Memory Function Representation for the Electrical Conductivity of Solids

TL;DR

This paper introduces a new formula for calculating the electrical conductivity of solids that incorporates relaxation, dissipation, and quantum coherence effects using a Mori memory function approach, improving practical evaluation methods.

Contribution

It presents a novel derivation of conductivity formula based on the Kubo formula and Mori memory functions, enabling better inclusion of dissipation effects in solid-state calculations.

Findings

Provides a practical method for conductivity evaluation with electronic-structure codes.

Avoids limitations of traditional Kubo formula in the thermodynamic limit.

Applicable to other transport coefficients and correlation functions.

Abstract

We derive a formula for the electrical conductivity of solids that includes relaxation, dissipation, and quantum coherence. The derivation is based on the Kubo formula, with a Mori memory function approach to include dissipation effects at all orders in the relaxation interaction. It offers a practical method to evaluate the conductivity with electronic-structure codes and avoids the complications and limitations of the Kubo formula in the thermodynamic limit. The derivation of our formula provides a method applicable to other transport coefficients and correlation functions.