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.

25 pages, 27 figures

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Fractional Quantum Hall Effect in the Second Landau Level
• Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
• Paired composite fermion wavefunctions
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
• Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field
• Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• 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
• Evidence for a finite temperature phase transition in a bilayer quantum Hall system
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Charge Imbalance and Bilayer 2D Electron Systems at ${\nu }_T=1$
• Fractional quantum Hall state at ν=1/4 in a wide quantum well
• Subband Engineering Even-Denominator Quantum Hall States

Cited by in corpus (12)

• Topological flat band models with arbitrary Chern numbers
• Competing Abelian and non-Abelian topological orders in $\nu =1/3+1/3$ quantum Hall bilayers
• Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4
• Composite-fermion pairing at half and quarter filled lowest Landau level
• $\nu =1/2$ Fractional Quantum Hall Effect in Tilted Magnetic Fields
• Composite fermion pairing induced by Landau level mixing
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• 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
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene