Charge-transfer insulation in twisted bilayer graphene

Abstract

We studied the real space structure of states in twisted bilayer graphene at the `magic angle' $\hat{I}¸=1.08^{\circ }$. 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.

8 pages, 6 figures. This second version contains more detailed computations on the Coulomb energy from the unequal charge distribution