Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits

TL;DR

This paper experimentally demonstrates $ Z$-class higher-order topological insulator phases in electric circuits, revealing multiple corner modes at each corner, which extends the understanding of HOTIs beyond the previously known $ Z_2$ class.

Contribution

The study reports the first experimental realization of $ Z$-class HOTI phases in electric circuits with multiple corner modes at each corner, expanding the classification of HOTIs.

Findings

Demonstration of $ Z$-class HOTI phases in electric circuits.

Observation of multiple corner modes at each corner.

Equal distribution of local density of states among corners for $N=4$.

Abstract

Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk topological invariants. So far, all previous realizations of HOTIs are hallmarked by $\mathbb{Z}_2$ topological invariants and therefore have only one corner state at each corner. Here we report an experimental demonstration of $\mathbb{Z}$-class HOTI phases in electric circuits, hosting $N$ corner modes at each single corner structure. By measuring the impedance spectra and distributions, we clearly demonstrate the $\mathbb{Z}$-class HOTI phases, including the zero-energy corner modes and their density distributions. Moreover, we reveal that the local density of states (LDOS) at each corner for $N=4$ are equally distributed at four corner unit cells, prominently differing from $\mathbb{Z}_2$-class case where the LDOS only dominates over one corner unit cell. Our results extend the observation of HOTIs from $\mathbb{Z}_2$ class to $\mathbb{Z}$ class and the coexistence of spatially overlapped large number of corner modes which may enable exotic topological devices that require high degeneracy boundary states.