Importance of interband transitions for the fractional quantum Hall effect in bilayer graphene

Abstract

Several recent works have proposed that electron-electron interactions in bilayer graphene can be tuned with the help of external parameters, making it possible to stabilize different fractional quantum Hall states. In these prior works, phase diagrams were calculated based on a single Landau level approximation. We go beyond this approximation and investigate the influence of polarization effects and virtual interband transitions on the stability of fractional quantum Hall states in bilayer graphene. We find that for realistic values of the dielectric constant, the phase diagram is strongly modified by these effects. We illustrate this by evaluating the region of stability of the Pfaffian state.

5 pages, 4 figures + 2 pages of Supplemental Material

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• 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
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• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
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• Interaction-induced insulating state in thick multilayer graphene
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Landau level transitions indoped graphene in a time dependent magnetic field
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• Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation
• Infinite energy solutions to vortex equations governing the fractional quantum Hall effect