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We study the origin of the large Seebeck coefficient despite the metallicconductivity in the La-doped SrTiO$_3$ and Ba-doped KTaO$_3$. We calculate theband structure of SrTiO$_3$ and KTaO$_3$, from which the Seebeck coefficient isobtained using the Boltzmann's equation. We conclude that the multiplicity ofthe $t_{2g}$ bands in these materials is one major origin of the goodthermoelectric property in that when compared at a fixed total number of dopedelectrons, the Seebeck coefficient and thus the power factor are larger inmultiple band systems than in single band ones because the number of dopedelectron bands {\it per band} is smaller in the former. We also find that thesecond nearest neighbor hopping integral, which generally has negative valuesin these materials and works destructively against the Seebeck effect, isnearly similar between KTaO$_3$ and SrTiO$_3$ despite the larger band width inthe former. This can be another factor favorable for thermopower in theBa-doped KTaO$_3$.

Origin of coexisting large Seebeck coefficient and metallic conductivity in the electron doped SrTiO$_3$ and KTaO$_3$