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.

当并非所有相互作用都能同时满足时，在晶格系统中就会出现几何挫败。最简单的例子是三角晶格上的反铁磁耦合自旋。受挫系统的特点是具有许多近乎简并的基态，从而导致非平凡的相，例如自旋冰和自旋液体。迄今为止，大多数研究都着眼于自旋的几何挫败，而轨道几何挫败的探索却少得多。对于扭曲双层石墨烯中的电子，当电子能带填充到分母为 3 的分数时，库仑相互作用和万尼尔轨道形状预计将强烈限制空间电荷排序，导致几何受挫基态，从而产生一类新的相关绝缘体状态。在这里，我们报告了在大角度扭曲双层石墨烯中观察到的主导、分母 3、分数填充、绝缘状态。这些状态在磁场中持续存在并显示磁排序特征和三重晶胞重建。这些结果与几何挫败分数态对称破缺的强耦合理论一致。