The self-consistent calculation of the edge states at quantum Hall effect (QHE) based Mach-Zehnder interferometers (MZI)

TL;DR

This paper uses a self-consistent Hartree model to analyze the spatial distribution of edge states in quantum Hall effect-based Mach-Zehnder interferometers, revealing conditions for observable interference patterns.

Contribution

It introduces a self-consistent calculation method for edge states in QHE MZIs, highlighting the impact of electron interactions and magnetic field on interference.

Findings

Interference occurs when two incompressible edge states merge or are close near quantum point contacts.

Being in a quantized Hall plateau does not ensure observable interference.

The spatial distribution of edge states is sensitive to magnetic field variations.

Abstract

The spatial distribution of the incompressible edge states (IES) is obtained for a geometry which is topologically equivalent to an electronic Mach-Zehnder interferometer, taking into account the electron-electron interactions within a Hartree type self-consistent model. The magnetic field dependence of these IES is investigated and it is found that an interference pattern may be observed if two IES merge or come very close, near the quantum point contacts. Our calculations demonstrate that, being in a quantized Hall plateau does not guarantee observing the interference behavior.