Transport and localization in a topological phononic lattice with correlated disorder

TL;DR

This study investigates how correlated disorder affects topologically protected phononic edge modes in a lattice, revealing robustness to uncorrelated disorder but vulnerability when disorder is spatially correlated, due to Anderson localization effects.

Contribution

It demonstrates the impact of spatially correlated disorder on topological phononic edge modes, highlighting their robustness or susceptibility depending on disorder correlation.

Findings

TPE mode transmission remains high with uncorrelated disorder

Spatial correlation in disorder reduces TPE transmission due to Anderson localization

Non-TPE channels show frequency-dependent transmittance changes with disorder correlation

Abstract

Recently proposed classical analogs of topological insulators in phononic lattices have the advantage of much more accessible experimental realization as compared to conventional materials. Drawn to their potential practical structural applications, we investigate how disorder, which is generically non-negligible in macroscopic realization, can attenuate the topologically protected edge (TPE) modes that constitute robust transmitting channels at zero disorder. We simulate the transmission of phonon modes in a quasi-one-dimensional classical lattice waveguide with mass disorder, and show that the TPE mode transmission remains highly robust ($\Xi\sim1$) in the presence of uncorrelated disorder, but diminishes when disorder is spatially correlated. This reduction in transmittance is attributed to the Anderson localization of states within the mass disorder domains. By contrast, non-TPE channels exhibit qualitatively different behavior, with spatial correlation in the mass disorder leading to significant transmittance reduction (enhancement) at low (high) frequencies. Our results demonstrate how topologically protected edge modes drastically modify the effect of spatial correlation on mode localization.