An embedding potential definition of channel functions

TL;DR

This paper introduces a new way to define conduction channels using the imaginary part of the embedding potential, linking eigenfunctions to Bloch states and simplifying transmission calculations.

Contribution

It presents a novel channel function definition based on the embedding potential's imaginary part, connecting eigenfunctions to Bloch states at interfaces.

Findings

Eigenfunctions are orthogonal and define conduction channels.

Relationship established between eigenfunctions and Bloch states.

Simplified derivation of total transmission using new channel functions.

Abstract

We show that the imaginary part of the embedding potential, a generalised logarithmic derivative, defined over the interface between an electrical lead and some conductor, has orthogonal eigenfunctions which define conduction channels into and out of the lead. In the case of an infinitely extended interface we establish the relationship between these eigenfunctions and the Bloch states evaluated over the interface. Using the new channel functions, a well-known result for the total transmission through the conductor system is simply derived.