Localization of Phonons in Two Component Superlattice with Random Thicknesses of the Layers

TL;DR

This paper investigates phonon localization in a two-component superlattice with randomly varying layer thicknesses, deriving the phonon spectrum and analyzing phonon transport properties including Landauer resistance.

Contribution

It provides an exact calculation of phonon Landauer resistance and reveals the existence of delocalized states at zero frequency in disordered superlattices.

Findings

At zero frequency, phonons are delocalized.

The correlation length index is equal to 2.

Landauer resistance of phonons is calculated exactly.

Abstract

Two component superlattice film of 2N layers is considered and dimensionally quantised spectrum of phonon-s is found. The problem of localization of phonon-s in the superlattice with random thicknesses of the layers is investigated. The Landauer resistance of the transport of phonon-s is calculated exactly. For short range disorder the numerical analyses shows, that at frequency \omega=0, there is delocalized state and the correlation length index \nu is equal to 2.