标题： 扭曲双层半导体在分数填充下的结构因子和拓扑约束 显示英文标题

标题： Structure factor and topological bound of twisted bilayer semiconductors at fractional fillings

摘要： 结构因子是用于探测实际材料中电荷密度相关性的有用可观测量，其由“量子权重”所概括的长波长行为最近在量子几何和物质拓扑相的研究中引起了广泛关注。 我们在这里使用静态结构因子 S(q)，来研究扭曲过渡金属二硫属化物（TMDs）tMoTe2 在填充因子 n=1/3、2/3 以及不同位移场下的相图。 我们的结果揭示了分数陈绝缘体（FCI）和广义威格纳晶体（GWC）之间的拓扑相变。 这一转变表现为在电荷密度波矢量处出现布拉格峰，同时在小 q 处 S(q) 的大幅下降降低了相互作用能量。 我们进一步计算了各种 FCI 态的量子权重，验证了普遍的拓扑边界。 我们的发现为扭曲 TMDs 的相图提供了新的见解，并建立了一个通过结构因子分析表征拓扑相的一般框架。 显示英文摘要

摘要： The structure factor is a useful observable for probing charge density correlations in real materials, and its long-wavelength behavior encapsulated by ``quantum weight'' has recently gained prominence in the study of quantum geometry and topological phases of matter. Here we employ the static structure factor, S(q), to explore the phase diagram of twisted transition metal dichalcogenides (TMDs), specifically tMoTe2, at filling factors n=1/3, 2/3 under varying displacement fields. Our results reveal a topological phase transition between a fractional Chern insulator (FCI) and a generalized Wigner crystal (GWC). This transition is marked by the appearance of Bragg peaks at charge-density-wave vectors, and simultaneously, large decrease of S(q) at small q which lowers the interaction energy. We further calculate the quantum weight of various FCI states, verifying the universal topological bound. Our findings provide new insights into the phase diagram of twisted TMDs and establish a general framework for characterizing topological phases through structure factor analysis.