Dynamics and Hall-edge-state mixing of localized electrons in a two-channel Mach-Zehnder interferometer

We present a numerical study of a multichannel electronic Mach-Zehnder interferometer, based on magnetically-driven non-interacting edge states. The electron path is defined by a full-scale potential landscape on the two-dimensional electron gas at filling factor two, assuming initially only the first Landau level as filled. We tailor the two beam splitters with 50% interchannel mixing and measure Aharonov-Bohm oscillations in the transmission probability of the second channel. We perform time-dependent simulations by solving the electron Schrödinger equation through a parallel implementation of the split-step Fourier method and we describe the charge-carrier wave function as a Gaussian wave packet of edge states. We finally develop a simplified theoretical model to explain the features observed in the transmission probability and propose possible strategies to optimize gate performances.