Designing Phononic Band Gaps with Sticky Potentials

TL;DR

This paper introduces a numerical scheme that efficiently creates spectral gaps in disordered solids using sticky potentials, avoiding complex tuning and applicable to various physical systems.

Contribution

The authors develop a rapid, tuning-free method to generate spectral gaps in disordered systems by employing sticky potentials to suppress soft modes.

Findings

Spectral gaps can be reliably produced without fine tuning.

The method works in relatively small disordered systems.

Applicable to diverse physical setups like colloids and 3D-printed networks.

Abstract

Spectral gaps in the vibrational modes of disordered solids are key design elements in the synthesis and control of phononic metamaterials that exhibit a plethora of novel elastic and mechanical properties. However, reliably producing these gaps often require a high degree of network specificity through complex control optimization procedures. In this work, we present as an additional tool to the existing repertoire, a numerical scheme that rapidly generates sizeable spectral gaps in absence of any fine tuning of the network structure or elastic parameters. These gaps occur even in disordered polydisperse systems consisting of relatively few particles ($N \sim 10^2-10^3$). Our proposed procedure exploits sticky potentials that have recently been shown to suppress the formation of soft modes, thus effectively recovering the linear elastic regime where band structures appear, at much shorter length scales than in conventional models of disordered solids. Our approach is relevant to design and realization of gapped spectra in a variety of physical setups ranging from colloidal suspensions to 3D-printed elastic networks.