Lattice dynamics in Bi2Te3and Sb2Te

The lattice dynamics in Bi${}_{2}$Te${}_{3}$ and Sb${}_{2}$Te${}_{3}$ were investigated both microscopically and macroscopically using ${}^{121}$Sb and ${}^{125}$Te nuclear inelastic scattering, x-ray diffraction, and heat capacity measurements. In combination with earlier inelastic neutron scattering data, the element-specific density of phonon states was obtained for both compounds and phonon polarization analysis was carried out for Bi${}_{2}$Te${}_{3}$. A prominent peak in the Te specific density of phonon states at $13\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$, that involves mainly in-plane vibrations, is mostly unaffected upon substitution of Sb with Bi revealing vibrations with essentially Te character. A significant softening is observed for the density of vibrational states of Bi with respect to Sb, consistently with the mass homology relation in the long-wavelength limit. In order to explain the energy mismatch in the optical phonon region, a $\ensuremath{\sim}$$20%$ force constant softening of the Sb-Te bond with respect to the Bi-Te bond is required. The reduced average speed of sound at $20\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ in Bi${}_{2}$Te${}_{3}$, $1.75(1)\phantom{\rule{0.28em}{0ex}}\mathrm{km}/\mathrm{s}$, compared to Sb${}_{2}$Te${}_{3}$, $1.85(4)\phantom{\rule{0.28em}{0ex}}\mathrm{km}/\mathrm{s}$, is not only related to the larger mass density but also to a larger Debye level. The observed low lattice thermal conductivity at $295\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, $2.4\phantom{\rule{4.pt}{0ex}}{\text{Wm}}^{\ensuremath{-}1}{\text{K}}^{\ensuremath{-}1}$ for Sb${}_{2}$Te${}_{3}$ and $1.6\phantom{\rule{4.pt}{0ex}}{\text{Wm}}^{\ensuremath{-}1}{\text{K}}^{\ensuremath{-}1}$ for Bi${}_{2}$Te${}_{3}$, cannot be explained by anharmonicity alone given the rather modest Gr\"uneisen parameters, $1.7(1)$ for Sb${}_{2}$Te${}_{3}$ and $1.5(1)$ for Bi${}_{2}$Te${}_{3}$, without accounting for the reduced speed of sound and more importantly the low acoustic cutoff energy.