 14 MSGs without spin-orbit coupling (SOC) and 10 MSGs with SOC are compatible with this exotic state. Furthermore, for nonmagnetic crystals, this configuration is uniquely realized in the spinless limit of chiral space groups 92 and 96. Guided by this principle, we predict an ideal realization in chiral three-dimensional boron allotropes (SDHBN-B$_{28}$ enantiomers). First-principles calculations unveil a $|C|=2$ WP at the $Γ$ point and a $|C|=2$ DP at the $A$ point, which constitute the only fermions near the Fermi level within a large $2$ eV energy window. Strikingly, the structural chirality rigidly dictates the sign of the topological charges, yielding two ultralong Fermi arcs spanning the surface Brillouin zone. Our work provides a complete crystallographic classification and a definitive material platform for exploring minimal heterogeneous chiral fermions.