Full electrical control of charge and spin conductance through interferometry of edge states in topological insulators

We investigate electron interferometry of edge states in topological insulators. We show that when interboundary coupling is induced at two quantum point contacts of a four terminal setup, both Fabry-Perot-like and Aharonov-Bohm-like loop processes arise. These underlying interference effects lead to a full electrically controllable system, where the magnitude of charge and spin linear conductances can be tuned by gate voltages, without applying magnetic fields. In particular we find that, under appropriate conditions, interboundary coupling can lead to negative values of the conductance. Furthermore, the setup also allows to selectively generate pure charge or pure spin currents by choosing the voltage bias configuration.