Perturbation theory and thermal transport in mass-disordered alloys: Insights from Green's function methods

TL;DR

This paper investigates thermal transport in mass-disordered alloys using Green's function methods, revealing why perturbation theory accurately predicts phonon scattering despite assumptions of weak disorder.

Contribution

It introduces a Chebyshev polynomials Green's function approach to analyze phonon linewidths and thermal transport in large disordered systems, clarifying the success of perturbation theory.

Findings

Perturbation theory's success is due to the specific form of mass disorder in Green's functions.

Disorder and anharmonic scattering interplay enhances phonon linewidth predictions.

Green's function methods enable analysis of systems with tens of millions of atoms.

Abstract

Lowest-order quantum perturbation theory (Fermi's golden rule) for phonon-disorder scattering has been used to predict thermal conductivities in several semiconducting alloys with surprising success given its underlying hypothesis of weak and dilute disorder. In this paper, we explain how this is possible by focusing on the case of maximally mass-disordered Mg$_2$Si$_{1-x}$Sn$_x$. We use a Chebyshev polynomials Green's function method that allows a full treatment of disorder on very large systems (tens of millions of atoms) to probe individual phonon linewidths and frequency-resolved thermal transport. We demonstrate that the success of perturbation theory originates from the specific form of mass disorder terms in the phonon Green's function and from the interplay between anharmonic and disorder scattering.