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

TL;DR

This paper reports the first experimental realization of a square-root higher-order topological insulator in electric circuits, demonstrating corner states at finite energies inherited from a parent topological phase.

Contribution

It introduces a novel experimental approach to realize and characterize square-root HOTIs in LC circuits, expanding the understanding of topological phases beyond condensed matter systems.

Findings

Square-root HOTI realized in electric circuits

Corner states pinned to non-zero energies observed

Bulk polarization used for topological characterization

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.