  Magic-angle ($\theta=1.05^\circ$) twisted bilayer graphene (MATBG) has shown
two seemingly contradictory characters: the localization and quantum-dot-like
behavior in STM experiments, and delocalization in transport experiments. We
construct a model, which naturally captures the two aspects, from the
Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local
flat-band orbitals ($f$) centered at the AA-stacking regions are responsible to
the localization. A set of extended topological conduction bands ($c$), which
are at small energetic separation from the local orbitals, are responsible to
the delocalization and transport. The topological flat bands of the BM model
appear as a result of the hybridization of $f$- and $c$-electrons. This model
then provides a new perspective for the strong correlation physics, which is
now described as strongly correlated $f$-electrons coupled to nearly free
topological semimetallic $c$-electrons - we hence name our model as the
topological heavy fermion model. Using this model, we obtain the U(4) and
U(4)$\times$U(4) symmetries as well as the correlated insulator phases and
their energies. Simple rules for the ground states and their Chern numbers are
derived. Moreover, features such as the large dispersion of the charge $\pm1$
excitations and the minima of the charge gap at the $\Gamma_M$ point can now,
for the first time, be understood both qualitatively and quantitatively in a
simple physical picture. Our mapping opens the prospect of using heavy-fermion
physics machinery to the superconducting physics of MATBG.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics