The Nielsen-Ninomiya theorem requires total topological charge in a crystal to vanish. This is usually satisfied by identical pairs: two Weyl points of opposite chirality, or two Dirac points related by symmetry. The bookkeeping balances because the partners are the same type with opposite signs.
Zheng and colleagues ask: can the balance be achieved by fundamentally different quasiparticle types? They systematically classify all 1,651 magnetic space groups and find 14 that can host a single charge-2 Weyl point paired with a single charge-2 Dirac point—no other nodes near the Fermi level.
A Weyl point is a two-band crossing with definite chirality. A Dirac point is a four-band crossing protected by additional symmetry. They are different mathematical objects, different quasiparticles, different physical phenomena. Yet one can be the topological “anti-particle” of the other.
The team predicts an ideal realization in chiral boron allotropes (SDHBN-B₂₈), where the charge-2 Weyl point sits at Γ and the charge-2 Dirac point at A, with no other crossings within a 2 eV window. The crystal's structural chirality—its handedness—determines which enantiomer carries which sign of topological charge, producing extended Fermi arcs spanning the entire surface Brillouin zone.
Conservation laws constrain totals but not compositions. The topology doesn't care what kind of entity carries the charge, only that the books balance. Different entities satisfying the same constraint is the heterogeneous route to charge cancellation—the universe's accounting department is type-agnostic.