First-principles calculations of transport coefficients in the Weyl semimetal TaAs

We study charge and heat transport from first principles in the topological Weyl semimetal TaAs. Electron-phonon coupling matrix elements are calculated using density-functional perturbation theory and used to derive the thermoelectric transport coefficients, including the electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and the Peltier coefficient. We compare the self-energy and momentum-relaxation-time approximations to the iterative solution of the Boltzmann transport equation, finding that they give similar results for TaAs provided the chemical potential is treated accurately. We derive a second equation in the iterative method to solve for transport under thermal gradients. Interestingly, the Onsager reciprocity between $S$ and $\mathrm{\ensuremath{\Pi}}$ is no longer imposed, allowing us to treat systems that break time-reversal symmetry, in particular, magnetic materials. We compare our results with available experimental data for TaAs: the agreement is excellent for ${\ensuremath{\sigma}}_{xx}$, while ${\ensuremath{\sigma}}_{zz}$ is overestimated, probably caused by differences in experimental carrier concentrations. The Seebeck coefficient is of the same order of magnitude in theory and in experiments, and we find that its low-$T$ behavior also strongly depends on the doping level.