The Kubo-type Formula for Conductivity of Spatially Inhomogeneous Systems

TL;DR

This paper derives a Kubo-type formula for electrical conductivity in spatially inhomogeneous systems, accounting for temperature effects and separating current densities into parts dependent on electric fields and their derivatives.

Contribution

It provides a new theoretical framework for calculating conductivity in inhomogeneous systems like quantum wells, wires, and dots, considering finite temperature effects.

Findings

Derived expressions for current and charge densities in inhomogeneous systems.

Separated average current into basic and additional parts based on electric field derivatives.

Applicable to semiconductor nanostructures such as quantum wells, wires, and dots.

Abstract

The expressions for average densities of currents and charges induced by a weak electromagnetic field in spatially inhomogeneous systems are obtained. The case of finite temperatures is considered. It is shown that average values are separated into "basic" and "additional" parts. The former depends on electric fields, and the latter depends on derivatives of electric fields on coordinates. Semiconductor quantum wells, wires or dots may be considered as spatially inhomogeneous systems.