标题： 魔角石墨烯中的凯库勒螺旋序：密度矩阵重正化群研究 显示英文标题

标题： Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study

摘要： 当扭曲莫尔系统中的两层受到不同程度的应变时，这种效应会随着反向扭转角而放大，例如在魔角扭曲双层石墨烯（TBG）中放大了50倍。 TBG样品通常具有0.1-0.7%的异质应变，使“平坦”带的带宽增加多达十倍，将TBG置于中间耦合 regime。 在这里，我们使用无偏见、大规模密度矩阵重整化群计算（bond dimension $\chi=24576$），研究异质应变存在下的TBG相图，包括所有自旋和谷自由度。 在填充 $\nu = -3$的情况下，我们发现应变为 $0.05\%$会驱动从量子异常霍尔绝缘体到不共格凯库勒螺旋（IKS）相的转变。 这种特殊的序是由Kwan等人（PRX 11, 041063）在平均场水平上提出并研究的，它破坏了谷守恒和平移对称性 $\hat{T}$，但保留了带有莫尔不共格相调制的修改后的平移对称性 $\hat{T}'$。 更高的应变会使系统进入完全对称的金属态。 显示英文摘要

摘要： When the two layers of a twisted moir\'e system are subject to different degrees of strain, the effect is amplified by the inverse twist angle, e.g., by a factor of 50 in magic angle twisted bilayer graphene (TBG). Samples of TBG typically have heterostrains of 0.1-0.7%, increasing the bandwidth of the "flat'' bands by as much as tenfold, placing TBG in an intermediate coupling regime. Here we study the phase diagram of TBG in the presence of heterostrain with unbiased, large-scale density matrix renormalization group calculations (bond dimension $\chi=24576$), including all spin and valley degrees of freedom. Working at filling $\nu = -3$, we find a strain of $0.05\%$ drives a transition from a quantized anomalous Hall insulator into an incommensurate-Kekul\'e spiral (IKS) phase. This peculiar order, proposed and studied at mean-field level by Kwan et al (PRX 11, 041063), breaks both valley conservation and translation symmetry $\hat{T}$, but preserves a modified translation symmetry $\hat{T}'$ with moir\'e-incommensurate phase modulation. Even higher strains drive the system to a fully symmetric metal.