Role of lattice relaxations in magic angle graphene

Understanding the origin of correlated effects in twisted bilayer graphene (tBLG) first requires a complete single-particle picture of its low-energy electronic states. Previous models of tBLG have had either high accuracy (e.g. DFT, tight-binding supercells), or high twist angle resolution (e.g. continnum or k-dot-p models), but not both. We introduce an ab initio k-dot-p model that includes lattice relaxations which can exactly reproduce DFT tight-binding electronic band-structures, but with the ability to continously tune the twist angle. Inclusion of relaxation significantly changes the bandstructure near tBLG's first magic angle, and suppresses the appearance of the second magic angle. We find that a geometric interpretation of tBLG's relaxed atomic structure extends to it's low-energy electronic states, creating a comprehensive picture of both mechanical and electronic effects at small twist angle.