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.