  We study theoretically many-body properties of magic-angle twisted bilayer
graphene for different doping levels. Our investigation is focused on the
emergence, stability, and manifestations of nematicity of the ordered
low-temperature electronic state. It is known that, at vanishing interactions,
the low-energy spectrum of the system studied consists of four almost-flat
almost-degenerate bands. Electron-electron repulsion lifts this degeneracy. To
account for such an interaction effect, a numerical mean-field theory is used.
Assuming that the ground state has spin-density-wave-like order, we introduce a
multicomponent order parameter describing spin magnetization. Our simulations
show that the order parameter structure depends on the doping level. In
particular, doping away from the charge neutrality point reduces the rotational
symmetry of the ordered state, indicating the appearance of an electron nematic
state. Manifestations of the nematicity can be observed in the spatial
distribution of the spin magnetization within a moir{\'e} cell, as well as in
the single-electron band structure. The nematicity is strongest at half-filling
(two extra electron or holes per supercell). We argue that nematic symmetry
breaking is a robust feature of the system ground state, stable against model
parameters variations. Specifically, it is shown that, away from the charge
neutrality point, it persists for all three parametrizations of the interlayer
hopping amplitudes discussed in the paper. Obtained theoretical results are
consistent with the available experimental data.
