Observation of quadrupole transitions and edge mode topology in an LC circuit network

High-order topological insulators are a recent development extending the topological theory of charge polarization to higher multipole moments. In these systems, the presence of a nontrivial n-dimensional bulk results in boundary modes of a dimension n - 2 or lower. Since their theoretical proposal, several experimental realizations of high-order topological insulators have been reported. However, high-order topological transitions have not been observed. In this Rapid Communication, we report on the observation of a high-order topological transition in a quadrupole topological insulator implemented in an LC circuit with nonlinear couplings. This system presents the ability to confine electromagnetic energy in its corner states, with a localization length that can be tuned over a broad range through the use of an external bias voltage. Additionally, we provide an experimental characterization and an effective theory for the boundary states, further corroborating their topological nature by direct measurement of the winding number.