We study electronic, charge, and magnetic properties of twisted bilayer graphene with fillings $2\le n\le 6$ per moire unit cell within the recently introduced formulation of extended dynamical mean-field theory for two-sublattice systems. We use previously obtained hopping parameters between the states, described by Wannier functions, centered at the lattice spots of AB and BA stacking, and the long-range Coulomb interaction, obtained within cRPA analysis. We show that account of spin exchange between AB and BA nearest-neighbor spots is crucial to introduce charge and spin correlations between these spots. The account of this exchange yields preferable concentration of electrons in the same valley, with the tendency of parallel spin alignment of electrons in AB and BA spots, in agreement with earlier results of the strong-coupling analysis, suggesting SU(2)$\times \mathrm{SU}$(2) emergent spin-valley symmetry. The local spectral functions show an almost gapped state at fillings $n=2,4,6$, and incoherent metal state for the other fillings. We find that in both cases the local states of electrons have rather long lifetimes. At the same time, the nonlocal charge and spin susceptibilities, obtained within the ladder approximation, are peaked at incommensurate wave vectors, which implies that the above-discussed ordering tendencies are characterized by an incommensurate pattern.

中文翻译：

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扭曲双层石墨烯绝缘和非相干金属态的电荷和自旋相关性

我们研究了带填充物的扭曲双层石墨烯的电子、电荷和磁性$2\le n\le 6$在最近引入的用于两个亚晶格系统的扩展动态平均场理论公式中的每个莫尔晶胞。我们使用先前获得的状态之间的跳跃参数，由 Wannier 函数描述，以 AB 和 BA 堆叠的晶格点为中心，以及在 cRPA 分析中获得的长程库仑相互作用。我们表明，AB 和 BA 最近邻点之间的自旋交换对于引入这些点之间的电荷和自旋相关性至关重要。这种交换的说明在同一谷中产生了优选的电子浓度，在 AB 和 BA 点中电子有平行自旋排列的趋势，这与强耦合分析的早期结果一致，表明 SU(2)$\times 苏$(2) 涌现的自旋谷对称性。局部谱函数在填充物处显示出几乎间隙状态$n=2,4,6$，以及其他填充物的非相干金属状态。我们发现在这两种情况下，电子的局部状态都有相当长的寿命。同时，在梯形近似中获得的非局部电荷和自旋磁化率在不相称的波向量处达到峰值，这意味着上述排序趋势的特征在于不相称的模式。