Basic concepts in single-molecule electronics

TL;DR

This tutorial explains the fundamental theoretical concepts of phase-coherent electron transport in single molecules, emphasizing quantum interference effects and providing practical tools for exploration.

Contribution

It introduces key quantum interference phenomena in single-molecule electronics and offers a MATLAB tool for studying these effects in simple models.

Findings

Quantum interference significantly influences electron transport in molecules.

The provided MATLAB code enables exploration of QI effects in multi-branched structures.

Discussion of the strengths and limitations of density functional theory in transport modeling.

Abstract

This tutorial outlines the basic theoretical concepts and tools which underpin the fundamentals of phase-coherent electron transport through single molecules. The key quantity of interest is the transmission coefficient T(E), which yields the electrical conductance, current-voltage relations, the thermopower S and the thermoelectric figure of merit ZT of single-molecule devices. Since T(E) is strongly affected by quantum interference (QI), three manifestations of QI in single-molecules are discussed, namely Mach-Zehnder interferometry, Breit-Wigner resonances and Fano resonances. A simple MATLAB code is provided, which allows the novice reader to explore QI in multi-branched structures described by a tight-binding (Huckel) Hamiltonian. More generally, the strengths and limitations of materials-specific transport modelling based on density functional theory are discussed.