Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation

Abstract

Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works make theoretical analysis of such systems extremely relevant. In this paper we describe a methodology for investigating the possibility of realizing specific fractional quantum Hall states in bilayer graphene taking into account polarization effects and virtual interband transitions. We apply this methodology to explore the possibility of realizing the Moore-Read Pfaffian state in bilayer graphene.

arXiv comment26 pages, 13 figures

References in corpus (24)

• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Observation of the Fractional Quantum Hall Effect in Graphene
• Multicomponent fractional quantum Hall effect in graphene
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
• Tunable Fractional Quantum Hall Phases in Bilayer Graphene
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Landau Level Mixing and the Fractional Quantum Hall Effect
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Paired composite fermion wavefunctions
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• A Stable Pfaffian State in Bilayer Graphene
• Antiferromagnetic state in bilayer graphene
• Landau Level Mixing in the Perturbative Limit
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Tunable Electron Interactions and Fractional Quantum Hall States in Graphene
• Importance of interband transitions for the fractional quantum Hall effect in bilayer graphene
• Tunable Strongly Correlated Band Insulator