Simulations of interference effects in gated two-dimensional ballistic electron systems

We present detailed simulations addressing recent electronic interference experiments, where a metallic gate is used to locally modify the Fermi wavelength of the charge carriers. Our numerical calculations are based on a solution of the one-particle Schrödinger equation for a realistic model of the actual sample geometry, including a Poisson equation-based determination of the potential due to the gate. The conductance is determined with the multiprobe Landauer-Büttiker formula, and in general we find conductance vs gate voltage characteristics, which closely resemble the experimental traces. A detailed examination based on quantum-mechanical streamlines suggests that the simple one-dimensional semiclassical model often used to describe the experiments has only a limited range of validity, and that certain “unexpected” periodicities should not be assigned any particular significance, they arise due to the complicated multiple scattering processes occurring in certain sample geometries.