Mode Localization and Suppressed Heat Transport in Amorphous Alloys

Glasses usually represent the lower limit for the thermal conductivity of solids, but a fundamental understanding of lattice heat transport in amorphous materials can provide design rules to beat such a limit. Here we investigate the role of mass disorder in glasses by studying amorphous silicon-germanium alloy (a-Si$_{1-x}$Ge$_x$) over the full range of atomic concentration from $x=0$ to $x=1$, using molecular dynamics and the quasi-harmonic Green-Kubo lattice dynamics formalism. We find that the thermal conductivity of a-Si$_{1-x}$Ge$_x$ as a function of $x$ exhibits a smoother U-shape than in crystalline mass-disordered alloys. The main contribution to the initial drop of thermal conductivity at low Ge concentration stems from the localization of otherwise extended modes that make up the lowest 8\% of the population by frequency. Contributions from intermediate frequency modes are decreased more gradually with increasing Ge to reach a broad minimum thermal conductivity between concentrations of Ge from $x=0.25$ to $0.75$.