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

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.

14 pages, 4 figures

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Cited by in corpus (16)

• Spin and valley quantum Hall ferromagnetism in graphene
• Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
• Even denominator fractional quantum Hall states at an isospin transition in monolayer graphene
• Fractional Quantum Hall Phase Transitions and Four-flux Composite Fermions in Graphene
• Composite Fermions and Broken Symmetries in Graphene
• Fractional and integer quantum Hall effects in the zeroth Landau level in graphene
• Broken SU(4) Symmetry and The Fractional Quantum Hall Effect in Graphene
• Phase Diagram of Fractional Quantum Hall Effect of Composite Fermions in Multi-Component Systems
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• SU(N) fractional quantum Hall effects in topological flat bands
• Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry
• SU(3) and SU(4) singlet quantum Hall states at $\nu =2/3$
• Quantum Hall Skyrmions at $\nu =0,\pm 1$ in monolayer graphene
• Spin and valley ordering of fractional quantum Hall states in monolayer graphene
• Dynamical Mass Generation of Composite Dirac Fermions and Fractional Quantum Hall Effects near Charge Neutrality in Graphene
• Study of polarization of even-denominator fractional quantum Hall states in SU(4) Graphene