Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance

Abstract

Two-component fractional quantum Hall systems are providing a major motivation for a large section of the physics community. Here we study two-component fractional quantum Hall systems in the spin-polarized half-filled lowest Landau level (filling factor 1/2) and second Landau level (filling factor 5/2) with exact diagonalization utilizing both the spherical and torus geometries. The two distinct two-component systems we consider are the true bilayer and effective bilayers (wide-quantum-well). In each model (bilayer and wide-quantum-well) we completely take into account inter-layer tunneling and charge imbalancing terms. We find that in the half-filled lowest Landau level, the FQHE is described by the two-component Abelian Halperin 331 state which is remarkably robust to charge imbalancing. In the half-filled second Landau, we find that the FQHE is likely described by the non-Abelian Moore-Read Pfaffian state which is also quite robust to charge imbalancing. Furthermore, we suggest the possibility of experimentally tuning from an Abelian to non-Abelian FQHE state in the second Landau level, and comment on recent experimental studies of FQHE in wide quantum well structures.

arXiv comment25 pages, 27 figures

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Cited by in corpus (26)

• Topological flat band models with arbitrary Chern numbers
• Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene
• Topological Phases in the Zeroth Landau Level of Bilayer Graphene
• Phase Diagrams for the $\nu$ = 1/2 Fractional Quantum Hall Effect in Electron Systems Confined to Symmetric, Wide GaAs Quantum Wells
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• 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
• Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4
• Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Variational Monte Carlo study of spin polarization stability of fractional quantum Hall states against realistic effects in half-filled Landau levels
• Composite fermion pairing induced by Landau level mixing
• $\nu =1/2$ Fractional Quantum Hall Effect in Tilted Magnetic Fields
• Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Two-Component Fractional Quantum Hall Effect in the Half-Filled Lowest Landau Level in an Asymmetric Wide Quantum Well
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Fractional quantum Hall state at $\nu =1/2$ with energy gap up to 6 K, and possible transition from one- to two-component state
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Topological Superfluidity of Spin-Orbit Coupled Bilayer Fermi Gases
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene