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Influence of strain on anisotropic thermoelectric transport of Bi$_2$Te$_3$ and Sb$_2$Te$_3$

On the basis of detailed first-principles calculations and semi-classical Boltzmann transport, the anisotropic thermoelectric transport properties of Bi$_2$Te$_3$ and Sb$_2$Te$_3$ under strain were investigated. It was found that due to compensation effects of the strain dependent thermopower and electrical conductivity, the related powerfactor will decrease under applied in-plane strain for Bi$_2$Te$_3, while being stable for Sb$_2$Te$_3$. A clear preference for thermoelectric transport under hole-doping, as well as for the in-plane transport direction was found for both tellurides. In contrast to the electrical conductivity anisotropy, the anisotropy of the thermopower was almost robust under applied strain. The assumption of an anisotropic relaxation time for Bi$_2$Te$_3$ suggests, that already in the single crystalline system strong anisotropic scattering effects should play a role.