Spin Superfluidity in the $\nu=0$ Quantum Hall State of Graphene

TL;DR

This paper proposes a method to detect spin superfluidity in the $ u=0$ quantum Hall state of graphene, suggesting that a dynamic Nél vector texture mediates nearly dissipationless spin transport, supporting the canted antiferromagnet model.

Contribution

It introduces a theoretical framework for observing spin superfluidity in graphene's quantum Hall state via a two-terminal setup, combining kinetic theory and Landau-Lifshitz-Gilbert modeling.

Findings

Prediction of nearly dissipationless spin transport mediated by Nél vector textures.

Proposal of a two-terminal experimental setup for detecting spin superfluidity.

Support for the canted antiferromagnet scenario in the $ u=0$ quantum Hall state.

Abstract

A proposal to detect the purported canted antiferromagnet order for the $\nu=0$ quantum Hall state of graphene based on a two-terminal spin transport setup is theoretically discussed. In the presence of a magnetic field normal to the graphene plane, a dynamic and inhomogeneous texture of the N\'eel vector lying within the plane should mediate (nearly dissipationless) superfluid transport of spin angular momentum polarized along the $z$ axis, which could serve as a strong support for the canted antiferromagnet scenario. Spin injection and detection can be achieved by coupling two spin-polarized edge channels of the $|\nu|=2$ quantum Hall state on two opposite ends of the $\nu=0$ region. A simple kinetic theory and Onsager reciprocity are invoked to model the spin injection and detection processes, and the transport of spin through the antiferromagnet is accounted for using the Landau-Lifshitz-Gilbert phenomenology.