In magic angle twisted bilayer graphene (TBG), 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 it is 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 order exhibits a pattern of alternating circulating currents that 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 $\mathrm{U}(4)\times \mathrm{U}(4)$ symmetry, resulting from the remarkable properties of the TBG band structure, which helps select a low-energy manifold of states that are further split to favor the K-IVC state. 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 semimetallic state, and we discuss the ground state at half-filling and give a comparison with experiments.

中文翻译：

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整角填充时魔角石墨烯的基态和隐藏对称性

在魔角扭曲双层石墨烯（TBG）中，电子-电子相互作用起着核心作用，从而导致某些整数填充处的绝缘状态相关。确定这些绝缘子的性质是一个中心问题，并且可能与在同一设备中观察到的相对高温超导性有关。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的有序状态，我们称其为Kramers间隔-相干（K-IVC）绝缘体。最简单的形式是，K-IVC阶跃显示出一种交替循环电流的模式，可使石墨烯晶胞增加三倍，导致“轨道磁化密度波”。尽管打破了平移和时间反向对称性，但保留了组合的“ Kramers”时间反向对称性。我们的分析论据建立在首先确定一个近似值的基础上$\mathrm{ü}（4）\times \mathrm{ü}（4）$TBG能带结构的显着特性产生了对称性，这有助于选择低能流形的状态，这些状态被进一步分解以支持K-IVC态。在Hartree-Fock数值计算中也发现了这种低能流形。我们证明了降低对称性的摄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。