Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom—charge, spin, and valley—gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted-hopping interaction that emerges due to the nontrivial topological properties of TBG. Such a nonlocal interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interactions. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

中文翻译：

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扭曲双层石墨烯在电荷中性时相关诱导的绝缘拓扑相

扭曲双层石墨烯（TBG）提供了一个独特的框架，以阐明二维系统中强相关性和拓扑现象之间的相互作用。多个电子自由度（电荷，自旋和谷值）的存在赋予了过多的可能的有序状态和不稳定性。识别其中的哪一个是在强相关机制中实现的，这是阐明TBG实验中观察到的超导和相关绝缘态性质的基础。在这里，我们使用无偏，无符号问题的量子蒙特卡洛模拟来解决电荷中性时TBG的有效相互作用晶格模型。除了通常的类Hubbard类排斥之外，该模型还包含由于TBG的非平凡拓扑特性而出现的辅助跳跃相互作用。这样的非局部相互作用从根本上改变了电荷中性时的相图，甚至对于无限小的相互作用，也使迪拉克锥裂开了。随着相互作用强度的增加，出现了一系列不同的相关绝缘相，包括具有拓扑边缘状态的量子谷霍尔状态，区间间隔相干绝缘体和价键固体。此处发现的与电荷中性相关的绝缘相提供了对于全面了解整数填充处的绝缘状态和TBG的近超导状态所需要的参考状态。出现了一系列不同的相关绝缘相，包括具有拓扑边缘态的量子谷霍尔态，区间间隔相干绝缘体和价键固体。此处发现的与电荷中性相关的绝缘相提供了对于全面了解整数填充处的绝缘状态和TBG的近超导状态所需要的参考状态。出现了一系列不同的相关绝缘相，包括具有拓扑边缘态的量子谷霍尔态，区间间隔相干绝缘体和价键固体。此处发现的与电荷中性相关的绝缘相提供了对于全面了解整数填充处的绝缘状态和TBG的近超导状态所需要的参考状态。