Fractional quantum Hall state at ν=1/4 in a wide quantum well

Abstract

We investigate, with the help of Monte-Carlo and exact-diagonalization calculations in the spherical geometry, several compressible and incompressible candidate wave functions for the recently observed quantum Hall state at the filling factor $\nu =1/4$ in a wide quantum well. The quantum well is modeled as a two-component system by retaining its two lowest subbands. We make a direct connection with the phenomenological effective-bilayer model, which is commonly used in the description of a wide quantum well, and we compare our findings with the established results at $\nu =1/2$ in the lowest Landau level. At $\nu =1/4$, the overlap calculations for the Halperin (5,5,3) and (7,7,1) states, the generalized Haldane-Rezayi state and the Moore-Read Pfaffian, suggest that the incompressible state is likely to be realized in the interplay between the Halperin (5,5,3) state and the Moore-Read Pfaffian. Our numerics shows the latter to be very susceptible to changes in the interaction coefficients, thus indicating that the observed state is of multicomponent nature.

14 pages, 8 figures; minor changes, accepted for publication in Phys. Rev. B

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• Observation of fractional quantum Hall effect at even-denominator 1/2 and 1/4 fillings in asymmetric wide quantum wells
• Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Phase Diagrams for the $\nu$ = 1/2 Fractional Quantum Hall Effect in Electron Systems Confined to Symmetric, Wide GaAs Quantum Wells
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Geometric construction of Quantum Hall clustering Hamiltonians
• Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases
• Fractional quantum Hall effects in bilayers in the presence of inter-layer tunneling and charge imbalance
• 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
• Classification of Abelian and Non-Abelian Multilayer Fractional Quantum Hall States Through the Pattern of Zeros
• Non-Abelian Two-component Fractional Quantum Hall States
• Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels
• $\nu =1/2$ Fractional Quantum Hall Effect in Tilted Magnetic Fields
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
• Subband Engineering Even-Denominator Quantum Hall States
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• 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 $\nu =1/4$
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Correlation-hole induced paired quantum Hall states in lowest Landau level
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
• Fractional quantum Hall states in charge-imbalanced bilayer systems