Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that the ${\mathbb{Z}}_N$ Berry phase (Berry phase quantized into $2\pi /N$) is a useful tool to characterize the symmetry-protected topological states, whereas the experimental evidence is still elusive. Recently, topolectrical circuits have emerged as a simple yet very powerful platform for studying topological physics that are challenging to realize in condensed-matter systems. Here, we present an experimental observation of second-order corner states characterized by the ${\mathbb{Z}}_3$ Berry phase in topolectrical circuits. We demonstrate theoretically and experimentally that the localized second-order topological states are protected by a generalized chiral symmetry of tripartite lattices, and they are pinned to “zero energy.” By introducing extra capacitors within sublattices in the circuit, we are able to examine the robustness of the zero modes against both chiral-symmetry-conserving and breaking disturbances. Our Rapid Communication paves the way for testing exotic topological band theory by electrical-circuit experiments.

• Received 10 January 2020
• Accepted 17 April 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.022028

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Published by the American Physical Society