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

Using a combination of first-principles simulations, based on the density functional theory and Boltzmann's semiclassical theory, we have calculated the transport and thermoelectric properties of the half-metallic two dimensional electron gas confined in single SrRuO$_3$ layers of SrTiO$_3$/SrRuO$_3$ periodic superlattices. Close to the Fermi energy we find that the semiconducting majority spin channel displays a very large in-plane component of the Seebeck tensor at room temperature, $S$ = 1500 $μ$V/K, and the minority spin channel shows good in-plane conductivity $σ$ = 2.5 (m$Ω$cm)$^{-1}$. However, contrary to the expectation of Hicks and Dresselhaus model about enhanced global thermoelectric properties due to the confinement of the metallic electrons, we find that the total power factor and thermoelectric figure of merit for reduced doping is too small for practical applications. The reason for this failure can be traced back on the electronic structure of the interfacial gas, which departs from the free electron behaviour on which the model was based. The evolution of the electronic structure, electrical conductivity, Seebeck coefficient, and power factor as a function of the chemical potential is explained by a simplified tight-binding model. We find that the electron gas in our system is composed by a pair of one dimensional electron gases orthogonal to each other. This reflects the fact the physical dimensionality of the electronic system can be even smaller than that of the spacial confinement of the carriers.