Majorana-like zero modes in Kekul\'e distorted sonic lattices

TL;DR

This paper demonstrates the creation and observation of a topologically protected, Majorana-like zero mode in a Kekule9-distorted acoustic lattice, combining numerical simulations and experimental validation.

Contribution

It introduces an acoustic analogue of Majorana bound states in a bosonic system, realized through a Kekule9 lattice with vortex defects, and confirms topological protection experimentally.

Findings

Topologically bound acoustic mode observed at vortex defect

Mode remains robust against local perturbations

Experimental spectrum matches numerical predictions

Abstract

Topological phases have recently been realised in bosonic systems. The associated boundary modes between regions of distinct topology have been used to demonstrate robust waveguiding, protected from defects by the topology of the surrounding bulk. A related type of topologically protected state that is not propagating but is bound to a defect has not been demonstrated to date in a bosonic setting. Here we demonstrate numerically and experimentally that an acoustic mode can be topologically bound to a vortex fabricated in a two-dimensional, Kekul\'e-distorted triangular acoustic lattice. Such lattice realises an acoustic analogue of the Jackiw-Rossi mechanism that topologically binds a bound state in a p-wave superconductor vortex. The acoustic bound state is thus a bosonic \edit{\emph{analogue}} of Majorana bound state, \edit{where the two valleys replace particle and hole components}. We numerically show that it is topologically protected against arbitrary symmetry-preserving local perturbations, and remains pinned to the Dirac frequency of the unperturbed lattice regardless of parameter variations. We demonstrate our prediction experimentally by 3D printing the vortex pattern in a plastic matrix and measuring the spectrum of the acoustic response of the device. Despite viscothermal losses, the measured topological resonance remains robust, with its frequency closely matching our simulations.