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

TL;DR

This study investigates two-component fractional quantum Hall systems in bilayer and wide-quantum-well structures, analyzing the effects of inter-layer tunneling and charge imbalance, and identifies conditions for Abelian and non-Abelian states.

Contribution

It provides a comprehensive analysis of FQHE in bilayer and wide-quantum-well systems considering tunneling and charge imbalance, highlighting the robustness of specific states.

Findings

FQHE in lowest Landau level described by Halperin 331 state, robust to charge imbalance.

FQHE in second Landau level likely described by Moore-Read Pfaffian state, robust to charge imbalance.

Potential to tune between Abelian and non-Abelian FQHE states experimentally.

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.