Dominant 1/3-filling Correlated Insulator States and Orbital Geometric Frustration in Twisted Bilayer Graphene

Geometric frustration is a phenomenon in a lattice system where not all interactions can be satisfied, the simplest example being antiferromagnetically coupled spins on a triangular lattice. Frustrated systems are characterized by their many nearly degenerate ground states, leading to non-trivial phases such as spin ice and spin liquids. To date most studies are on geometric frustration of spins; much less explored is orbital geometric frustration. For electrons in twisted bilayer graphene at denominator 3 fractional filling, 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 insulators. 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 of symmetry-breaking of geometrically frustrated fractional states.