Band Structure Engineering of Coupled-Resonator Phononic Polyacetylene and Polyaminoborane

TL;DR

This paper introduces a method to engineer band structures in coupled-resonator phononic metamaterials by designing artificial analogs of molecular structures, revealing topologically protected states in the process.

Contribution

It presents a novel approach to construct and analyze phononic metamaterials based on molecular analogs using tight-binding models and topological concepts.

Findings

Successful design of phononic analogs of trans-polyacetylene and trans-polyaminoborane.

Identification of topologically protected states in the artificial trans-polyacetylene.

Application of SSH model and $$-deformed Dirac equation to analyze band structures.

Abstract

A methodology for constructing a quasi-one-dimensional coupled-resonator phononic metamaterial is presented. This is achieved through the design of artificial phononic analogs of two molecular structures: trans-polyacetylene and trans-polyaminoborane. The band structure of trans-polyacetylene is analyzed in relation to the Su-Schrieffer-Heeger (SSH) model, while that of trans-polyaminoborane is examined using the $\kappa$-deformed Dirac equation, both within a tight-binding framework. Additionally, the obtained finite realization of the artificial trans-polyacetylene exhibits topologically protected states.