Charge-transfer insulation in twisted bilayer graphene.

We studied the real space structure of states in twisted bilayer graphene at the "magic angle" θ = 1.08^○. The flat bands close to charge neutrality are composed of a mix of "ring" and "center" orbitals around the AA stacking region. An effective model with localized orbitals is constructed, which necessarily includes more than just the four flat bands. Long-range Coulomb interaction causes a charge-transfer at half-filling of the flat bands from the "center" to the "ring" orbitals. Consequently, the Mott phase is a featureless spin-singlet paramagnet. We estimate the effective Heisenberg coupling that favors the singlet coupling to be J = 3.3 K, consistent with experimental values. The superconducting state depends on the nature of the dopants: hole-doping yields p+ip-wave whereas electron-doping yields d+id-wave pairing symmetry.