Mode-matching technique for transmission calculations in electron waveguides at high magnetic fields

In this paper we present a mode-matching technique to study the transmission coefficient of mesoscopic devices such as electron waveguides in the presence of high magnetic fields for different situations. A detailed study of the difficulties arising due to the presence of the magnetic field is given and the differences with the zero-magnetic-field case are stressed. We apply this technique to calculating the transmission at nonzero magnetic field of two completely different systems: (a) a quantum box built up on a quantum wire (or electron waveguide) by means of two barriers and (b) a multiply bent quantum wire, i.e., a wire with changes in the guiding direction. In the former case, we analyze the so-called Coulomb-blockade and Aharanov-Bohm regimes, and in the latter one we focus on the realistic case of soft, circular bends joining the different sections of the wire.