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

TL;DR

This paper uses self-consistent numerical calculations to analyze the interference conditions and edge-state transport properties in quantum Hall Aharonov-Bohm interferometers, aligning with experimental electron density data.

Contribution

It introduces a detailed numerical approach employing a 4th order grid technique to accurately model electrostatic and edge-state distributions in quantum Hall interferometers.

Findings

Results agree with experimental electron density distributions.

Identifies optimal sample design for maximum interference visibility.

Provides insights into transport properties of edge states.

Abstract

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.