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

Abstract

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 non-zero 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. 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.

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• Non-Abelian inverse Anderson transitions
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• Square-root Floquet topological phases and time crystals
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• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Observation of type-III corner states induced by long-range interactions
• Engineering topological states and quantum-inspired information processing using classical circuits
• Electrical analogue of one-dimensional and quasi-one-dimensional Aubry-André-Harper lattices
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• Topological phase diagram of the Haldane model on a Bishamon-kikko--honeycomb lattice
• Kitaev Chain with a Fractional Twist
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• $q$th-root non-Hermitian Floquet topological insulators
• Realization of second-order photonic square-root topological insulators