Mismatched atomic bonds and ultralow thermal conductivity in Ag-based ternary chalcopyrites

Diamond like ternary chalcopyrites $MB{X}_{2}$ ($M=\text{Cu},\text{Ag}$; $B=\text{Ga},\text{In},\text{Tl}$; $X=\text{S},\text{Se},\text{Te}$) have attracted tremendous research interest in thermoelectric society due to the competitive performance and a great variety of transport properties. Interestingly, the lattice thermal conductivity of $\text{Ag}B{X}_{2}$ is systematically two to five times lower that of $\text{Cu}B{X}_{2}$, in spite of their similar crystal and band structures. Based on the careful theoretical analysis, we show that the ultralow thermal conductivity of $\text{Ag}B{X}_{2}$ originates in the mismatched atomic bonds between Ag-$X$ and B-$X$ pairs. Owing to the very expanded $4d$ orbital of Ag, the bonding strength of Ag-$X$ is much weaker than that of $B\text{\ensuremath{-}}X$. As a result, the vibrations of Ag-$X$ and B-$X$ are well separated within the low-frequency modes. The phonon density of states of $\text{Ag}B{X}_{2}$ exhibits four divided peaks, compared with the three peaks in $\text{Cu}B{X}_{2}$. The calculated joint phonon density of states reveals that such characteristic in $\text{Ag}B{X}_{2}$ would increase the scattering rate of low-frequency phonons significantly. This study provides essential understandings on the ultralow thermal conductivity of Ag-based ternary chalcopyrites and indicates a general strategy to suppress the thermal conductivity in ternary compounds.