标题： 干扰度量拓扑 显示英文标题

标题： Interferences Measure Topology

摘要： 拓扑材料的特点是由整数不变量所支撑的其鲁棒的量子化电子特性，这在整数量子霍尔效应中的陈数中得到了著名的例证。 然而，在大多数候选系统中，与拓扑不变量相关的可观测量尚不清楚，这阻碍了对其拓扑性质的直接验证。 在这里，我们提出了一种通用方法，通过分析局部电子密度$\delta \rho(\boldsymbol{r})$并将其与阿蒂亚-辛格指标定理联系起来，以识别拓扑材料。 这种方法使得可以通过由拓扑缺陷产生的$\delta \rho(\boldsymbol{r})$的干涉形成的与路径无关的位错图案，直接测量具有手征对称性的哈密顿量的绕数，即拓扑不变量。 因此，我们的方法为检测和表征量子拓扑态提供了一条直接途径，为它们在量子技术中作为鲁棒且可纠缠的构建模块的应用铺平了道路。 显示英文摘要

摘要： Topological materials are characterized by integer invariants that underpin their robust quantized electronic features, as famously exemplified by the Chern number in the integer quantum Hall effect. Yet, in most candidate systems, the observable linked to the topological invariant is unknown, preventing direct verification of their topological nature. Here we present a general method to identify topological materials by analyzing the local electronic density, $\delta \rho(\boldsymbol{r})$, and connecting it to Atiyah Singer index theorems. This approach enables a direct measurement of the winding number, the topological invariant of Hamiltonians with chiral symmetry, through a contour independent dislocation pattern of $\delta \rho(\boldsymbol{r})$ created by interference from topological defects. Our method thus provides a direct route to detect and characterize quantum topological states, paving the way for their use as robust and entangleable building blocks in quantum technologies.