Interactions on the edge of a quantum spin Hall insulator

Abstract: Effects from electron-electron interactions on the edge of a quantum spin Hall insulator are studied using bosonisation and renormalisation group methods. First, a quantum spin Hall device with a point contact connecting two of its edges is considered. The interaction strength necessary to support the tunnelling of a spin current through the point contact is calculated. Adding a voltage to drive the tunnelling current, the conductance in the point contact is also calculated. It is found that the tunnelling current scales with the temperature and voltage in a way that depends nonlinearly on the interaction strength. The effect of a spatially disordered Rashba interaction is also studied. The edge modes are found to localise for sufficiently large Rashba and electron interaction strengths. A periodically modulated Rashba coupling, with a single Fourier mode, is found to make the edge insulating even at lower strengths of the electron-electron interaction. The thesis also contains a brief introduction to the subject of topological insulators, with focus on the quantum spin Hall effect.