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Higher-order topological insulator (HOTI) represents a new phase of matter,the characterization of which goes beyond the conventional bulk-boundarycorrespondence and is attracting significant attention by the broad community.Using a square-root operation, it has been suggested that a square-root HOTImay emerge in a hybrid honeycomb-kagome lattice. Here, we report the firstexperimental realization of the square-root HOTI in topological LC circuits. Weshow theoretically and experimentally that the square-root HOTI inherits thefeature of wave function from its parent, with corner states pinned to non-zeroenergies. The topological feature is fully characterized by the bulkpolarization. To directly measure the finite-energy corner modes, we introduceextra grounded inductors to each node. Our results experimentally substantiatethe emerging square-root HOTI and pave the way to realizing exotic topologicalphases that are challenging to observe in condensed matter physics.

Realization of the square-root higher-order topological insulator in electric circuits