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Ab initio study of the strain dependence of thermopower in electron-doped SrTiO$_3$

In this paper we explore the different mechanisms that affect the thermopower of a band insulating perovskite (in this case, SrTiO$_3$) when subject to strain (both compressive or tensile). We analyze the high temperature, entropy dominated limit and the lower temperature, energy-transport regime. We observe that the effect of strain in the high-temperature Seebeck coefficient is small at the concentration levels of interest for thermoelectric applications. However, the effective mass changes substantially with strain, which produces an opposite effect to that of the degeneracy-breakups produced by strain. In particular, we find that the thermopower can be enhanced by applying tensile strain in the adequate regime. We conclude that the detrimental effect of strain in thermopower due to band splitting is a minor effect that will not hamper the optimization of the thermoelectric properties of oxides with t$_{2g}$-active bands by applying strain.