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Higher-order topological insulators are a new class of topological phases ofmatter, originally conceived for electrons in solids. It has been suggestedthat $\mathbb{Z}_N$ Berry phase (Berry phase quantized into $2\pi/N$) is auseful tool to characterize the symmetry protected topological states, whilethe experimental evidence is still elusive. Recently, topolectrical circuitshave emerged as a simple yet very powerful platform for studying topologicalphysics that are challenging to realize in condensed matter systems. Here, wepresent the first experimental observation of second-order corner statescharacterized by $\mathbb{Z}_3$ Berry phase in topolectrical circuits. Wedemonstrate theoretically and experimentally that the localized second-ordertopological states are protected by a generalized chiral symmetry of tripartitelattices, and they are pinned to "zero energy". By introducing extra capacitorswithin sublattices in the circuit, we are able to examine the robustness of thezero modes against both chiral-symmetry conserving and breaking disturbances.Our work paves the way for testing exotic topological band theory byelectrical-circuit experiments.

Observation of symmetry protected zero modes in topolectrical circuits