Fractional correlated insulating states at one-third filled magic angle twisted bilayer graphene

The observation of superconductivity and correlated insulating states in twisted bilayer graphene has motivated much theoretical progress at integer fillings. However, 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 state we name a "fractional correlated insulator" at commensurate fractional filling of nu = n +/- 1/3. Specifically for the filling of 1/3 electrons per moire unit cell, we show that short-range interactions lead to an 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 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 ref. (1).