Mesoscopic Electronic Transport through Ring-Shaped Nano-Structures

Abstract

In this thesis we investigate the mesoscopic electronic transport properties of ring-shaped nano-structures connected to two leads at low temperatures in the wideband limit. In particular we consider the current due to a constant chemical potential bias and the linear response DC conductance. This is done in the Landauer-Büttiker formalism using equilibrium Green function techniques to compute transmission amplitudes.

The thesis starts with an introduction to second quantisation and derivations of the aforementioned formalism and techniques. We then move on to apply the theory to the specific cases of a single site impurity and an asymmetric four site ring.

We find that the transmission amplitude as a function of energy is sharply peaked around energy levels of the nano-structure, but has finite width and a small shift in resonance due to effective broadening by the coupling between leads and nano-structure. In the four site ring we also find signs of self-interference effects when the energy of the incoming electron is exactly half of the on-site energy.

We conclude with a discussion of possible generalisations of our model, a schematic overview of the necessary techniques, and areas of current research.