  A detailed understanding of interacting electrons in twisted bilayer graphene
(tBLG) near the magic angle is required to gain insights into the physical
origin of the observed broken symmetry phases. Here, we present extensive
atomistic Hartree theory calculations of the electronic properties of tBLG in
the (semi-)metallic phase as function of doping and twist angle. Specifically,
we calculate quasiparticle properties, such as the band structure, density of
states (DOS) and local density of states (LDOS), which are directly accessible
in photoemission and tunnelling spectroscopy experiments. We find that
quasiparticle properties change significantly upon doping - an effect which is
not captured by tight-binding theory. In particular, we observe that the
partially occupied bands flatten significantly which enhances the density of
states at the Fermi level. We predict a clear signature of this band flattening
in the LDOS in the AB/BA regions of tBLG which can be tested in scanning
tunneling experiments. We also study the dependence of quasiparticle properties
on the dielectric environment of tBLG and discover that these properties are
surprisingly robust as a consequence of the strong internal screening. Finally,
we present a simple analytical expression for the Hartree potential which
enables the determination of quasiparticle properties without the need for
self-consistent calculations.
