标题： 莫尔系统中实空间拓扑的鲁棒性 显示英文标题

标题： Robustness of real-space topology in moiré systems

摘要： 在莫尔系统中出现分数陈绝缘体可以通过与层分辨电子波函数的空间纹理相关的虚构磁场来解释。 在这里，我们对莫尔系统中的实空间拓扑结构和相关的虚构磁场进行了系统研究。 我们首先表明，在单个布洛赫波函数的层面上，实空间陈数类似于庞特里亚金指标，是一个脆弱的标记。 它通常为零，除非在特定极限情况下，布洛赫函数在原胞内表现出精细调节的零点，例如扭曲双层石墨烯（TBG）的手性极限或扭曲同质双层过渡金属二硫属化物（TMD）的绝热区域。 然后我们表明，这些限制不适用于与布洛赫波函数集合相关的纹理，例如整个能带或给定能量下的状态集合。 这些纹理的陈数定义了一个由能隙保护的鲁棒拓扑指数。 我们发现，对称性使得在所有扭转角度和皱褶程度下，扭曲的TMD和TBG的该指数都非零，这意味着在扫描隧道显微镜测量中存在实验信号。 我们还研究了TBG的拓扑重费米子模型中的实空间拓扑结构，发现实空间的拓扑特征仅由轻的c电子支持。 显示英文摘要

摘要： The appearance of fractional Chern insulators in moir\'e systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moir\'e systems. We first show that at the level of individual Bloch wavefunctions, the real-space Chern number, akin to a Pontryagin index, is a fragile marker. It generically vanishes except for specific limits where the Bloch functions exhibit fine-tuned zeroes within the unit cell, such as the chiral limit of twisted bilayer graphene (TBG) or the adiabatic regime of twisted homobilayer transition metal dichalcogenides (TMD). We then show that these limitations do not apply to textures associated with ensembles of Bloch wavefunctions, such as entire bands or the ensemble of states at a given energy. The Chern number of these textures defines a robust topological index protected by a spectral gap. We find that symmetries constrain it to be nonzero for both twisted TMDs and TBG across all twist angles and levels of corrugation, implying experimental signatures in scanning tunneling microscopy measurements. We also study real-space topology within the topological heavy fermion model of TBG, finding that the real-space topological features are supported only by the light c-electrons.