The Characterisation and Manipulation of Novel Topological Phases of Matter

This thesis contains work in three areas. The works are presented chronologically starting with my work on the decomposition and measurement of Chern numbers in four component topological insulators and superconductors. This is followed by the work done in the discovery and analysis of four new models of topological superconductivity in three spatial dimensions. Lastly, I present the work done on dimensional reduction through localisation of Majorana modes at the boundary of topological superconductors in three spatial dimensions. Each work is presented in a separate chapter.