In magic angle twisted bilayer graphene, electron-electron interactions play a central role resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question and potentially linked to the relatively high temperature superconductivity observed in the same devices. Here we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC exhibits a pattern of alternating circulating currents which triples the graphene unit cell leading to an “orbital magnetization density wave”. Although translation and time reversal symmetry are broken, a combined `Kramers’ time reversal symmetry is preserved. Our analytic arguments are built on first identifying an approximate $\U(4) \times \U(4)$ symmetry, resulting from the remarkable properties of the tBG band structure, which helps select a low energy manifold of states, which are further split to favor the K-IVC. This low energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry lowering perturbations can stabilize other insulators and the semi-metallic state, and discuss the ground state at half filling and a comparison with experiments.

中文翻译：

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偶数整数填充下魔角石墨烯的基态和隐藏对称性

在魔角扭曲的双层石墨烯中，电子-电子相互作用起着核心作用，导致在某些整数填充处相关的绝缘态。确定这些绝缘子的性质是一个中心问题，并且可能与在相同设备中观察到的相对较高的温度超导性有关。在这里，我们通过结合分析强耦合参数和全面的Hartree-Fock数值计算（包括远程频带的影响）来解决此问题。我们在电荷中性时获得的基态是一种异常有序状态，我们称其为Kramers间隔-相干（K-IVC）绝缘体。以最简单的形式，K-IVC表现出交流循环电流的模式，该模式使石墨烯晶胞增加三倍，从而产生“轨道磁化密度波”。尽管打破了平移和时间反转对称性，但保留了组合的“ Kramers”时间反转对称性。我们的分析论据建立在首先确定一个近似值的基础上tBG能带结构的显着特性导致了\ U（4）\ times \ U（4）$的对称性，这有助于选择状态的低能流形，并进一步拆分以支持K-IVC。在Hartree-Fock数值计算中也发现了这种低能流形。我们证明对称降低扰动可以稳定其他绝缘子和半金属状态，并讨论了半填充时的基态并与实验进行了比较。