Collective Edge Modes of a Quantum Hall Ferromagnet in Graphene

TL;DR

This paper develops an effective field-theoretical model for one-dimensional collective modes at domain walls in quantum Hall ferromagnets in graphene, revealing how coupling to a 2D environment influences the system.

Contribution

It introduces a novel model linking domain wall modes in graphene's quantum Hall ferromagnet to a ferromagnetic spin ladder and maps it to an antiferromagnetic chain.

Findings

Coupling induces anisotropy in exchange interactions.

The spin ladder can be mapped to an antiferromagnetic chain.

Provides insights into edge mode behavior in graphene quantum Hall systems.

Abstract

We derive an effective field-theoretical model for the one-dimensional collective mode associated with a domain wall in a quantum Hall ferromagnetic state, as realized in confined graphene systems at zero filling. To this end, we consider the coupling of a quantum spin ladder forming near a kink in the Zeeman field to the spin fluctuations of a neighboring spin polarized two-dimensional environment. It is shown, in particular, that such coupling may induce anisotropy of the exchange coupling in the legs of the ladder. Furthermore, we demonstrate that the resulting ferromagnetic spin-1/2 ladder, subject to a kinked magnetic field, can be mapped to an antiferromagnetic spin chain at zero magnetic field.