Phonon Lifetimes and Thermal Transport in Mass-Disordered Systems Using the Dynamical Cluster Approximation

Disorder is an inherent feature of real materials and needs to be properly accounted for when analyzing thermal transport and phonon dynamics. In this work, we apply several Green's function-based approaches—including the Average T-matrix Approximation (ATA), the Coherent Potential Approximation (CPA), and the Dynamical Cluster Approximation (DCA)—to study phonon lifetimes in three-dimensional mass-disordered systems. We compare these approximations against results obtained from a phonon unfolding algorithm using exact diagonalization, providing a comprehensive evaluation of commonly used approximation schemes and determining the range in which their predictions remain valid. Furthermore, we use the Boltzmann transport equation and the Green-Kubo formula to relate the computed phonon lifetimes to thermal conductivity, offering insights on how disorder affects thermal transport in realistic systems.