First-principles treatments of electron transport properties for nanoscale junctions

We present an efficient and highly accurate calculation method to provide first-principles electronic structures, current flow under steady states, and electric conductance for a nanoscale junction attached to truly semi-infinite crystalline electrodes on both sides. This method is formulated by the real-space finite-difference approach within the framework of the density functional theory. In our formalism, a scattering wave function infinitely extending over the entire system can be determined by carrying out the wave-function matching based on a boundary-value problem near the boundaries of the transition region which intervenes between the two electrodes with bulklike potentials, and consequently, for each incident propagating wave, the scattering wave function is constructed from the Green's function matrix defined in the transition region and the ratio matrices whose matrix elements are the ratios of the bulk solutions on neighboring grid points in the respective electrodes. This scheme completely eliminates numerical instability caused by the appearance of exponentially growing and decaying evanescent waves. In order to demonstrate the general applicability of the method, the calculation of the conductance of a gold nanowire suspended between semi-infinite Au(100) electrodes is presented as an example. We find that the transition from a metallic conductance of the quantum unit ${(2e}^{2}/h)$ to an insulating one takes place as the nanowire is stretched.

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