Transport calculations in complex materials: A comparison of the Kubo formula, the Kubo-Greenwood formula and the microscopic response method

TL;DR

This paper compares three methods for calculating transport properties in complex materials, demonstrating that the microscopic response method aligns with established formulas and simplifies under certain conditions.

Contribution

The paper introduces the microscopic response method (MRM) for conductivity calculations and proves its equivalence to the Kubo formula, simplifying to the Kubo-Greenwood formula in specific cases.

Findings

MRM is equivalent to the Kubo formula for canonical ensembles.

MRM reduces to the Kubo-Greenwood formula when carrier density gradients are small.

The methods are validated for complex systems with disorder.

Abstract

Recently we have introduced the microscopic response method (MRM) to compute the conductivity and Hall mobility for complex system with topological and thermal disorder, which is more convenient than the Kubo formula. We prove that for a canonical ensemble the MRM leads to the same expression as the Kubo formula. When the gradient of carrier density is small, the MRM reduces to the widely used Kubo-Greenwood formula.