Electrical resistance: an atomistic view

TL;DR

This tutorial provides an atomistic perspective on electrical resistance, explaining key concepts from energy levels to quantum effects, and introduces the NEGF formalism for nanoscale electron transport.

Contribution

It offers a comprehensive, accessible overview of nanoscale electrical conduction, emphasizing a bottom-up approach without heavy quantum mechanics, and introduces the NEGF formalism with practical MATLAB examples.

Findings

Maximum conductance per level is limited to q^2/h due to broadening effects.

Shape changes in potential profiles can induce rectification in current-voltage characteristics.

Many molecular electronic effects can be understood through simple models.

Abstract

This tutorial article presents a "bottom-up" view of electrical resistance starting from something really small, like a molecule, and then discussing the issues that arises as we move to bigger conductors. Remarkably, no serious quantum mechanics is needed to understand electrical conduction through something really small, except for unusual things like the Kondo effect that are seen only for a special range of parameters. This article starts with energy level diagrams (section 2), shows that the broadening that accompanies coupling limits the conductance to a maximum of q^2/h per level (sections 3, 4), describes how a change in the shape of the self-consistent potential profile can turn a symmetric current-voltage characteristic into a rectifying one (sections 5, 6), shows that many interesting effects in molecular electronics can be understood in terms of a simple model (section 7), introduces the non-equilibrium Green function (NEGF) formalism as a sophisticated version of this simple model with ordinary numbers replaced by appropriate matrices (section 8) and ends with a personal view of unsolved problems in the field of nanoscale electron transport (section 9). Appendix A discusses the Coulomb blockade regime of transport, while appendix B presents a formal derivation of the NEGF equations. MATLAB codes for numerical examples are listed in the appendix C.