Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks

Flat-band topologies and localizations in noninteracting systems are extensively studied in different quantum and classical-wave systems. Recently, the exploration on the novel physics of flat-band localizations and topologies in interacting systems has aroused great interest. In particular, it is theoretically shown that the strong interaction could drive the formation of nontrivial topological flat bands; even dispersive trivial bands dominate the single-particle counterparts. However, the experimental observation of those interesting phenomena is still lacking. Here, we experimentally simulate the interaction-induced flat-band localizations and topological edge states in electrical circuit networks. We directly map the eigenstates of two correlated bosons in one-dimensional Aharonov-Bohm cages to modes of two-dimensional circuit lattices. In this case, by tuning the effective interaction strength through circuits' groundings, the two-boson flat bands and topological edge states are detected by measuring frequency-dependent impedance responses and voltage dynamics in the time domain. Our finding suggests a flexible platform to simulate the interaction-induced flat-band topology, and may possess potential applications in designing novel electronic devices.