Phonon limited electronic transport in Pb

We present a fully ab initio based scheme to compute electronic transport properties, i.e. the electrical conductivity σ and thermopower S, in the presence of electron–phonon interaction. We explicitly investigate the $k\text{-dependent}$ structure of the Éliashberg spectral function, the coupling strength, the linewidth and the relaxation time τ. We obtain a state-dependent τ and show its necessity to reproduce the increased thermopower for temperatures below the Debye temperature, without accounting for the phonon-drag effect. Despite the detailed investigations of various $k$- and $q$-dependencies, the presented scheme can be easily applied to more complicated systems. (paper)