  Electric-field-controlled charge transport is a key concept of modern
computers, embodied namely in field effect transistors. The metallic gate
voltage controls charge population, thus it is possible to define logical
elements which are the key to computational processes. Here, we investigate a
similar system defined by metallic gates inducing quasi-one-dimensional
transport channels on a high-mobility electron system in the presence of a
strong perpendicular magnetic field. Firstly, we solve the three-dimensional
Poisson equation, self-consistently imposing relevant boundary conditions, and
use the output as an initial condition to calculate charge density and
potential distribution in the plane of a two-dimensional electron system, in
the presence of an external magnetic field. Subsequently, we impose an external
current and obtain the spatial distribution of the transport charges,
considering various magnetic field and gate voltage strengths at sufficiently
low (< 10 Kelvin) temperatures. We show that magnetic field breaks the spatial
symmetry of the current distribution, whereas voltage applied to metallic gates
determines the scattering processes.
