Inferring the transport properties of edge-states formed at quantum Hall based Aharonov-Bohm interferometers theoretically

Here, we report on our results where self-consistent calculations are performed to investigate the interference conditions, numerically. We employ the successful 4${}^{th}$ order grid technique to obtain the actual electrostatic quantities of the samples used at the quantum Hall based Aharonov-Bohm interferometers. By knowing the electron density distribution we calculate the spatial distribution of the edge-states, which are considered as mono-energetic current channels. Our results are in accord with the experimental findings concerning the electron density distribution. Finally, we also comment on the “optimized” sample design in which highest visibility oscillations can be measured.