  Although much progress has been made on the physics of magic angle twisted
bilayer graphene at integer fillings, little attention has been given to
fractional fillings. Here we show that the three-peak structure of Wannier
orbitals, dictated by the symmetry and topology of flat bands, facilitates the
emergence of a novel state at commensurate fractional filling of $\nu = n \pm
1/3$. We dub this state a "fractional correlated insulator". Specifically for
the filling of $\pm 1/3$ electrons per moir\'{e} unit cell, we show that
short-range interactions alone imply an approximate extensive entropy due to
the "breathing" degree of freedom of an irregular honeycomb lattice that
emerges through defect lines. The leading further-range interaction lifts this
degeneracy and selects a novel ferromagnetic nematic state that breaks AB/BA
sublattice symmetry. The proposed fractional correlated insulating state might
underlie the suppression of superconductivity at $\nu = 2-1/3$ filling observed
in arXiv:2004.04148. Further investigation of the proposed fractional
correlated insulating state would open doors to new regimes of correlation
effects in MATBG.

Mesoscale and Nanoscale Physics