Emergence of helical edge conduction in graphene at the \nu=0 quantum Hall state

TL;DR

This paper develops a theoretical model explaining the emergence of helical edge conduction in graphene at the =0 quantum Hall state, linking collective spin excitations to charge transport and back-scattering mechanisms.

Contribution

It introduces an effective field theory describing edge and bulk excitations, elucidating how bulk spin fluctuations influence edge conductance in the FM phase.

Findings

Conductance depends on temperature and Zeeman energy.

Back-scattering arises from coupling between edge modes and bulk spin excitations.

Model agrees qualitatively with experimental observations.

Abstract

The conductance of graphene subject to a strong, tilted magnetic field exhibits a dramatic change from insulating to conducting behavior with tilt-angle, regarded as evidence for the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) \nu=0 quantum Hall state. We develop a theory for the electric transport in this system based on the spin-charge connection, whereby the evolution in the nature of collective spin excitations is reflected in the charge-carrying modes. To this end, we derive an effective field theoretical description of the low-energy excitations, associated with quantum fluctuations of the spin-valley domain wall ground-state configuration which characterizes the two-dimensional (2D) system with an edge. This analysis yields a model describing a one-dimensional charged edge mode coupled to charge-neutral spin-wave excitations in the 2D bulk. Focusing particularly on the FM phase, naively expected to exhibit perfect conductance, we study a mechanism whereby the coupling to these bulk excitations assists in generating back-scattering. Our theory yields the conductance as a function of temperature and the Zeeman energy - the parameter that tunes the transition between the FM and CAF phases - with behavior in qualitative agreement with experiment.