Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach

TL;DR

This paper analytically investigates how correlated disorder in harmonic chains affects phonon localization and transport, revealing methods to control thermal properties through disorder correlations for potential thermal management applications.

Contribution

It provides a perturbative analytical expression for localization length in disordered harmonic chains with arbitrary correlations, and demonstrates how to engineer mobility edges and transparent windows via disorder correlations.

Findings

Localization length depends on disorder correlations.

Effective mobility edges can be generated with long-range correlations.

Transport properties can be manipulated through disorder correlations.

Abstract

We study the localization properties of normal modes in harmonic chains with mass and spring weak disorder. Using a perturbative approach, an expression for the localization length is obtained, which is valid for arbitrary correlations of the disorder, and for practically the whole frequency band. In addition, we show how to generate effective mobility edges by the use of disorder with long range self-correlations and cross-correlations. Finally, the transport of phonons is also analyzed showing effective transparent windows that can be manipulated through the disorder correlations even for relative short chain sizes. Our results may have applications in modulating thermal transport, particularly in the design of thermal filters or in manufacturing high-thermal-conductivity materials.