Self-consistent calculation of the electron distribution near a quantum point contact in the integer quantum Hall effect

In this work we implement the self-consistent Thomas-Fermi-Poisson approach to a homogeneous two-dimensional electron system. We compute the electrostatic potential produced inside a semiconductor structure by a quantum point contact (QPC) placed at the surface of the semiconductor and biased with appropriate voltages. The model is based on a semianalytical solution of the Laplace equation. Starting from the calculated confining potential, the self-consistent (screened) potential and the electron densities are calculated for finite temperature and magnetic field. We observe that there are mainly three characteristic rearrangements of the incompressible edge states which will determine the current distribution near a QPC.