Circuit realization of quadrupole topological insulator coexisting edge and corner states

Two-dimensional higher-order topological insulators (2D-HOTIs) have recently attracted significant attention, which feature topologically protected corner states and trivial edge states, manifesting bulk-corner correspondence. In this work, we report the experimental realization of the quadrupole topological insulator (QTI) in a circuit system. This QTI is theoretically proposed in the square-octagon lattice with time-reversal symmetry and inversion symmetry where the Berry curvature vanishes throughout the whole Brillouin zone. Distinct from the conventional 2D-HOTIs, topologically protected edge and corner states coexist in this model, demonstrating the bulk-edge-corner correspondence. We also experimentally realize this QTI in the circuit and the coexistence of edge (characterized by quantized polarization) and corner (characterized by quantized quadrupole) states is observed. Our study demonstrates the topologically protected edge and corner states in the QTI, and opens new avenues for the realization of other unique topological states.