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Quantized electric quadrupole insulators have recently been proposed as novelquantum states of matter in two spatial dimensions. Gapped otherwise, they canfeature zero-dimensional topological corner mid-gap states protected by thebulk spectral gap, reflection symmetries and a spectral symmetry. Here weintroduce a topolectrical circuit design for realizing such corner modesexperimentally and report measurements in which the modes appear as topologicalboundary resonances in the corner impedance profile of the circuit. Whereas thequantized bulk quadrupole moment of an electronic crystal does not have adirect analogue in the classical topolectrical-circuit framework, the cornermodes inherit the identical form from the quantum case. Due to the flexibilityand tunability of electrical circuits, they are an ideal platform for studyingthe reflection symmetry-protected character of corner modes in detail. Our worktherefore establishes an instance where topolectrical circuitry is employed tobridge the gap between quantum theoretical modelling and the experimentalrealization of topological band structures.

Topolectrical circuit realization of topological corner modes