Motivated by the recently observed insulating states in twisted bilayer graphene (TBG), we study the nature of the correlated insulating phases of the TBG at commensurate filling fractions. We use the continuum model and project the Coulomb interaction onto the flat bands to study the ground states by using a Hartree-Fock approximation. In the absence of the hexagonal boron nitride (hBN) substrate, the ground states are the intervalley coherence states at the charge neutrality (filling $\nu =0$, or 4 electron per moir'e cell), and at $\nu$=-1/4 and -1/2 (3 and 2 electrons per cell, respectively), and the $C_2𝒯$ symmetry broken state at $\nu$= -3/4 (1 electron per cell). The hBN substrate drives the ground states at all $\nu$ into $C_2𝒯$ symmetry broken states. Our results provide good reference points for further study of the rich correlated physics in the TBG.

中文翻译：

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Hartree-Fock研究表明，双绞线石墨烯在相应的填充率下具有相关的绝缘相

受最近在扭曲双层石墨烯（TBG）中观察到的绝缘状态的影响，我们研究了在适当填充分数下TBG相关绝缘相的性质。我们使用连续模型并将库仑相互作用投影到平坦带上，以通过使用Hartree-Fock近似来研究基态。在没有六方氮化硼（hBN）衬底的情况下，基态为电荷中性（填充$\nu =0$，或每个莫尔电池4个电子），并且在 $\nu$= -1 / 4和-1/2（每个单元分别有3和2个电子），并且 $C_2𝒯$ 处的对称破坏状态 $\nu$= -3/4（每个电池1个电子）。hBN基板完全驱动基态$\nu$ 进入 $C_2𝒯$对称破坏状态。我们的研究结果为进一步研究TBG中丰富的相关物理提供了很好的参考点。