Phonon transmittance of one dimensional quasicrystals

TL;DR

This paper investigates how one-dimensional quasicrystals exhibit unique phonon transport properties due to their quasi-periodic structure, revealing topologically protected critical phonon modes that influence thermal transmittance.

Contribution

It introduces a topological classification of phonon modes in quasicrystals and demonstrates their impact on thermal transmittance, with specific examples like metallic-mean and Cantor tilings.

Findings

Identification of topologically protected critical phonon modes

Universal features of resonant and decaying phonon modes

Classification of thermal transmittance in quasiperiodic systems

Abstract

In quasicrystals, special tiling patterns could give rise to unique physical phenomena such as critical states distinct from periodic systems. In this paper, we study how quasi-periodicity in aperiodic systems results in anomalous phonon modes, especially focusing on thermal transmittance in one-dimensional quasicrystals. Unlike periodic or compeletly random systems, we classify certain quasicrystals could host critical phonon modes whose transport properties are topologically protected based on their pattern equivariant cohomology group of supertilings. Starting from discussing general rule to find such critical phonon modes, we discuss classification of topologically distinct thermal transmittance in quasiperiodic systems. To be more specific, we exemplify (decorated) metallic-mean tilings and Cantor tiling, and derive universal features for resonant and decaying phonon modes as a function of quasi-periodic strength. Our study paves a new way to understand thermal transmittance of quasi-periodic systems based on the topological classification and offers quasicrystals as strong candidates to control drastic phonon modes.