Weyl semimetals host topologically protected band crossings (Weyl nodes) with chirality χ = ±1.
Nielsen-Ninomiya theorem: Weyl nodes come in pairs. Chiral anomaly: ∂_t n₅ = e²/(2π²ℏ²) E·B (quantum anomaly in a solid!).
Chiral magnetic effect (CME): J = e²μ₅B/(2π²ℏ²) — current without dissipation driven by B field alone.
Surface states form Fermi arcs connecting projected Weyl nodes (topological surface states, robust to perturbation).