First-principles study on the high thermoelectric efficiency originating from ``pudding-mold'' bands in n- and p-type SnSe

The performance of thermoelectric conversion is evaluated by the dimensionless figure of merit \textit{ZT}$=(\sigma S^{2}/\kappa )T,$ where $\sigma $, $S$, $\kappa $, and $T$ are the electrical conductivity, thermopower, thermal conductivity, and temperature, respectively. Recently, it has been experimentally found that SnSe exhibits a high \textit{ZT}$=$2.6 at 923 K [1]. Its high \textit{ZT} is mainly due to the ultralow thermal conductivity. Some theoretical studies have shown that the ultralow thermal conductivity originates from strong anharmonicity of the phonons, and suggested that \textit{ZT} could be further increased by doping electrons or holes[2,3]. In the present study, we analyze the thermoelectric properties of the carrier-doped SnSe to reveal the origin of its even higher performance. Using the first-principles calculation and adopting the Boltzmann equation, we obtain the electrical conductivity and the thermopower. We find that the pudding-mold-shaped band structure [4] enhances its thermoelectric performance not only in the hole-doped [2] but also in the electron-doped regime, where the Bloch states at the Fermi level originate from Se $p_{x}$ in the former, and Sn $p_{y}$ in the latter. [1] L.-D. Zhao \textit{et al}., Nature \textbf{508}, 373 (2014). [2] K. Kutorasinski \textit{et al}., Phys. Rev. B \textbf{91}, 205201 (2015). [3] R. Guo \textit{et al}., Phys. Rev. B \textbf{92}, 115202 (2015). [4] K. Kuroki and R. Arita, J. Phys. Soc. Jpn. \textbf{76}, 083707 (2007).