Real-space finite-difference method for conductance calculations

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 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.