Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States

Abstract

The quantum Hall phase diagram of the half-filled bilayer system in the second Landau level is studied as a function of tunneling and layer separation using exact diagonalization. We make the striking prediction that bilayer structures would manifest two distinct branches of incompressible fractional quantum Hall effect (FQHE) corresponding to the Abelian 331 state (at moderate to low tunneling and large layer separation) and the non-Abelian Pfaffian state (at large tunneling and small layer separation). The observation of these two FQHE branches and the quantum phase transition between them will be compelling evidence supporting the existence of the non-Abelian Pfaffian state in the second Landau level.

4 pages, 3 figures

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Cited by in corpus (37)

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• Fractional charge and fractional statistics in the quantum Hall effects
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• Fibonacci Anyons From Abelian Bilayer Quantum Hall States
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
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• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
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• Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance
• Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
• Even-denominator Fractional Quantum Hall Effect at a Landau Level Crossing
• Fractional Quantum Hall Effect at $\nu =1/2$ in Hole Systems Confined to GaAs Quantum Wells
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
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• Two-component quantum Hall effects in topological flat bands
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• Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
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• Disorder-generated non-Abelions
• Subband Engineering Even-Denominator Quantum Hall States
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Developing fractional quantum Hall states at even-denominator fillings 1/6 and 1/8
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Two-component parton fractional quantum Hall state in graphene
• Composite fermions in a wide quantum well in the vicinity of the filling factor 1/2
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
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• Large Zeeman Splitting in Out-of-Plane Magnetic Field in a Double-Layer Quantum Point Contact
• Interlayer-correlated fractional quantum Hall state in a trilayer electron system