Observation of bulk-edge correspondence in topological pumping based on a tunable electric circuit

Abstract

In topological phases, localized edge states protected by the bulk topological number appear. This phenomenon is known as the bulk-edge correspondence, which has been theoretically established in various topological systems including topological pumping. There have been experimental works on topological edge states. However, direct observation of bulk topological numbers remains challenging. Here, we experimentally observe both topological edge states and bulk Chern numbers near the topological phase transition in a tunable electric circuit system. The admittance matrix of the system is accurately engineered by using variable capacitors, leading to the implementation of classical analogue of the quantum Hall phase and the topological transition. The topological numbers of the edge states are determined experimentally, where the locations of the edge states are flipped in the topological transition. The corresponding bulk Chern numbers are determined by the Středa’s formula to the impedance spectrum. Our electric circuit scheme is a promising platform to provide a crucial understanding of topological phenomena, and opens up the possibility toward functional energy transfer mechanisms.