Electronic thermal conductivity as derived by density functional theory

Reliable evaluation of the lattice thermal conductivity is of importance for optimizing the figure-of-merit of thermoelectric materials. Traditionally, when deriving the phonon mediated thermal conductivity $\kappa_{ph} = \kappa - \kappa_{el}$ from the measured total thermal conductivity $\kappa$ the constant Lorenz number $L_0$ of the Wiedemann-Franz law \mbox{$\mathbf{\kappa_{el}}=T L_0 \sigma$} is chosen. The present study demonstrates that this procedure is not reliable when the Seebeck coefficient $|S|$ becomes large which is exactly the case for a thermoelectric material of interest. Another approximation using $L_0-S^2$, which seem to work better for medium values of $S^2$ also fails when $S^2$ becomes large, as is the case when the system becomes semiconducting/insulating. For a reliable estimation of $\kappa_{el}$ it is proposed, that a full first-principles calculations by combining density functional theory with Boltzmann's transport theory has to be made. For the present study such an approach was chosen for investigating the clathrate type-I compound Ba$_8$Au$_{6-x}$Ge$_{40+x}$ for a series of dopings or compositions $x$. For a doping of $0.8$ electrons corresponding to $x=0.27$ the calculated temperature dependent Seebeck coefficient agrees well with recent experiments corroborating the validity of the density functional theory approach.