Superconducting nanowires: the role of topology and morphology

In this thesis we explore two unique low dimensional systems where this confinement induces novel behaviour of the electrons which travel through them. These systems are; nanowires (quasi 1-dimensional wires) made from granular aluminium thin films (films which consist of no more than a few layers, making them essentially two-dimensional), and 1-dimensional superconductors that manifest Majorana fermions at their boundaries.

We generate a computational model which emulates the structure of granular aluminium nanowires. This model consists of regions of crystalline aluminium surrounded by amorphous aluminium-oxide. The electronic properties of these materials are calculated using a graph theory approach to the network of interconnected crystalline aluminium grains. The effect of applying a current across such materials to induce intrinsic electromigration and effectively condition the wires, is also investigated.

The study of Majorana fermions begins with the Kitaev nanowire, a 1D p-wave superconductor which can host isolated Majorana fermions at its boundaries. This forms the basis of the Aharonov-Bohm ring, which is a composite of two Kitaev nanowires joined into a ring geometry. In the presence of an applied magnetic field, Aharonov-Bohm interference is induced in the ring, and the interplay between this effect and the presence of Majorana fermions was investigated. It is found from the computational models that zero energy conductance channels due the presence of Majorana fermions are robust against Aharonov-Bohm interference.