Transport measurement of fractional charges in topological models

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 that 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. We also show that the Anderson disorder effect, which breaks certain symmetry related to the TFC, is significant in higher-dimensional systems while has 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.