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Real space finite difference method for conductance calculations

Petr A. Khomyakov·Geert Brocks
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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.

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Petr A. Khomyakov, Geert Brocks. 2004-11-10. Real space finite difference method for conductance calculations. https://doi.org/10.1103/physrevb.70.195402

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