Carbon Nanotube Chirality — Unrolled Graphene Lattice (2D)

🔬 Unrolled Graphene Sheet

A nanotube's identity comes from rolling a graphene honeycomb along the chiral vector Cℎ = n a₁ + m a₂. This is that sheet, flat and unrolled, with the vector drawn on it.

🔢 Chirality vector (n, m)

n = 8 m = 4

Show chiral vector Cℎ Show lattice vectors a₁, a₂

📐 Properties

Diameter

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Chiral angle

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Type

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Bandgap

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ℹ️ Physics

Diameter: d = a₀√(n²+nm+m²)/π, a₀ = 0.246 nm
Chiral angle: θ = atan(√3·m / (2n+m))

Armchair when n = m (θ=30°), zigzag when m = 0 (θ=0°), otherwise chiral.

Metallic if (n−m) mod 3 = 0; otherwise semiconductor with E_g ≈ 0.9 eV·nm / d.