DC Conductance of Molecular Wires

TL;DR

This paper develops a theoretical framework for understanding the dc conductance of molecular wires, deriving exact expressions and analyzing the effects of chain length and contact properties, with numerical illustrations.

Contribution

It introduces a formal exact expression for adiabatic conductance within Time Dependent Current-Density Functional Theory and analyzes its asymptotic behavior for long molecular chains.

Findings

Exact asymptotic conductance behavior derived for long chains

Exponential decay of conductance in insulating chains

Contact properties significantly influence conductance amplitudes

Abstract

Inspired by the work of Kamenev and Kohn, we present a general discussion of the two-terminal dc conductance of molecular devices within the framework of Time Dependent Current-Density Functional Theory. We derive a formally exact expression for the adiabatic conductance and we discuss the dynamical corrections. For junctions made of long molecular chains that can be either metallic or insulating, we derive the exact asymptotic behavior of the adiabatic conductance as a function of the chain's length. Our results follow from the analytic structure of the bands of a periodic molecular chain and a compact expression for the Green's functions. In the case of an insulating chain, not only do we obtain the exponentially decaying factors, but also the corresponding amplitudes, which depend very sensitively on the electronic properties of the contacts. We illustrate the theory by a numerical study of a simple insulating structure connected to two metallic jellium leads.