Weyl Semimetal — Weyl Points & Fermi Arcs

Topological band crossings in momentum space, chirality, and protected surface states

Bulk Band Structure E(k) along k_z

Fermi Arcs on Surface BZ (k_x, k_z)

Chern Number / Berry Flux Visualization

Theory & Topology

Weyl Hamiltonian:
H(k) = v_x k_x σ_x + v_y k_y σ_y + v_z k_z σ_z
Topological charge: C = (1/2π)∮ Ω(k)·dS
Ω_n = i⟨∂u|×|∂u⟩ (Berry curvature)
No-go theorem: ΣC_i = 0 (Weyl pts in pairs)
Fermi arc: surface state connecting
projections of Weyl pts of opposite chirality
Bulk-boundary correspondence (topological)
Weyl point pairs1
Chern number C±1
Separation in BZ
Arc length