Resistance of a Molecule
  In recent years, several experimental groups have reported measurements of the current-voltage (I-V) characteristics of individual or small numbers of molecules. Our purpose in this chapter is to provide an intuitive explanation for the observed I-V characteristics using simple models to illustrate the basic physics. In contrast to the MOSFET, whose I-V is largely dominated by classical electrostatics, the I-V characteristics of molecules is determined by a more interesting interplay between nineteenth century physics (electrostatics) and twentieth century physics (quantum transport) and it is important to do justice to both aspects.   We start with a qualitative discussion of the main factors affecting the I-V characteristics of molecular conductors, using a simple toy model to illustrate their role. Including the effects of: (1) Shift in the energy level due to charging effects and (2) broadening of the energy levels due to the coupling to the two contacts we obtain realistic I-V plots, even though the toy model assumes that conduction takes place independently through individual molecular levels. In general, however, the full non-equilibrium Green's function (NEGF) formalism is needed. Here, we describe the NEGF formalism as a generalized version of the one-level model. This formalism provides a convenient framework for describing quantum transport and can be used in conjunction with ab initio or semi-empirical Hamiltonians. A simple semi-empirical model for a gold wire serves to illustrate the full NEGF formalism. This example is particularly instructive because it shows the lowest possible "Resistance of a 'Molecule'" per channel. 
Magnus Paulsson, Ferdows Zahid and Supriyo Datta