Atomistic Hartree theory of twisted double bilayer graphene near the magic angle

The discovery of superconductivity and correlated states in magic angle twisted bilayer graphene (tBLG) has prompted the study of other twisted graphene heterostructures for novel electronic properties. In this work [1] we used atomistic Hartree theory to calculate the electronic response of twisted double bilayer graphene (tDBLG) to gate doping and the application of perpendicular external electric fields when long-range electron-electron interactions are included. In stark constrast to tBLG, we find that tDBLG does not exhibit any significant deformations of its bandstructure when doped. However, we find that an electric field changes the band gap and breaks the valley degeneracy of the bands. Finally, whilst Hartree theory predicts the difference in on-site energies between the inner and outer graphene layers in tDBLG (also called the crystal field) at a qualitative level, we show that the subtle interplay between electron-ion and electron-electron interactions necessitates first-principles calculations for quantitative predictions.