Low lattice thermal conductivity and good thermoelectric performance of cinnabar

Based on the combination of first-principles calculations, Boltzmann transport equation, and electron-phonon interaction (EPI), we investigate the thermal and electronic transport properties of crystalline cinnabar $(\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{HgS})$. The calculated lattice thermal conductivity ${\ensuremath{\kappa}}_{L}$ is remarkably low, e.g., $0.60\phantom{\rule{4pt}{0ex}}{\mathrm{Wm}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at $300\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, which is about $30%$ of the value for the typical thermoelectric material PbTe. Via taking fully into account the k dependence of the electron relaxation time computed from the EPI matrix, the accurate numerical results of thermopower $S$, electrical conductivity $\ensuremath{\sigma}$, and electronic thermal conductivity ${\ensuremath{\kappa}}_{E}$ are obtained. The calculated power factor ${S}^{2}\ensuremath{\sigma}$ is relatively high while the value of ${\ensuremath{\kappa}}_{E}$ is negligible, which, together with the fairly low ${\ensuremath{\kappa}}_{L}$, leads to a good thermoelectric performance in the $n$-type doped $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{HgS}$, with the figure of merit $zT$ even exceeding 1.4. Our analyses reveal that (i) the large weighted phase space and the quite low phonon group velocity result in the low ${\ensuremath{\kappa}}_{L}$, (ii) the presence of flat band around the Fermi level combined with the large band gap causes the high $S$, and (iii) the small electron linewidths of the conduction band lead to a large relaxation time and thus a relatively high $\ensuremath{\sigma}$. These results support that $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{HgS}$ is a potential candidate for thermoelectric applications.