How do edge states position themselves in a quantum Hall graphene pn junction?

TL;DR

This paper investigates the spatial positioning of edge states in graphene quantum Hall pn junctions, revealing that their separation is primarily determined by sample geometry rather than exchange interactions, which challenges previous assumptions.

Contribution

It demonstrates that edge state separation in graphene pn junctions is governed by geometry, not exchange interaction strength, supported by numerical calculations.

Findings

Edge state separation is dictated by sample geometry.

Exchange interaction does not significantly influence edge state positioning.

Numerical models align with experimental geometries.

Abstract

Recent experiments have shown that electronic Mach-Zehnder interferometers of unprecedented fidelities could be built using a graphene pn junction in the quantum Hall regime. In these junctions, two different edge states corresponding to two different valley configurations are spatially separated and form the two arms of the interferometer. The observed separation, of several tens of nanometers, has been found to be abnormally high and thus associated to unrealistic values of the exchange interaction. In this work, we show that, although the separation is due to exchange interaction, its actual value is entirely governed by the sample geometry and independent of the value of the exchange splitting. Our analysis follows the lines of the classical work of Chklovski-Shklovskii- Glazman on electrostatically induced edge state reconstruction and includes quantitative numerical calculations in the experimental geometries.