Dominant 1/3-filling correlated insulator states and orbital geometric frustration in twisted bilayer graphene

Geometric frustration occurs in a lattice system when not all the interactions can be satisfied simultaneously. The simplest example is antiferromagnetically coupled spins on a triangular lattice. Frustrated systems are characterized by having many nearly degenerate ground states, leading to non-trivial phases, such as spin ice and spin liquids. To date, most studies have looked at geometric frustration of spins whereas orbital geometric frustration has been much less explored. For electrons in twisted bilayer graphene, when the electronic bands are filled to a fraction with denominator 3, Coulomb interactions and the Wannier orbital shapes are predicted to strongly constrain spatial charge ordering, leading to geometrically frustrated ground states that produce a new class of correlated insulating states. Here we report the observation of dominant, denominator 3, fractional-filling, insulating states in large-angle twisted bilayer graphene. These states persist in magnetic fields and display magnetic ordering signatures and tripled unit cell reconstruction. These results are in agreement with a strong-coupling theory for symmetry-breaking in geometrically frustrated fractional states.