Nanoscale conductors, such as ultrasmall molecular wires, allow us to test our understanding of fundamental non-equilibrium transport physics, as well as explore new device possibilities. I will start with a generic treatment of current flow through a single energy level, and then generalize to include realistic bandstructure models and a full quantum kinetic theory of current flow. This allows us to interpolate between semi-empirical models that provide quick physical insights, and ‘first-principles’ models with no adjustable parameters. Using this formalism, we can quantitatively explain various experimental features and fundamental performance limits of molecular electronics.
In the above treatments, we treat electrons as weakly interacting, operating in the ‘mean field limit’. However, ultra-short molecules are unique in that they often possess large electronic and vibronic correlation energies with prominent experimental signatures. Strong correlation requires a completely different transport approach in the molecular many-body Fock space that accounts for non-perturbative interactions. I will show that many features such as negative differential resistance, Coulomb Blockade, hysteretic switching and random-telegraph noise can be understood in terms of
the dynamics of such many-body levels and their state filling under bias. A lot of the applications of nanoelectronics could involve bridging the mean-field and strongly correlated regimes, where the theory becomes particularly challenging. For instance, the tunable quantum coupling of current flow
in present day silicon transistors with engineered molecular adsorbates could lead to devices
operating on completely novel principles.