First-Principles Studies on Lattice Dynamical Properties of Zn$_4$Sb$_3$ Compounds*

The origin of extremely low lattice thermal conductivity in Zn$_4$Sb$_3$ compound has attracted great interests but remains not fully understood due to its complex crystal structure. We have performed extensive first-principles calculations on the lattice vibration modes and thermodynamics of Zn$_4$Sb$_3$ based on its experimental crystal structure. The low frequency modes and structural inhomogeneity that could be responsible for the low thermal conductivity have been discussed.