  We investigate the correlated electrons in the magic-angle twisted bilayer
graphene by using the slave-rotor mean-field theory. Owing to the extended
figure of Wannier orbitals, we study the two-orbital cluster Hubbard model with
spin-valley fourfold degeneracy, focusing around half filling of valence bands
below the neutrality point. The theory predicts multiple Mott insulator phases
at fractional fillings not only for integer charges per moir{\'e} site, and it
demonstrates that long-range electron hopping is highly suppressed because
multiple-charge excitations are induced. Furthermore, the Kekul{\'e} valence
bond order is investigated and is found to extend the Mott insulator phases to
occupy a finite doping region. Adjacent to Mott insulator phases,
superconducting domes emerges by virtue of spin-valley fluctuations. This work
has provided a primal understanding and interesting phenomena of the correlated
system, and for its novel interaction the model might produce plenty of
possibilities waiting to be explored.
