Acoustic square-root topological insulators

TL;DR

This paper introduces the first realization of square-root topological insulators in phononic crystals, demonstrating novel topological states with localized modes and proposing a new three-dimensional topological semimetal.

Contribution

It experimentally demonstrates first- and second-order square-root topological insulators in acoustic systems, a novel class of topological phases inherited from the square of the Hamiltonian.

Findings

Localized end and corner states confirmed experimentally

Bulk gap doubling due to square-root procedure

Proposal of a 3D square-root topological semimetal

Abstract

Square-root topological states are new topological phases, whose topological property is inherited from the square of the Hamiltonian. We realize the first-order and second-order square-root topological insulators in phononic crystals, by putting additional cavities on connecting tubes in the acoustic Su-Schrieffer-Heeger model and the honeycomb lattice, respectively. Because of the square-root procedure, the bulk gap of the squared Hamiltonian is doubled. In both two bulk gaps, the square-root topological insulators possess multiple localized modes, i.e., the end and corner states, which are evidently confirmed by our calculations and experimental observations. We further propose a second-order square-root topological semimetal by stacking the decorated honeycomb lattice to three dimensions.