Conductance and polarization in quantum junctions

TL;DR

This paper revisits the theoretical expression for conductance in nanostructures, linking it to the system's polarization and enabling direct ab-initio calculations without special boundary conditions.

Contribution

It provides a new formula for conductance based on polarization, facilitating ab-initio calculations for finite systems without transport boundary conditions.

Findings

Conductance is related to the Drude singularity in conductivity.

A formula for conductance in terms of polarization is derived.

Conductance can be computed from finite system calculations.

Abstract

We revisit the expression for the conductance of a general nanostructure -- such as a quantum point contact -- as obtained from the linear response theory. We show that the conductance represents the strength of the Drude singularity in the conductivity $\sigma(k,k';i\omega \to 0)$. Using the equation of continuity for electric charge we obtain a formula for conductance in terms of polarization of the system. This identification can be used for direct calculation of the conductance for systems of interest even at the {\it ab-initio} level. In particular, we show that one can evaluate the conductance from calculations for a finite system without the need for special ``transport'' boundary conditions.