Quantum Transport in Topological Insulator Nanowires

Sammanfattning: Three-dimensional topological insulators are materials that have a bulk band gap like a traditional insulator, but which hold topologically protected conducting surface states. In this thesis we present a numerical analysis of the surface states of topological insulator nanowires in the tight-binding approximation. We carry out the calculations at zero temperature under the presence of coaxial and perpendicular magnetic fields using Dirac Hamiltonians to model the surface. The results are obtained using Kwant, a Python package first developed in 2014 by Groth et al. for the purpose of aiding in the creation of quantum transport simulations in tight-binding models. The main focus is the self-contained and complete study of the behaviour of the conductance in clean and disordered systems, as well as to serve as an introduction to Kwant. We first study the main properties of quantum transport in mesoscopic systems, and present the scattering problem in the tight-binding approximation, which is the one treated in Kwant. We review the main properties of topological insulators, as well as the history of their discovery. We then present Kwant in detail, and illustrate its inner workings by considering the example of a clean wire. We study clean wires and show the existence of the perfectly transmitted mode under a coaxial magnetic field, obtain the quantisation of the conductance expected from the Laundauer-Büttiker formalism, and recover Fabry-Pérot oscillations when considering highly doped leads. We discuss how disorder can be introduced in our systems to simulate more realistic models, analyse its effects in the period of the conductance oscillations, and recover the robustness to disorder of the perfectly transmitted mode. Finally, we comment on how this thesis can be expanded to cover a wider range of systems and phenomena.