Abstract
The local density of states (LDOS), which describes the space-resolved density of states, has been studied in the context of exploring topological materials. Here, we report the observation of the fractional mode charge of topological states in a four-dimensional synthetic acoustic system, which is based on coupled acoustic cavities. We experimentally measured the LDOS of topological boundary states and corner states of this system and observed one-half and one-quarter fractional mode charges. In addition, we also obtained the LDOS in a three-dimensional acoustic system by simulation and observed the one-eighth fractional mode charge of the system. The results show that the appearance of topological states can correspond to the fractional charges, which is useful for the understanding of topology in acoustic systems and provides a new method for the characterization of topological states in topological acoustic systems.
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