Theoretical expectations for a 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.

6 pages, 1 figure; review article for Solid State Comm. (Graphene Week 2008)

References in corpus (8)

• The electronic properties of graphene
• Unconventional Integer Quantum Hall effect in graphene
• Theory of integer quantum Hall effect in graphene
• Order from Disorder in Graphene Quantum Hall Ferromagnet
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Entanglement Skyrmions in multicomponent quantum Hall systems
• Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach