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Using a combination of first-principles simulations, based on the densityfunctional theory and Boltzmann's semiclassical theory, we have calculated thetransport and thermoelectric properties of the half-metallic two dimensionalelectron gas confined in single SrRuO$_3$ layers of SrTiO$_3$/SrRuO$_3$periodic superlattices. Close to the Fermi energy we find that thesemiconducting majority spin channel displays a very large in-plane componentof the Seebeck tensor at room temperature, $S$ = 1500 $\mu$V/K, and theminority spin channel shows good in-plane conductivity $\sigma$ = 2.5(m$\Omega$cm)$^{-1}$. However, contrary to the expectation of Hicks andDresselhaus model about enhanced global thermoelectric properties due to theconfinement of the metallic electrons, we find that the total power factor andthermoelectric figure of merit for reduced doping is too small for practicalapplications. The reason for this failure can be traced back on the electronicstructure of the interfacial gas, which departs from the free electronbehaviour on which the model was based. The evolution of the electronicstructure, electrical conductivity, Seebeck coefficient, and power factor as afunction of the chemical potential is explained by a simplified tight-bindingmodel. We find that the electron gas in our system is composed by a pair of onedimensional electron gases orthogonal to each other. This reflects the fact thephysical dimensionality of the electronic system can be even smaller than thatof the spacial confinement of the carriers.

First-principles modeling of the thermoelectric properties of SrTiO$_3$/SrRuO$_3$ superlattices