Realization of the Square-Root Higher-Order Topological Insulator in Electric Circuits

Higher-order topological insulator (HOTI) represents a new phase of matter, the characterization of which goes beyond the conventional bulk-boundary correspondence and is attracting significant attention by the broad community. Using a square-root operation, it has been suggested that a square-root HOTI may emerge in a hybrid honeycomb-kagome lattice. Here, we report the first experimental realization of the square-root HOTI in topological LC circuits. We show theoretically and experimentally that the square-root HOTI inherits the feature of wave function from its parent with corner states pinned to nonzero energies. The topological feature is fully characterized by the bulk polarization. To directly measure the finite-energy corner modes, we introduce extra grounded inductors to each node, which shifts corner states to zero-energy without affecting their spatial distributions. Our results experimentally substantiate the emerging square-root HOTI and pave the way to realizing exotic topological phases that are challenging to observe in condensed matter physics.