Carbon Nanotube Band Structure

Tight-Binding · Armchair / Zigzag / Chiral · Metallic vs Semiconducting

Chiral Vector (n, m)

METALLIC
E(k,μ) = ±γ₀|Σ exp(ik·δⱼ)|
(n−m) mod 3 = 0 → metallic
else → semiconductor with Eg = 4γ₀aCC/3d
Zone-folding of graphene: quantized k⊥ = 2πμ/L. Armchair (n,n) always metallic; zigzag/chiral metallic when (n-m) mod 3 = 0. The selection rule arises from graphene's Dirac cones at K,K' points.