Charge-transfer insulation in twisted bilayer graphene

We studied the real space structure of states in twisted bilayer graphene at the magic angle' $\theta = 1.08^\circ$. 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.