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

High-order topological insulators are a recent development extending the\ntopological theory of charge polarization to higher multipole moments. Since\ntheir theoretical proposal, several experimental realizations of high-order\ntopological insulators have been reported. However, high order topological\ntransitions have not been observed. In this letter, we report on the\nobservation of a high-order topological transition in a quadrupole topological\ninsulator implemented in an LC circuit with nonlinear couplings. This system\npresents the ability to confine electromagnetic energy in its corner states,\nwith a localization length that can be tuned over a broad range through the use\nof an external bias voltage. Additionally, we provide an experimental\ncharacterization and an effective theory for the boundary states, further\ncorroborating their topological nature by direct measurement of the winding\nnumber.\n