First-principles Study of Lattice Thermal Conductivity of Cu$_{3}$SbS$_{4}$ and Cu$_{3}$SbSe$_{4}$

Linearized self-consistent Boltzmann transport equation (BTE), utilizing interatomic force constants (IFCs) obtained via compressive sensing lattice dynamics (CSLD), is used to study the lattice thermal conductivity ($\kappa_{l}$) of Cu$_{3}$SbS$_{4}$, Cu$_{3}$SbSe$_{4}$ and their solid solutions. With these IFCs we obtain bulk lattice thermal conductivity in good agreement with experimental measurements. We also compare Cu$_{3}$SbS$_{4}$ and Cu$_{3}$SbSe$_{4}$ with respect to Gr\"uneisen parameter, group velocity, phonon lifetime, mean free path and cumulative $\kappa_{l}$. All the analysis indicates that (1) slightly larger group velocity and lifetime of acoustic modes found in Cu$_{3}$SbS$_{4}$ lead to larger $\kappa_{l}$ compared with Cu$_{3}$SbSe$_{4}$ over the whole temperature range. Contributions from optical modes to $\kappa_{l}$ for both compounds are about 25\% at temperature higher than 300K. This large portion of $\kappa_{l}$ can not be neglected if one aims to predict accurate $\kappa_{l}$; (2) Nanostructures with length less than 10nm can effectively reduce $\kappa_{l}$ by about 80\% for both of the compounds; (3) solid solution of two compounds can effectively reduce $\kappa_{l}$ as much as 40\% at room temperature.