Analogue of the Kubo Formula for Conductivity of Spatially Inhomogeneous Systems and Electric Fields

TL;DR

This paper generalizes the Kubo formula to calculate conductivity in spatially inhomogeneous systems and fields, relevant for quantum wells, wires, and dots, by deriving a tensor that accounts for inhomogeneity effects.

Contribution

It introduces a generalized Kubo formula for conductivity tensors in inhomogeneous systems, including electric field derivatives, applicable to quantum nanostructures.

Findings

Derived a generalized conductivity tensor for inhomogeneous systems.

Identified contributions from electric fields and their derivatives.

Applicable to semiconductor quantum wells, wires, and dots.

Abstract

The average of densities of currents and charges, induced by a weak electromagnetic field in spatially inhomogeneous are calculated at final temperatures. The Kubo formula for a conductivity tensor is generalized for spatially inhomogeneous systems and fields. The contributions containing electric fields and derivative from fields on coordinates are allocated. The Semiconductor quantum wells, wires and dots may be considered as spatially inhomogeneous systems.