Real space finite difference method for conductance calculations

TL;DR

This paper introduces a real space finite difference method for calculating electronic conductance in quantum wires and tunnel junctions, emphasizing high accuracy and computational efficiency through high order approximations.

Contribution

It presents a novel wave function matching approach using high order finite difference representations for conductance calculations in quantum transport.

Findings

High order finite difference methods improve accuracy.

The method is effective for sodium atomic wires.

Computational costs are moderate for high accuracy.

Abstract

We present a general method for calculating coherent electronic transport in quantum wires and tunnel junctions. It is based upon a real space high order finite difference representation of the single particle Hamiltonian and wave functions. Landauer's formula is used to express the conductance as a scattering problem. Dividing space into a scattering region and left and right ideal electrode regions, this problem is solved by wave function matching (WFM) in the boundary zones connecting these regions. The method is tested on a model tunnel junction and applied to sodium atomic wires. In particular, we show that using a high order finite difference approximation of the kinetic energy operator leads to a high accuracy at moderate computational costs.