Weyl semimetals host topological features — Weyl points where conduction and valence bands touch with definite chirality. In magnetic materials, you can have as few as two Weyl points. In nonmagnetic materials, time-reversal symmetry forces them to come in pairs of pairs: the theoretical minimum is four. But most real materials host many more, because additional band crossings clutter the Fermi surface with extraneous Weyl points that obscure the topological physics.
Xue, Pang, Bai et al. (2026) solve both problems simultaneously. They enumerate all 76 spinless and 83 spinful space groups that permit exactly four conventional Weyl points in nonmagnetic crystals, then predict two boron allotropes — P6-B₄₈ and TBIN-B₄₈ — that achieve this minimum with exceptionally clean electronic structures and experimentally accessible surface states.
The irony is that the “ideal” topological semimetal — the one with the most pristine topological features — requires the most electronically boring host. A material with a rich, complicated band structure will generically produce extra Weyl points that dilute the signal. Boron allotropes achieve the minimum not through exotic chemistry but through simplicity: their electronic structure is sparse enough that only the symmetry-mandated Weyl points appear. The topological physics is at its clearest when the material contributes nothing beyond what the symmetry requires.
The general principle: reaching a theoretical minimum is not an engineering challenge but a subtraction problem. The minimum is always present — imposed by symmetry, guaranteed by mathematics. What prevents a system from reaching it is surplus structure that the theory didn't ask for. The path to the ideal is not adding capability. It is removing clutter.