The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in electronic systems is quite challenging. We propose an electronic transport measurement scheme in which both the charge amount and the spatial distribution of the TFC can be extracted from the differential conductance through a quantum dot coupled to the topological system being measured. For one-dimensional Su–Schrieffer–Heeger (SSH) model, both the e/2 charge of the TFC and its distribution can be verified. As for the disorder effect, it is shown that the Anderson disorder, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while having little effect on the one-dimensional SSH chain. Nonetheless, our measurement scheme can still work well for specific higher-order topological insulator materials, for instance, the 2e/3 TFC in the breathing kagome model could be confirmed even in the presence of disorder effect. These conclusions about spatial dimension and disorder effect are quite universal, which also applies to other topological systems such as topological classic wave system.

凝聚态系统中的静态拓扑分数电荷 (TFC) 与能带拓扑有关，因此在拓扑量子计算中具有潜在的应用。然而，电子系统中这些 TFC 的实验测量非常具有挑战性。我们提出了一种电子传输测量方案，其中可以通过耦合到被测拓扑系统的量子点从微分电导中提取 TFC 的电荷量和空间分布。对于一维 Su–Schrieffer–Heeger (SSH) 模型，e/2 TFC 的收费及其分配可以验证。至于无序效应，表明破坏与 TFC 相关的某些对称性的 Anderson 无序在高维系统中显着，而对一维 SSH 链的影响很小。尽管如此，我们的测量方案仍然适用于特定的高阶拓扑绝缘体材料，例如，即使存在无序效应，呼吸 kagome 模型中的2 e /3 TFC 也可以得到证实。这些关于空间维数和无序效应的结论具有很强的普适性，同样适用于其他拓扑系统，如拓扑经典波系统。