Theory of electron transport through single molecules

Understanding the electronic transport properties of junctions consisting of a scattering region such as a nanoscale region or molecule connected two electrodes is of fundamental interest. The theoretical work carried out in this thesis presents the electrical properties of two different types of two terminal nanojunctions: one dealing with gold electrodes which form gold | molecule | gold structures and the other with graphene sheet electrodes forming graphene | molecule | graphene junctions. Chapter 2 presents an introduction to the theoretical concept of density functional theory (DFT) and its implemented in this thesis, via the SIESTA code. The second tool is the quantum transport code Gollum which is based on Green’s function-based scattering theory. To introduce this technique in Chapter 3, I present solutions of Green’s functions for infinite and semi-infinite chains and the transmission coefficient equation which forms the theoretical basis of this code. The first original topic I investigate in chapter 4 addresses anti-resonance features of destructive quantum interference in single-molecule thiophene junctions. This study is a collaborative work with experimentalists in Xiamen University, China. Controlling the electrical conductance and in particular the occurrence of quantum interference in single-molecule junctions through gating effects, has potential for the realization of high-performance functional molecular devices. In this work, I demonstrate the underling science behind the tunable electronic structure of thiophene-based molecular junctions using electrochemically-gated. This is explained by destructive quantum interference (DQI) features in these molecules. Using electrochemical gating the Fermi energy is moved towards the DQI feature leading to two orders of magnitude changes in electrical conductance. This is a promising strategy for obtaining improved in-situ control over the electrical performance of interference-based molecular devices. In the second original work in chapter 5, I investigate quantum transport across graphene nanogaps bridged by carbon atomic chains. To realise the technological potential of electroburnt graphene junctions, there is a need to understand how their electronic and spintronic properties are controlled by edge terminations and by the carbon chains bridging their gaps. Here I study a wide variety of such structures and find that junctions with zigzag edges tend to have lower conductances than those with armchair edges, while junctions with ferromagnetically aligned edges have a higher transmission than anti-ferromagnetically aligned edges, because ferromagnetic alignment tends to increase the transmission of one of the spins. I also find that nanogaps formed from graphene with saturated edges tend to have a lower conductance than unsaturated edges, five-membered saturated terminal rings with saturated edges are poor conductors, while five- membered terminal rings (saturated or unsaturated) with unsaturated edges are highly conducting. In addition I find that junctions bridged by even-numbered chains of carbon atoms tend to have a lower conductance than those bridged by odd-numbered atomic chains, while chains attached to six-membered terminal rings and unsaturated edges tend to have a lower conductance than those attached to five-membered terminal rings and unsaturated edges