  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.
