Theoretical expectations for a fractional quantum Hall effect in graphene

TL;DR

This paper explores the theoretical possibility of fractional quantum Hall states in graphene, considering its fourfold degeneracy, and predicts specific unpolarized states at certain filling factors using trial-wavefunction and exact-diagonalisation methods.

Contribution

It extends the Halperin wavefunction approach to graphene's four-component system, predicting novel fractional quantum Hall states at specific filling factors.

Findings

Predicts unpolarized states at nu=2/5 and nu=4/9 in graphene.

Suggests these states are present in multiple Landau levels.

Extends theoretical framework for fractional quantum Hall effect in graphene.

Abstract

Due to its fourfold spin-valley degeneracy, graphene in a strong magnetic field may be viewed as a four-component quantum Hall system. We investigate the consequences of this particular structure on a possible, yet unobserved, fractional quantum Hall effect in graphene within a trial-wavefunction approach and exact-diagonalisation calculations. This trial-wavefunction approach generalises an original idea by Halperin to account for the SU(2) spin in semiconductor heterostructures with a relatively weak Zeeman effect. Whereas the four-component structure at a filling factor nu=1/3 adds simply a SU(4)-ferromagnetic spinor ordering to the otherwise unaltered Laughlin state, the system favours a valley-unpolarised state at nu=2/5 and a completely unpolarised state at nu=4/9. Due to the similar behaviour of the interaction potential in the zero-energy graphene Landau level and the first excited one, we expect these states to be present in both levels.