Electronic Transport in Tunnel Junctions of Quantum Spin Hall Effect Topological Insulators

The present thesis aims to investigate the electronic transport of the helical states flowing at the edges of a 2D Topological Insulator (TI). A particular interest is devoted to the problem of electron tunnelling between helical edge states. This can for instance be realized with a set up where tunnelling is induced by a constriction etched in a quantum well of a Quantum Spin Hall Effect (QSHE) system. I investigate this problem by taking into account two types of tunnelling: spin preserving (it reverses the group velocity of the electron) and spin flipping (it flips the spin orientation) coupling coefficients. As first I analyse how the currents and the multi-terminal conductance depend on the physical features of the tunnel junction and how they can be controlled. I then consider the role of disorder in the tunnel junction and address to the analysis of the spin preserving transmission coefficients in the Anderson localization regime.