Measurement of topologically protected corner states in a microwave metamaterial quadrupole insulator

The electric polarization of a crystalline insulator can be expressed in terms of the Berry phase of its electronic ground state. Recently, this concept was extended to higher electric multipole moments and a new class of previously unobserved topological phases was predicted. Using a GHz frequency reconfigurable microwave metamaterial circuit, we implemented the first member of this class -- a topological insulator with a quantized bulk quadrupole moment. We experimentally confirm the existence of the new topological phase through spectroscopic measurements and identify corner states manifested by the bulk topology. By deforming the edge of our metamaterial, we observe that these corner states are robustly protected by the bulk topology.