Acoustic-optical phonon branch crossings and lattice thermal transport in La$_3$Cu$_3$X$_4$ (X = P, As, Sb, and Bi) systems

Thermoelectric properties of La$_3$Cu$_3$X$_4$ (X = P, As, Sb, and Bi) compounds are examined using first-principles density functional theory and Boltzmann transport calculations. It is well known that the lattice thermal conductivity ($\kappa_{l}$) of bulk materials typically decreases with increasing atomic masses of the constituent elements. In this study, however, we observe contrary behavior: lighter mass, larger sound velocity La$_3$Cu$_3$P$_4$ and La$_3$Cu$_3$As$_4$ systems have lower $\kappa_{l}$ than heavier mass, smaller sound velocity La$_3$Cu$_3$Sb$_4$ and La$_3$Cu$_3$Bi$_4$ systems. Analysis of three phonon scattering rates and other phonon properties demonstrate that the trend in $\kappa_{l}$ behavior is governed by Gr\"{u}neisen parameters, a measure of phonon anharmonicity. The Gr\"{u}neisen parameters and lower $\kappa_{l}$ of the P and As compounds are closely related to an avoided crossing between the lowest optical branches and the longitudinal acoustic branch, which results in abrupt changes in Gr\"{u}neisen parameters. Additionally, electronic structure calculations show heavy and light bands near the band edges, which lead to large power factors important for good thermoelectric performance.