标题： 扭曲双层石墨烯中的混合价态莫特绝缘体和复合激发 显示英文标题

标题： Mixed valence Mott insulator and composite excitation in twisted bilayer graphene

摘要： 强关联和扁平拓扑能带之间的相互作用是莫尔系统（如魔角扭曲双层石墨烯（TBG））中的核心问题。最近的研究表明，尽管存在Wannier障碍，TBG中仍可能存在类似莫特态的状态。然而，这种非常规状态的性质仍未被充分理解。在本工作中，我们利用拓扑重费米子模型的部分子平均场理论，构建了对称相关半金属或绝缘体在偶数整数填充下的基态波函数和奇异激发态。我们根据 $f$轨道的占据情况来标记其价态 $n_f$。在 $\nu=-2$时，我们发现 $f$轨道并未处于从平凡莫特局域化预期的简单 $f^{2+}$价态。相反，在AA位点 $1/3$附近发生了自掺杂，空穴进入远离AA位点的 $c$轨道。 因此，$f$轨道处于$f^{2+}$和$f^{3+}$价态的叠加态，不应被视为局域磁矩。我们将这种相称为\textit{混合价态莫特绝缘体}。这种非常规绝缘体具有大的杂化$\langle c^\dagger f \rangle\neq 0$，与通常的“Kondo破坏”图像有明显区别。在远离$\Gamma$点的大部分动量空间中，存在等于Hubbard$U$的Mott能隙。 在$\Gamma$点，我们有一个“电荷转移能隙”，比$U$小得多。 特别是，下带的顶部由一种复合激发主导，这是一种$|f^{1+}\rangle\langle f^{2+}|$和$|f^{2+}\rangle\langle f^{3+}|$的线性组合，其符号结构使得它与微观的$f$算符正交。 在$\nu=0$处，类似的方法导致了一种莫特半金属。 我们希望这项工作能激发更多对大杂化安德森模型的探索，这一领域可能包含超出熟悉科恩多或重费米子系统的新的物理现象。 显示英文摘要

摘要： Interplay of strong correlation and flat topological band has been a central problem in moir\'e systems such as the magic angle twisted bilayer graphene (TBG). Recent studies show that Mott-like states may still be possible in TBG despite the Wannier obstruction. However, the nature of such unconventional states is still not well understood. In this work we construct the ground state wavefunction and exotic excitations of a symmetric correlated semimetal or insulator at even integer filling using a parton mean field theory of the topological heavy fermion model. We label the valence of the $f$ orbital based on its occupation $n_f$. At $\nu=-2$, we show that the $f$ orbital is not in the simple $f^{2+}$ valence expected from a trivial Mott localization. Instead, around $1/3$ of AA sites are self doped, with holes entering the $c$ orbitals away from AA sites. As a result, the $f$ orbital is in a superposition of $f^{2+}$ and $f^{3+}$ valences and should not be viewed as local moment. We dub the phase as \textit{mixed valence Mott insulator}. This unconventional insulator has a large hybridization $\langle c^\dagger f \rangle\neq 0$ and is sharply distinct from the usual `kondo breakdown' picture. In most of the momentum space away from the $\Gamma$ point, there is a Mott gap equal to the Hubbard $U$. At the $\Gamma$ point, we have a `charge transfer gap' much smaller than $U$. In particular, the top of the lower band is dominated by a composite excitation, which is a linear combination of $|f^{1+}\rangle\langle f^{2+}|$ and $|f^{2+}\rangle\langle f^{3+}|$ with a sign structure such that it is orthogonal to the microscopic $f$ operator. At $\nu=0$, similar approach leads to a Mott semimetal. We hope this work will inspire more explorations of the Anderson models with a large hybridization, a regime which may host new physics beyond the familiar Kondo or heavy fermion systems.