# On the delta function broadening in the Kubo-Greenwood equation

## TL;DR

This paper presents a new nonlinear extrapolation method for calculating DC electrical conductivity from first principles, reducing finite-size effects and ambiguities in the Kubo-Greenwood approach.

## Contribution

A novel nonlinear extrapolation scheme for the Kubo-Greenwood equation that improves accuracy in finite systems and aligns well with Landauer-based methods.

## Key findings

- Method predicts conductivity close to the thermodynamic limit for small systems.
- Overcomes common ambiguities in finite-system conductivity calculations.
- Results are consistent with Landauer equation-based approaches.

## Abstract

Understanding DC electrical conductivity is crucial for the study of materials. Macroscopic DC conductivity can be calculated from first principles using the Kubo-Greenwood equation. The procedure involves finding the thermodynamic limit of the current response to an electric field that is slowly switched on, and then taking the limit of the switching rate to zero. We introduce a nonlinear extrapolation procedure executed in systems with periodic boundary conditions, which predicts conductivity close to the thermodynamic limit even for very small systems. The scheme also overcomes a large part of the usual ambiguities of the DC conductivity definition for finite systems. We numerically compare our method to the Landauer equation-based approach and find both techniques to be consistent with each other.