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Two-component fractional quantum Hall systems are providing a majormotivation for a large section of the physics community. Here we studytwo-component fractional quantum Hall systems in the spin-polarized half-filledlowest Landau level (filling factor 1/2) and second Landau level (fillingfactor 5/2) with exact diagonalization utilizing both the spherical and torusgeometries. The two distinct two-component systems we consider are the truebilayer and effective bilayers (wide-quantum-well). In each model (bilayer andwide-quantum-well) we completely take into account inter-layer tunneling andcharge 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 isremarkably robust to charge imbalancing. In the half-filled second Landau, wefind that the FQHE is likely described by the non-Abelian Moore-Read Pfaffianstate which is also quite robust to charge imbalancing. Furthermore, we suggestthe possibility of experimentally tuning from an Abelian to non-Abelian FQHEstate in the second Landau level, and comment on recent experimental studies ofFQHE in wide quantum well structures.

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