Magic-Angle Twisted Bilayer Graphene
Band Flattening · Flat Band at θ≈1.1° · Mott Insulator at Half Filling
Parameters
Twist angle θ (degrees):
1.10
°
Interlayer coupling w (meV):
110
Filling ν (electrons/moiré unit cell):
2
Near magic angle!
θ
magic
≈ 1.05° (Bistritzer-MacDonald)
w/v
F
|K
θ
| ≈ α ≈ 0.35 (magic)
Flat band → ρ(E
F
) → ∞
U/W → ∞: Mott insulator at ν=2
At magic angle θ≈1.1°, the moiré wavelength λ=a/2sin(θ/2)≈13nm creates a flat band where kinetic energy W is suppressed and Coulomb interactions U dominate, driving correlated states.