Twist angle & moiré wavelength in layered materials
Small-angle approximation: θ ≈ a / λ
Carrier density relation: ns = 2 / (√3 · λ²) × 4 × 10¹⁴ cm⁻²
ns → θ (forward):
θ = a · √(√3 · ns,cm² / (8 × 10¹⁴))
θ → ns (reverse):
ns = (8 × 10¹⁴ · θ²) / (√3 · a² · 10¹²) [×10¹² cm⁻²]
agraphene = 0.246 nm | θ in radians