Non-perturbative $ab$ $initio$ approach for calculating the electrical conductivity of a liquid metal

TL;DR

This paper introduces a non-perturbative ab initio method for calculating the electrical conductivity of liquid metals, explicitly accounting for electron-ion interactions via electron-phonon coupling, and demonstrates its effectiveness on liquid sodium.

Contribution

The paper develops a fully ab initio, non-perturbative approach based on the Kubo formula and electron-phonon coupling theory, improving accuracy over empirical methods.

Findings

Accurately predicts electrical conductivity of liquid sodium

Shows good agreement with experimental data

Provides an efficient, rigorous method applicable to various metallic liquids

Abstract

We propose a non-perturbative $ab$ $initio$ approach to calculate the electrical conductivity of a liquid metal. Our approach is based on the Kubo formula and the theory of electron-phonon coupling (EPC), and unlike the conventional empirical approach based on the Kubo-Greenwood formula, fully takes into account the effect of coupling between electrons and moving ions. We show that the electrical conductivity at high temperature is determined by an EPC parameter $\lambda_{\mathrm{tr}}$, which can be inferred, non-perturbatively, from the correlation of electron scattering matrices induced by ions. The latter can be evaluated in a molecular dynamics simulation. Based on the density-functional theory and pseudopotential methods, we implement the approach in an $ab$ $initio$ manner. We apply it to liquid sodium and obtain results in good agreement with experiments. This approach is efficient and based on a rigorous theory, suitable for applying to general metallic liquid systems.