Abstract
Doping twisted bilayer graphene away from charge neutrality leads to an enormous buildup of charge inhomogeneities within each moir\'e unit cell. Here, we show, using unbiased real-space self-consistent Hartree calculations on a relaxed lattice, that Coulomb interactions smoothen this charge imbalance by changing the occupation of earlier identified ``ring'' orbitals in the AB/BA region and ``center'' orbitals at the AA region. For hole doping, this implies an increase of the energy of the states at the $\mathrm{\ensuremath{\Gamma}}$ point, leading to a further flattening of the flat bands and a pinning of the Van Hove singularity at the Fermi level. The charge smoothening will affect the subtle competition between different possible correlated phases.
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