2D electronic states in 1D nanowires and 3D topological insulators

The behaviour of electrons in crystals underpins the technology that defines our modern-day information society. Confining electrons to only two or even a single dimension leads to unexpected and strange behaviour, whose understanding and control is an active field of physics. In this thesis, data from direct experimental probes of the behaviour of electrons in 1D metallic nanowire systems and 2D states at the surface of 3D topological insulators (TIs) are discussed. In both these systems, the interesting physics takes place at the interface - for the nanowires the boundary between the substrate and deposited metal adatoms; for the TIs the surface dividing the topologically non-trivial bulk and the topologically trivial world outside the crystal. The Au/Ge(110) and Au/Ge(100) nanowire systems were studied. The former is new, and our experiments show the surface electronic surface to be 2D, not 1D. The well-known Au/Ge(100) system has been proposed to harbour Tomonaga-Luttinger-liquid-like 1D states at the surface, yet our comprehensive combination of ARPES, STM/S and theory shows that although the relevant electronic states are interestingly incoherent, they are 2D, not 1D. The second focus is on the tetradymite family of 3D TIs. The topological surface states of these materials are discussed as candidates for future spintronics technologies. Detailed investigations of the surface electronic structure of these materials are presented and numerous control pathways over the electronic band structure at the surface are highlighted, such as using illumination to tune the binding energy of the Dirac point, removing unwanted bulk bands.