Twisted bilayer graphene — magic angle ~1.1° flattens the band
At the magic angle θ_magic ≈ 1.1°, the moiré superlattice period λ = a/(2sin(θ/2)) ≈ 13 nm. Interlayer tunneling t_⊥ competes with kinetic energy ∝ ℏv_F|K|θ, creating nearly flat bands with bandwidth W → 0. Flat bands enormously enhance interactions (U/W → ∞), enabling correlated insulator, superconductor, and orbital magnet phases discovered by Cao et al. (Nature 2018).