Edge state distribution in an Aharonov-Bohm electron interferometer in the integer quantum Hall regime

In this study we analyze the density distributions of the two dimensional electron system for an experimental geometry which is topologically equivalent of an Aharonov-Bohm interferometer in three dimensions in the quantum Hall regime and obtain the spatial distribution of the edge states. We employ the Thomas-Fermi approximation in our analysis and solve the Poisson equation in three dimensional using a multi grid technique. Also we obtain the distribution of incompressible strips for a wide range of magnetic fields strengths and comment on their relation with experimental results in literature.