Strong Coupling Phases of Partially Filled Twisted Bilayer Graphene Narrow Bands

To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is U(00)=9.3  eV in close vicinity to the critical value separating conducting graphene from an insulating phase emphasizing the importance of nonlocal Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to U(01)=5.5  eV. In the long-wavelength limit, we find the effective background dielectric constant of graphite to be ϵ=2.5 in very good agreement with experiment.

Significance For small twist angles, bilayer graphene forms long-wavelength Moiré patterns. For specific, so-called magic, angles of the order of 1 degree, very narrow bands have been seen that lead to superconductivity. The underlying mechanisms have since been discussed in a variety of theoretical approaches. We show that the modulation of the charge density significantly modifies the electronic structure. These changes can make an important contribution to superconductivity through electron-assisted hopping.