In this study, we employed first-principles calculations combined with the Boltzmann transport equation to investigate the thermal transport and thermoelectric properties of $\mathrm{Cs}\mathrm{Ca}X$ ($X=\mathrm{Bi},\mathrm{P}$). Both $\mathrm{Cs}\mathrm{Ca}\mathrm{Bi}$ and $\mathrm{Cs}\mathrm{Ca}\mathrm{P}$ exhibited low lattice thermal conductivity, with ${\kappa }_L$ values of $0.79$ and $0.81{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$, respectively, at room temperature. The strong anharmonicity in both materials was attributed to the rattlers behavior of $\mathrm{Cs}$ atoms. Furthermore, our analysis revealed an anomalous contribution of approximately 72.1% to ${\kappa }_L$ along the $a$ axis from the optical acoustic branches in $\mathrm{Cs}\mathrm{Ca}\mathrm{P}$. Through the investigation of vibrational modes, we found that this was primarily caused by the out-of-phase vibrations of $\mathrm{Ca}$ and $\mathrm{P}$ atoms. The flat bands near the valence-band maximum resulted in a high Seebeck coefficient, leading to a high power factor. Consequently, the ZT values for $p$-type $\mathrm{Cs}\mathrm{Ca}\mathrm{Bi}$ and $\mathrm{Cs}\mathrm{Ca}\mathrm{P}$ at 700 K under optimal doping conditions reached 2.99 and 2.97, respectively.

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• Electrical conductivity
• Lattice dynamics
• Thermal conductivity
• Thermoelectric effects
• Semiconductor compounds
• Ab initio molecular dynamics
• Boltzmann theory
• Density functional calculations