Long-range interactions (LRIs) are ubiquitous in nature. Higher-order topological (HOT) insulators represent a new phase of matter. A critical issue is how LRI dictates the HOT phases. In this work, we discover four topologically distinct phases, i.e., HOT phase, bound state in the continuum, Dirac semimetal (DSM) phase, and trivial insulator phase in a breathing kagome circuit with tunable LRIs. We find an emerging type-III corner state in the HOT phase, which splits from the edge state continuum and originates from the strong coupling between nodes at different edges. We experimentally detect this novel state by impedance and voltage measurements. In the DSM phase, the Dirac cone exhibits an itinerant feature with a tunable position that depends on the LRI strength. Our findings provide a deeper understanding of the LRI effect on exotic topological states and pave the way for regulating interactions in topolectrical circuits.

• Received 11 April 2022
• Revised 18 July 2022
• Accepted 19 August 2022

DOI:https://doi.org/10.1103/PhysRevB.106.075427