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Twisted double bilayer graphene (tDBLG) is a moir\'e material that hasrecently generated significant interest because of the observation ofcorrelated phases near the magic angle. We carry out atomistic Hartree theorycalculations to study the role of electron-electron interactions in the normalstate. In contrast to twisted bilayer graphene (tBLG), we find that suchinteractions do not result in significant doping-dependent deformations of theelectronic band structure. However, interactions play an important role for theelectronic structure in the presence of a perpendicular electric field as theyscreen the external field. Finally, we analyze the contribution of the Hartreepotential to the crystal field, i.e. the on-site energy difference between theinner and outer layers. We find that the on-site energy obtained from Hartreetheory has the same sign, but a smaller magnitude compared to previous studiesin which the on-site energy was determined by fitting tight-binding results toab initio density-functional theory (DFT) band structures. To understand thisquantitative difference, we analyze the ab initio Kohn-Sham potential obtainedfrom DFT and find that a subtle interplay of electron-electron and electron-ioninteractions determines the magnitude of the on-site potential.

Atomistic hartree theory and crystal field of twisted double bilayer graphene near the magic angle