Nematic stripe density wave order and Mott insulating ground states in small-angle twisted bilayer graphene

In this work, we determine states of electronic order of small-angle twisted bilayer graphene. Ground states are determined for weak- and strong-couplings being representatives for varying distance of the twist-angle from its magic value. In the weak-coupling regime, charge density waves emerge which break translational and $C_{3}$-rotational symmetry. In the strong coupling-regime, we find rotational and translational symmetry breaking Mott insulating states for all commensurate moire band fillings. Depending on the local occupation of superlattice sites hosting up to four electrons, global spin-(ferromagnetic) and valley symmetries are also broken giving rise to characteristic Landau level degeneracies in detailed agreement with observations for commensurate band fillings of $\nu=0,\pm1/2,\pm3/4,$. The formation of those particular electron orders is traced back to the important role of characteristic non-local interactions which connect states sharing one hexagon of AB- and BA-stacked regions of the superlattice.