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We analyze the current and the shot-noise of an electron interferometer madeof the helical edge states of a two-dimensional topological insulator withinthe framework of non-equilibrium Green's functions formalism. We study indetail setups with a single and with two quantum point contacts inducingscattering between the different edge states. We consider processes preservingthe spin as well as the effect of spin-flip scattering. In the case of a singlequantum point contact, a simple test based on the shot-noise measurement isproposed to quantify the strength of the spin-flip scattering. In the case oftwo single point contacts with the additional ingredient of gate voltagesapplied within a finite-size region at the top and bottom edges of the sample,we identify two type of interference processes in the behavior of the currentsand the noise. One of such processes is analogous to that taking place in aFabry-P\'erot interferometer, while the second one corresponds to aconfiguration similar to a Mach-Zehnder interferometer. In the helicalinterferometer these two processes compete.

Transport phenomena in helical edge states interferometers. A Green's function approach