Finite size effects on transport coefficients for models of atomic wires coupled to phonons

TL;DR

This paper investigates how the size and lateral coupling of atomic wire models influence electronic diffusion, using a linear Boltzmann framework to reveal significant dependencies relevant for nanoscale device applications.

Contribution

It introduces a numerically feasible collision term and Boltzmann equation approach to analyze size effects on transport in coupled atomic wires.

Findings

Diffusion coefficients depend significantly on wire width and lateral coupling.

Intermediate coupling regimes show non-trivial diffusion behavior.

Results suggest potential for atomic wires in electronic switching devices.

Abstract

We consider models of quasi-1-d, planar atomic wires consisting of several, laterally coupled rows of atoms, with mutually non-interacting electrons. This electronic wire system is coupled to phonons, corresponding, e.g., to some substrate. We aim at computing diffusion coefficients in dependence on the wire widths and the lateral coupling. To this end we firstly construct a numerically manageable linear collision term for the dynamics of the electronic occupation numbers by following a certain projection operator approach. By means of this collision term we set up a linear Boltzmann equation. A formula for extracting diffusion coefficients from such Boltzmann equations is given. We find in the regime of a few atomic rows and intermediate lateral coupling a significant and non-trivial dependence of the diffusion coefficient on both, the width and the lateral coupling. These results, in principle, suggest the possible applicability of such atomic wires as electronic devices, such as, e.g., switches.