Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

TL;DR

This paper investigates the fractional quantum Hall effect in graphene, emphasizing the role of SU(4) and SU(2) symmetries, and predicts new low-energy modes affecting state stability.

Contribution

It provides a theoretical analysis distinguishing between SU(4) and SU(2) symmetries in graphene's fractional quantum Hall states, predicting the emergence of Goldstone modes.

Findings

Some experimental features align with a two-component fractional quantum Hall effect.

Goldstone modes influence the stability of certain fractional states.

SU(4) skyrmions are not relevant for low-energy physics.

Abstract

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effect in different parameter regions. We argue that some, though not all, apparently puzzling features observed in recent experiments are consistent with a two-component fractional quantum Hall effect, with the electron spin frozen but the Dirac-valley symmetry approximately intact. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7 etc.; SU(4) skyrmions are not relevant for the low-energy physics.