# Phonon limited thermoelectric transport in Pb

## TL;DR

This paper introduces an ab initio method to accurately compute thermoelectric transport properties considering electron-phonon interactions, capturing temperature-dependent effects without phonon-drag.

## Contribution

The study develops a detailed ab initio scheme to compute transport properties with state-dependent relaxation times, improving accuracy over previous models.

## Key findings

- State-dependent relaxation time is essential for accurate thermopower prediction.
- The scheme successfully reproduces increased thermopower below Debye temperature.
- Method is adaptable to complex systems.

## Abstract

We present a fully ab initio based scheme to compute transport properties, i.e. the electrical conductivity {\sigma} and thermopower S, in the presence of electron-phonon interaction. Therefore, we explicitly investigate the k-dependent structure of the Eliashberg spectral function , the coupling strength, the linewidth and the relaxation time {\tau}. We obtain a state-dependent {\tau} and show its necessity to reproduce the increased thermopower at 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.