Moiré Flat Bands — Twisted Bilayer Graphene
Magic angle, flat bands & correlated insulator
At the magic angle (~1.1°), twisted bilayer graphene develops nearly flat bands near the Fermi level. The bandwidth W ~ v_F·|Δk| · (1 − 3α²)/(1+6α²+...) collapses: α = w/(ħv_F|Δk|). When α ~ 1/√3 the bandwidth vanishes. With bandwidth W < U (Coulomb), the system enters Mott-insulating or unconventional superconducting phases at fractional fillings (±2 electrons per moiré cell). The moiré wavelength λ = a/2sin(θ/2).